/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) CR [EQUIVALENT, 0 ms] (4) HASKELL (5) IFR [EQUIVALENT, 0 ms] (6) HASKELL (7) BR [EQUIVALENT, 0 ms] (8) HASKELL (9) COR [EQUIVALENT, 0 ms] (10) HASKELL (11) LetRed [EQUIVALENT, 0 ms] (12) HASKELL (13) NumRed [SOUND, 9 ms] (14) HASKELL (15) Narrow [SOUND, 0 ms] (16) AND (17) QDP (18) DependencyGraphProof [EQUIVALENT, 0 ms] (19) AND (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) QDPSizeChangeProof [EQUIVALENT, 0 ms] (25) YES (26) QDP (27) TransformationProof [EQUIVALENT, 0 ms] (28) QDP (29) TransformationProof [EQUIVALENT, 0 ms] (30) QDP (31) UsableRulesProof [EQUIVALENT, 0 ms] (32) QDP (33) QReductionProof [EQUIVALENT, 0 ms] (34) QDP (35) TransformationProof [EQUIVALENT, 0 ms] (36) QDP (37) TransformationProof [EQUIVALENT, 0 ms] (38) QDP (39) UsableRulesProof [EQUIVALENT, 0 ms] (40) QDP (41) QReductionProof [EQUIVALENT, 0 ms] (42) QDP (43) TransformationProof [EQUIVALENT, 0 ms] (44) QDP (45) TransformationProof [EQUIVALENT, 0 ms] (46) QDP (47) UsableRulesProof [EQUIVALENT, 0 ms] (48) QDP (49) QReductionProof [EQUIVALENT, 0 ms] (50) QDP (51) QDPSizeChangeProof [EQUIVALENT, 0 ms] (52) YES (53) QDP (54) TransformationProof [EQUIVALENT, 0 ms] (55) QDP (56) TransformationProof [EQUIVALENT, 0 ms] (57) QDP (58) UsableRulesProof [EQUIVALENT, 0 ms] (59) QDP (60) QReductionProof [EQUIVALENT, 0 ms] (61) QDP (62) TransformationProof [EQUIVALENT, 0 ms] (63) QDP (64) TransformationProof [EQUIVALENT, 0 ms] (65) QDP (66) UsableRulesProof [EQUIVALENT, 0 ms] (67) QDP (68) QReductionProof [EQUIVALENT, 0 ms] (69) QDP (70) TransformationProof [EQUIVALENT, 0 ms] (71) QDP (72) TransformationProof [EQUIVALENT, 0 ms] (73) QDP (74) UsableRulesProof [EQUIVALENT, 0 ms] (75) QDP (76) QReductionProof [EQUIVALENT, 0 ms] (77) QDP (78) QDPSizeChangeProof [EQUIVALENT, 0 ms] (79) YES (80) QDP (81) TransformationProof [EQUIVALENT, 4 ms] (82) QDP (83) TransformationProof [EQUIVALENT, 0 ms] (84) QDP (85) UsableRulesProof [EQUIVALENT, 0 ms] (86) QDP (87) QReductionProof [EQUIVALENT, 0 ms] (88) QDP (89) QDPSizeChangeProof [EQUIVALENT, 0 ms] (90) YES (91) QDP (92) TransformationProof [EQUIVALENT, 0 ms] (93) QDP (94) TransformationProof [EQUIVALENT, 0 ms] (95) QDP (96) UsableRulesProof [EQUIVALENT, 0 ms] (97) QDP (98) QReductionProof [EQUIVALENT, 0 ms] (99) QDP (100) QDPSizeChangeProof [EQUIVALENT, 0 ms] (101) YES (102) QDP (103) TransformationProof [EQUIVALENT, 0 ms] (104) QDP (105) UsableRulesProof [EQUIVALENT, 0 ms] (106) QDP (107) QReductionProof [EQUIVALENT, 0 ms] (108) QDP (109) QDPSizeChangeProof [EQUIVALENT, 0 ms] (110) YES (111) QDP (112) TransformationProof [EQUIVALENT, 4 ms] (113) QDP (114) TransformationProof [EQUIVALENT, 0 ms] (115) QDP (116) UsableRulesProof [EQUIVALENT, 0 ms] (117) QDP (118) QReductionProof [EQUIVALENT, 0 ms] (119) QDP (120) TransformationProof [EQUIVALENT, 0 ms] (121) QDP (122) DependencyGraphProof [EQUIVALENT, 0 ms] (123) QDP (124) TransformationProof [EQUIVALENT, 0 ms] (125) QDP (126) TransformationProof [EQUIVALENT, 0 ms] (127) QDP (128) TransformationProof [EQUIVALENT, 0 ms] (129) QDP (130) TransformationProof [EQUIVALENT, 0 ms] (131) QDP (132) DependencyGraphProof [EQUIVALENT, 0 ms] (133) QDP (134) UsableRulesProof [EQUIVALENT, 0 ms] (135) QDP (136) QReductionProof [EQUIVALENT, 0 ms] (137) QDP (138) TransformationProof [EQUIVALENT, 0 ms] (139) QDP (140) UsableRulesProof [EQUIVALENT, 0 ms] (141) QDP (142) QReductionProof [EQUIVALENT, 0 ms] (143) QDP (144) TransformationProof [EQUIVALENT, 0 ms] (145) QDP (146) UsableRulesProof [EQUIVALENT, 0 ms] (147) QDP (148) QReductionProof [EQUIVALENT, 0 ms] (149) QDP (150) TransformationProof [EQUIVALENT, 0 ms] (151) QDP (152) UsableRulesProof [EQUIVALENT, 0 ms] (153) QDP (154) QReductionProof [EQUIVALENT, 0 ms] (155) QDP (156) QDPSizeChangeProof [EQUIVALENT, 0 ms] (157) YES (158) QDP (159) TransformationProof [EQUIVALENT, 0 ms] (160) QDP (161) TransformationProof [EQUIVALENT, 0 ms] (162) QDP (163) UsableRulesProof [EQUIVALENT, 0 ms] (164) QDP (165) QReductionProof [EQUIVALENT, 0 ms] (166) QDP (167) QDPSizeChangeProof [EQUIVALENT, 0 ms] (168) YES (169) QDP (170) TransformationProof [EQUIVALENT, 0 ms] (171) QDP (172) TransformationProof [EQUIVALENT, 0 ms] (173) QDP (174) UsableRulesProof [EQUIVALENT, 0 ms] (175) QDP (176) QReductionProof [EQUIVALENT, 0 ms] (177) QDP (178) QDPSizeChangeProof [EQUIVALENT, 0 ms] (179) YES (180) QDP (181) TransformationProof [EQUIVALENT, 0 ms] (182) QDP (183) TransformationProof [EQUIVALENT, 0 ms] (184) QDP (185) UsableRulesProof [EQUIVALENT, 0 ms] (186) QDP (187) QReductionProof [EQUIVALENT, 0 ms] (188) QDP (189) QDPSizeChangeProof [EQUIVALENT, 0 ms] (190) YES (191) QDP (192) QDPSizeChangeProof [EQUIVALENT, 0 ms] (193) YES (194) QDP (195) DependencyGraphProof [EQUIVALENT, 0 ms] (196) AND (197) QDP (198) QDPSizeChangeProof [EQUIVALENT, 0 ms] (199) YES (200) QDP (201) QDPSizeChangeProof [EQUIVALENT, 0 ms] (202) YES (203) QDP (204) QDPSizeChangeProof [EQUIVALENT, 0 ms] (205) YES (206) QDP (207) QDPSizeChangeProof [EQUIVALENT, 0 ms] (208) YES (209) QDP (210) QDPSizeChangeProof [EQUIVALENT, 0 ms] (211) YES (212) QDP (213) QDPSizeChangeProof [EQUIVALENT, 0 ms] (214) YES (215) QDP (216) QDPSizeChangeProof [EQUIVALENT, 0 ms] (217) YES (218) QDP (219) TransformationProof [EQUIVALENT, 0 ms] (220) QDP (221) TransformationProof [EQUIVALENT, 0 ms] (222) QDP (223) UsableRulesProof [EQUIVALENT, 0 ms] (224) QDP (225) QReductionProof [EQUIVALENT, 0 ms] (226) QDP (227) TransformationProof [EQUIVALENT, 0 ms] (228) QDP (229) DependencyGraphProof [EQUIVALENT, 0 ms] (230) QDP (231) TransformationProof [EQUIVALENT, 0 ms] (232) QDP (233) TransformationProof [EQUIVALENT, 0 ms] (234) QDP (235) TransformationProof [EQUIVALENT, 0 ms] (236) QDP (237) TransformationProof [EQUIVALENT, 0 ms] (238) QDP (239) DependencyGraphProof [EQUIVALENT, 0 ms] (240) QDP (241) UsableRulesProof [EQUIVALENT, 0 ms] (242) QDP (243) QReductionProof [EQUIVALENT, 0 ms] (244) QDP (245) TransformationProof [EQUIVALENT, 0 ms] (246) QDP (247) UsableRulesProof [EQUIVALENT, 0 ms] (248) QDP (249) QReductionProof [EQUIVALENT, 0 ms] (250) QDP (251) TransformationProof [EQUIVALENT, 0 ms] (252) QDP (253) UsableRulesProof [EQUIVALENT, 0 ms] (254) QDP (255) QReductionProof [EQUIVALENT, 0 ms] (256) QDP (257) TransformationProof [EQUIVALENT, 0 ms] (258) QDP (259) UsableRulesProof [EQUIVALENT, 0 ms] (260) QDP (261) QReductionProof [EQUIVALENT, 0 ms] (262) QDP (263) QDPSizeChangeProof [EQUIVALENT, 0 ms] (264) YES (265) QDP (266) TransformationProof [EQUIVALENT, 0 ms] (267) QDP (268) TransformationProof [EQUIVALENT, 0 ms] (269) QDP (270) UsableRulesProof [EQUIVALENT, 0 ms] (271) QDP (272) QReductionProof [EQUIVALENT, 0 ms] (273) QDP (274) QDPSizeChangeProof [EQUIVALENT, 0 ms] (275) YES (276) QDP (277) QDPSizeChangeProof [EQUIVALENT, 0 ms] (278) YES (279) QDP (280) TransformationProof [EQUIVALENT, 0 ms] (281) QDP (282) TransformationProof [EQUIVALENT, 0 ms] (283) QDP (284) UsableRulesProof [EQUIVALENT, 0 ms] (285) QDP (286) QReductionProof [EQUIVALENT, 0 ms] (287) QDP (288) TransformationProof [EQUIVALENT, 0 ms] (289) QDP (290) DependencyGraphProof [EQUIVALENT, 0 ms] (291) QDP (292) TransformationProof [EQUIVALENT, 0 ms] (293) QDP (294) TransformationProof [EQUIVALENT, 0 ms] (295) QDP (296) TransformationProof [EQUIVALENT, 0 ms] (297) QDP (298) TransformationProof [EQUIVALENT, 0 ms] (299) QDP (300) DependencyGraphProof [EQUIVALENT, 0 ms] (301) QDP (302) UsableRulesProof [EQUIVALENT, 0 ms] (303) QDP (304) QReductionProof [EQUIVALENT, 0 ms] (305) QDP (306) TransformationProof [EQUIVALENT, 0 ms] (307) QDP (308) UsableRulesProof [EQUIVALENT, 0 ms] (309) QDP (310) QReductionProof [EQUIVALENT, 0 ms] (311) QDP (312) TransformationProof [EQUIVALENT, 0 ms] (313) QDP (314) UsableRulesProof [EQUIVALENT, 0 ms] (315) QDP (316) QReductionProof [EQUIVALENT, 0 ms] (317) QDP (318) TransformationProof [EQUIVALENT, 0 ms] (319) QDP (320) UsableRulesProof [EQUIVALENT, 0 ms] (321) QDP (322) QReductionProof [EQUIVALENT, 0 ms] (323) QDP (324) QDPSizeChangeProof [EQUIVALENT, 0 ms] (325) YES (326) QDP (327) TransformationProof [EQUIVALENT, 2 ms] (328) QDP (329) TransformationProof [EQUIVALENT, 0 ms] (330) QDP (331) UsableRulesProof [EQUIVALENT, 0 ms] (332) QDP (333) QReductionProof [EQUIVALENT, 0 ms] (334) QDP (335) TransformationProof [EQUIVALENT, 0 ms] (336) QDP (337) DependencyGraphProof [EQUIVALENT, 0 ms] (338) QDP (339) TransformationProof [EQUIVALENT, 0 ms] (340) QDP (341) TransformationProof [EQUIVALENT, 0 ms] (342) QDP (343) TransformationProof [EQUIVALENT, 0 ms] (344) QDP (345) TransformationProof [EQUIVALENT, 0 ms] (346) QDP (347) DependencyGraphProof [EQUIVALENT, 0 ms] (348) QDP (349) UsableRulesProof [EQUIVALENT, 0 ms] (350) QDP (351) QReductionProof [EQUIVALENT, 0 ms] (352) QDP (353) TransformationProof [EQUIVALENT, 0 ms] (354) QDP (355) UsableRulesProof [EQUIVALENT, 0 ms] (356) QDP (357) QReductionProof [EQUIVALENT, 0 ms] (358) QDP (359) TransformationProof [EQUIVALENT, 0 ms] (360) QDP (361) UsableRulesProof [EQUIVALENT, 0 ms] (362) QDP (363) QReductionProof [EQUIVALENT, 0 ms] (364) QDP (365) TransformationProof [EQUIVALENT, 0 ms] (366) QDP (367) UsableRulesProof [EQUIVALENT, 0 ms] (368) QDP (369) QReductionProof [EQUIVALENT, 0 ms] (370) QDP (371) QDPSizeChangeProof [EQUIVALENT, 0 ms] (372) YES (373) QDP (374) QDPSizeChangeProof [EQUIVALENT, 0 ms] (375) YES (376) QDP (377) QDPSizeChangeProof [EQUIVALENT, 0 ms] (378) YES ---------------------------------------- (0) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; instance (Eq a, Eq b) => Eq FiniteMap b a where { (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; } addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; addToFM fm key elt = addToFM_C (\old new ->new) fm key elt; addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; addToFM_C combiner EmptyFM key elt = unitFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; emptyFM :: FiniteMap b a; emptyFM = EmptyFM; findMax :: FiniteMap a b -> (a,b); findMax (Branch key elt _ _ EmptyFM) = (key,elt); findMax (Branch key elt _ _ fm_r) = findMax fm_r; findMin :: FiniteMap a b -> (a,b); findMin (Branch key elt _ EmptyFM _) = (key,elt); findMin (Branch key elt _ fm_l _) = findMin fm_l; fmToList :: FiniteMap a b -> [(a,b)]; fmToList fm = foldFM (\key elt rest ->(key,elt) : rest) [] fm; foldFM :: (b -> a -> c -> c) -> c -> FiniteMap b a -> c; foldFM k z EmptyFM = z; foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find | key_to_find > key = lookupFM fm_r key_to_find | otherwise = Just elt; mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R | size_r > sIZE_RATIO * size_l = case fm_R of { Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R | otherwise -> double_L fm_L fm_R; } | size_l > sIZE_RATIO * size_r = case fm_L of { Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R | otherwise -> double_R fm_L fm_R; } | otherwise = mkBranch 2 key elt fm_L fm_R where { double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); size_l = sizeFM fm_L; size_r = sizeFM fm_R; }; mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkBranch which key elt fm_l fm_r = let { result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; } in result where { balance_ok = True; left_ok = case fm_l of { EmptyFM-> True; Branch left_key _ _ _ _-> let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key; } ; left_size = sizeFM fm_l; right_ok = case fm_r of { EmptyFM-> True; Branch right_key _ _ _ _-> let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key; } ; right_size = sizeFM fm_r; unbox :: Int -> Int; unbox x = x; }; mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) | otherwise = mkBranch 13 key elt fm_l fm_r where { size_l = sizeFM fm_l; size_r = sizeFM fm_r; }; plusFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; plusFM_C combiner EmptyFM fm2 = fm2; plusFM_C combiner fm1 EmptyFM = fm1; plusFM_C combiner fm1 (Branch split_key elt2 _ left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { gts = splitGT fm1 split_key; lts = splitLT fm1 split_key; new_elt = case lookupFM fm1 split_key of { Nothing-> elt2; Just elt1-> combiner elt1 elt2; } ; }; sIZE_RATIO :: Int; sIZE_RATIO = 5; sizeFM :: FiniteMap b a -> Int; sizeFM EmptyFM = 0; sizeFM (Branch _ _ size _ _) = size; splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; splitGT EmptyFM split_key = emptyFM; splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r | otherwise = fm_r; splitLT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; splitLT EmptyFM split_key = emptyFM; splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) | otherwise = fm_l; unitFM :: b -> a -> FiniteMap b a; unitFM key elt = Branch key elt 1 emptyFM emptyFM; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\oldnew->new" is transformed to "addToFM0 old new = new; " The following Lambda expression "\keyeltrest->(key,elt) : rest" is transformed to "fmToList0 key elt rest = (key,elt) : rest; " ---------------------------------------- (2) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; instance (Eq a, Eq b) => Eq FiniteMap a b where { (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; } addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; addToFM fm key elt = addToFM_C addToFM0 fm key elt; addToFM0 old new = new; addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; addToFM_C combiner EmptyFM key elt = unitFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; emptyFM :: FiniteMap a b; emptyFM = EmptyFM; findMax :: FiniteMap a b -> (a,b); findMax (Branch key elt _ _ EmptyFM) = (key,elt); findMax (Branch key elt _ _ fm_r) = findMax fm_r; findMin :: FiniteMap a b -> (a,b); findMin (Branch key elt _ EmptyFM _) = (key,elt); findMin (Branch key elt _ fm_l _) = findMin fm_l; fmToList :: FiniteMap a b -> [(a,b)]; fmToList fm = foldFM fmToList0 [] fm; fmToList0 key elt rest = (key,elt) : rest; foldFM :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a; foldFM k z EmptyFM = z; foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find | key_to_find > key = lookupFM fm_r key_to_find | otherwise = Just elt; mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R | size_r > sIZE_RATIO * size_l = case fm_R of { Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R | otherwise -> double_L fm_L fm_R; } | size_l > sIZE_RATIO * size_r = case fm_L of { Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R | otherwise -> double_R fm_L fm_R; } | otherwise = mkBranch 2 key elt fm_L fm_R where { double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); size_l = sizeFM fm_L; size_r = sizeFM fm_R; }; mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkBranch which key elt fm_l fm_r = let { result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; } in result where { balance_ok = True; left_ok = case fm_l of { EmptyFM-> True; Branch left_key _ _ _ _-> let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key; } ; left_size = sizeFM fm_l; right_ok = case fm_r of { EmptyFM-> True; Branch right_key _ _ _ _-> let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key; } ; right_size = sizeFM fm_r; unbox :: Int -> Int; unbox x = x; }; mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) | otherwise = mkBranch 13 key elt fm_l fm_r where { size_l = sizeFM fm_l; size_r = sizeFM fm_r; }; plusFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; plusFM_C combiner EmptyFM fm2 = fm2; plusFM_C combiner fm1 EmptyFM = fm1; plusFM_C combiner fm1 (Branch split_key elt2 _ left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { gts = splitGT fm1 split_key; lts = splitLT fm1 split_key; new_elt = case lookupFM fm1 split_key of { Nothing-> elt2; Just elt1-> combiner elt1 elt2; } ; }; sIZE_RATIO :: Int; sIZE_RATIO = 5; sizeFM :: FiniteMap b a -> Int; sizeFM EmptyFM = 0; sizeFM (Branch _ _ size _ _) = size; splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; splitGT EmptyFM split_key = emptyFM; splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r | otherwise = fm_r; splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; splitLT EmptyFM split_key = emptyFM; splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) | otherwise = fm_l; unitFM :: b -> a -> FiniteMap b a; unitFM key elt = Branch key elt 1 emptyFM emptyFM; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (3) CR (EQUIVALENT) Case Reductions: The following Case expression "case compare x y of { EQ -> o; LT -> LT; GT -> GT} " is transformed to "primCompAux0 o EQ = o; primCompAux0 o LT = LT; primCompAux0 o GT = GT; " The following Case expression "case lookupFM fm1 split_key of { Nothing -> elt2; Just elt1 -> combiner elt1 elt2} " is transformed to "new_elt0 elt2 combiner Nothing = elt2; new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; " The following Case expression "case fm_r of { EmptyFM -> True; Branch right_key _ _ _ _ -> let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key} " is transformed to "right_ok0 fm_r key EmptyFM = True; right_ok0 fm_r key (Branch right_key _ _ _ _) = let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key; " The following Case expression "case fm_l of { EmptyFM -> True; Branch left_key _ _ _ _ -> let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key} " is transformed to "left_ok0 fm_l key EmptyFM = True; left_ok0 fm_l key (Branch left_key _ _ _ _) = let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key; " The following Case expression "case fm_R of { Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R} " is transformed to "mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; " The following Case expression "case fm_L of { Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R} " is transformed to "mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; " ---------------------------------------- (4) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; instance (Eq a, Eq b) => Eq FiniteMap a b where { (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; } addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; addToFM fm key elt = addToFM_C addToFM0 fm key elt; addToFM0 old new = new; addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; addToFM_C combiner EmptyFM key elt = unitFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; emptyFM :: FiniteMap a b; emptyFM = EmptyFM; findMax :: FiniteMap b a -> (b,a); findMax (Branch key elt _ _ EmptyFM) = (key,elt); findMax (Branch key elt _ _ fm_r) = findMax fm_r; findMin :: FiniteMap b a -> (b,a); findMin (Branch key elt _ EmptyFM _) = (key,elt); findMin (Branch key elt _ fm_l _) = findMin fm_l; fmToList :: FiniteMap b a -> [(b,a)]; fmToList fm = foldFM fmToList0 [] fm; fmToList0 key elt rest = (key,elt) : rest; foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a; foldFM k z EmptyFM = z; foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find | key_to_find > key = lookupFM fm_r key_to_find | otherwise = Just elt; mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L | otherwise = mkBranch 2 key elt fm_L fm_R where { double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R | otherwise = double_L fm_L fm_R; mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R | otherwise = double_R fm_L fm_R; single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); size_l = sizeFM fm_L; size_r = sizeFM fm_R; }; mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkBranch which key elt fm_l fm_r = let { result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; } in result where { balance_ok = True; left_ok = left_ok0 fm_l key fm_l; left_ok0 fm_l key EmptyFM = True; left_ok0 fm_l key (Branch left_key _ _ _ _) = let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key; left_size = sizeFM fm_l; right_ok = right_ok0 fm_r key fm_r; right_ok0 fm_r key EmptyFM = True; right_ok0 fm_r key (Branch right_key _ _ _ _) = let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key; right_size = sizeFM fm_r; unbox :: Int -> Int; unbox x = x; }; mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) | otherwise = mkBranch 13 key elt fm_l fm_r where { size_l = sizeFM fm_l; size_r = sizeFM fm_r; }; plusFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; plusFM_C combiner EmptyFM fm2 = fm2; plusFM_C combiner fm1 EmptyFM = fm1; plusFM_C combiner fm1 (Branch split_key elt2 _ left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { gts = splitGT fm1 split_key; lts = splitLT fm1 split_key; new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); new_elt0 elt2 combiner Nothing = elt2; new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; }; sIZE_RATIO :: Int; sIZE_RATIO = 5; sizeFM :: FiniteMap b a -> Int; sizeFM EmptyFM = 0; sizeFM (Branch _ _ size _ _) = size; splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; splitGT EmptyFM split_key = emptyFM; splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r | otherwise = fm_r; splitLT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; splitLT EmptyFM split_key = emptyFM; splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) | otherwise = fm_l; unitFM :: a -> b -> FiniteMap a b; unitFM key elt = Branch key elt 1 emptyFM emptyFM; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) 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; " ---------------------------------------- (6) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; instance (Eq a, Eq b) => Eq FiniteMap b a where { (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; } addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; addToFM fm key elt = addToFM_C addToFM0 fm key elt; addToFM0 old new = new; addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; addToFM_C combiner EmptyFM key elt = unitFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; emptyFM :: FiniteMap b a; emptyFM = EmptyFM; findMax :: FiniteMap a b -> (a,b); findMax (Branch key elt _ _ EmptyFM) = (key,elt); findMax (Branch key elt _ _ fm_r) = findMax fm_r; findMin :: FiniteMap b a -> (b,a); findMin (Branch key elt _ EmptyFM _) = (key,elt); findMin (Branch key elt _ fm_l _) = findMin fm_l; fmToList :: FiniteMap b a -> [(b,a)]; fmToList fm = foldFM fmToList0 [] fm; fmToList0 key elt rest = (key,elt) : rest; foldFM :: (c -> a -> b -> b) -> b -> FiniteMap c a -> b; foldFM k z EmptyFM = z; foldFM k z (Branch key elt _ fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt _ fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find | key_to_find > key = lookupFM fm_r key_to_find | otherwise = Just elt; mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L | otherwise = mkBranch 2 key elt fm_L fm_R where { double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R | otherwise = double_L fm_L fm_R; mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R | otherwise = double_R fm_L fm_R; single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); size_l = sizeFM fm_L; size_r = sizeFM fm_R; }; mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkBranch which key elt fm_l fm_r = let { result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; } in result where { balance_ok = True; left_ok = left_ok0 fm_l key fm_l; left_ok0 fm_l key EmptyFM = True; left_ok0 fm_l key (Branch left_key _ _ _ _) = let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key; left_size = sizeFM fm_l; right_ok = right_ok0 fm_r key fm_r; right_ok0 fm_r key EmptyFM = True; right_ok0 fm_r key (Branch right_key _ _ _ _) = let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key; right_size = sizeFM fm_r; unbox :: Int -> Int; unbox x = x; }; mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch key elt fm_l@(Branch key_l elt_l _ fm_ll fm_lr) fm_r@(Branch key_r elt_r _ fm_rl fm_rr) | sIZE_RATIO * size_l < size_r = mkBalBranch key_r elt_r (mkVBalBranch key elt fm_l fm_rl) fm_rr | sIZE_RATIO * size_r < size_l = mkBalBranch key_l elt_l fm_ll (mkVBalBranch key elt fm_lr fm_r) | otherwise = mkBranch 13 key elt fm_l fm_r where { size_l = sizeFM fm_l; size_r = sizeFM fm_r; }; plusFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; plusFM_C combiner EmptyFM fm2 = fm2; plusFM_C combiner fm1 EmptyFM = fm1; plusFM_C combiner fm1 (Branch split_key elt2 _ left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { gts = splitGT fm1 split_key; lts = splitLT fm1 split_key; new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); new_elt0 elt2 combiner Nothing = elt2; new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; }; sIZE_RATIO :: Int; sIZE_RATIO = 5; sizeFM :: FiniteMap b a -> Int; sizeFM EmptyFM = 0; sizeFM (Branch _ _ size _ _) = size; splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; splitGT EmptyFM split_key = emptyFM; splitGT (Branch key elt _ fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r | otherwise = fm_r; splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; splitLT EmptyFM split_key = emptyFM; splitLT (Branch key elt _ fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) | otherwise = fm_l; unitFM :: a -> b -> FiniteMap a b; unitFM key elt = Branch key elt 1 emptyFM emptyFM; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (7) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. Binding Reductions: The bind variable of the following binding Pattern "fm_l@(Branch vuv vuw vux vuy vuz)" is replaced by the following term "Branch vuv vuw vux vuy vuz" The bind variable of the following binding Pattern "fm_r@(Branch vvv vvw vvx vvy vvz)" is replaced by the following term "Branch vvv vvw vvx vvy vvz" ---------------------------------------- (8) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; instance (Eq a, Eq b) => Eq FiniteMap a b where { (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; } addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; addToFM fm key elt = addToFM_C addToFM0 fm key elt; addToFM0 old new = new; addToFM_C :: Ord b => (a -> a -> a) -> FiniteMap b a -> b -> a -> FiniteMap b a; addToFM_C combiner EmptyFM key elt = unitFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt) | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r; emptyFM :: FiniteMap a b; emptyFM = EmptyFM; findMax :: FiniteMap a b -> (a,b); findMax (Branch key elt vxy vxz EmptyFM) = (key,elt); findMax (Branch key elt vyu vyv fm_r) = findMax fm_r; findMin :: FiniteMap b a -> (b,a); findMin (Branch key elt wvw EmptyFM wvx) = (key,elt); findMin (Branch key elt wvy fm_l wvz) = findMin fm_l; fmToList :: FiniteMap a b -> [(a,b)]; fmToList fm = foldFM fmToList0 [] fm; fmToList0 key elt rest = (key,elt) : rest; foldFM :: (c -> b -> a -> a) -> a -> FiniteMap c b -> a; foldFM k z EmptyFM = z; foldFM k z (Branch key elt wuw fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt wvv fm_l fm_r) key_to_find | key_to_find < key = lookupFM fm_l key_to_find | key_to_find > key = lookupFM fm_r key_to_find | otherwise = Just elt; mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkBalBranch key elt fm_L fm_R | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L | otherwise = mkBranch 2 key elt fm_L fm_R where { double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R | otherwise = double_L fm_L fm_R; mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R | otherwise = double_R fm_L fm_R; single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); size_l = sizeFM fm_L; size_r = sizeFM fm_R; }; mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkBranch which key elt fm_l fm_r = let { result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; } in result where { balance_ok = True; left_ok = left_ok0 fm_l key fm_l; left_ok0 fm_l key EmptyFM = True; left_ok0 fm_l key (Branch left_key vww vwx vwy vwz) = let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key; left_size = sizeFM fm_l; right_ok = right_ok0 fm_r key fm_r; right_ok0 fm_r key EmptyFM = True; right_ok0 fm_r key (Branch right_key vxu vxv vxw vxx) = let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key; right_size = sizeFM fm_r; unbox :: Int -> Int; unbox x = x; }; mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) | sIZE_RATIO * size_l < size_r = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz | sIZE_RATIO * size_r < size_l = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)) | otherwise = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) where { size_l = sizeFM (Branch vuv vuw vux vuy vuz); size_r = sizeFM (Branch vvv vvw vvx vvy vvz); }; plusFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; plusFM_C combiner EmptyFM fm2 = fm2; plusFM_C combiner fm1 EmptyFM = fm1; plusFM_C combiner fm1 (Branch split_key elt2 zz left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { gts = splitGT fm1 split_key; lts = splitLT fm1 split_key; new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); new_elt0 elt2 combiner Nothing = elt2; new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; }; sIZE_RATIO :: Int; sIZE_RATIO = 5; sizeFM :: FiniteMap b a -> Int; sizeFM EmptyFM = 0; sizeFM (Branch wux wuy size wuz wvu) = size; splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; splitGT EmptyFM split_key = emptyFM; splitGT (Branch key elt vwu fm_l fm_r) split_key | split_key > key = splitGT fm_r split_key | split_key < key = mkVBalBranch key elt (splitGT fm_l split_key) fm_r | otherwise = fm_r; splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; splitLT EmptyFM split_key = emptyFM; splitLT (Branch key elt vwv fm_l fm_r) split_key | split_key < key = splitLT fm_l split_key | split_key > key = mkVBalBranch key elt fm_l (splitLT fm_r split_key) | otherwise = fm_l; unitFM :: b -> a -> FiniteMap b a; unitFM key elt = Branch key elt 1 emptyFM emptyFM; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (9) 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 wwu = gcd'2 x wwu; gcd' x y = gcd'0 x y; " "gcd'0 x y = gcd' y (x `rem` y); " "gcd'1 True x wwu = x; gcd'1 wwv www wwx = gcd'0 www wwx; " "gcd'2 x wwu = gcd'1 (wwu == 0) x wwu; gcd'2 wwy wwz = gcd'0 wwy wwz; " 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 wxu wxv = gcd3 wxu wxv; gcd x y = gcd0 x y; " "gcd0 x y = gcd' (abs x) (abs y) where { gcd' x wwu = gcd'2 x wwu; gcd' x y = gcd'0 x y; ; gcd'0 x y = gcd' y (x `rem` y); ; gcd'1 True x wwu = x; gcd'1 wwv www wwx = gcd'0 www wwx; ; gcd'2 x wwu = gcd'1 (wwu == 0) x wwu; gcd'2 wwy wwz = gcd'0 wwy wwz; } ; " "gcd1 True wxu wxv = error []; gcd1 wxw wxx wxy = gcd0 wxx wxy; " "gcd2 True wxu wxv = gcd1 (wxv == 0) wxu wxv; gcd2 wxz wyu wyv = gcd0 wyu wyv; " "gcd3 wxu wxv = gcd2 (wxu == 0) wxu wxv; gcd3 wyw wyx = gcd0 wyw wyx; " 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; } ; " The following Function with conditions "compare x y|x == yEQ|x <= yLT|otherwiseGT; " is transformed to "compare x y = compare3 x y; " "compare2 x y True = EQ; compare2 x y False = compare1 x y (x <= y); " "compare0 x y True = GT; " "compare1 x y True = LT; compare1 x y False = compare0 x y otherwise; " "compare3 x y = compare2 x y (x == y); " The following Function with conditions "addToFM_C combiner EmptyFM key elt = unitFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt|new_key < keymkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r|new_key > keymkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)|otherwiseBranch new_key (combiner elt new_elt) size fm_l fm_r; " is transformed to "addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; " "addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); " "addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; " "addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; " "addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); " "addToFM_C4 combiner EmptyFM key elt = unitFM key elt; addToFM_C4 wzu wzv wzw wzx = addToFM_C3 wzu wzv wzw wzx; " The following Function with conditions "mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz)|sIZE_RATIO * size_l < size_rmkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz|sIZE_RATIO * size_r < size_lmkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz))|otherwisemkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) where { size_l = sizeFM (Branch vuv vuw vux vuy vuz); ; size_r = sizeFM (Branch vvv vvw vvx vvy vvz); } ; " is transformed to "mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); " "mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_l < size_r) where { mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); ; mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; ; mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_r < size_l); ; size_l = sizeFM (Branch vuv vuw vux vuy vuz); ; size_r = sizeFM (Branch vvv vvw vvx vvy vvz); } ; " "mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch4 xuv xuw xux xuy = mkVBalBranch3 xuv xuw xux xuy; " "mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch5 xvu xvv xvw xvx = mkVBalBranch4 xvu xvv xvw xvx; " The following Function with conditions "splitGT EmptyFM split_key = emptyFM; splitGT (Branch key elt vwu fm_l fm_r) split_key|split_key > keysplitGT fm_r split_key|split_key < keymkVBalBranch key elt (splitGT fm_l split_key) fm_r|otherwisefm_r; " is transformed to "splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; splitGT (Branch key elt vwu fm_l fm_r) split_key = splitGT3 (Branch key elt vwu fm_l fm_r) split_key; " "splitGT2 key elt vwu fm_l fm_r split_key True = splitGT fm_r split_key; splitGT2 key elt vwu fm_l fm_r split_key False = splitGT1 key elt vwu fm_l fm_r split_key (split_key < key); " "splitGT0 key elt vwu fm_l fm_r split_key True = fm_r; " "splitGT1 key elt vwu fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; splitGT1 key elt vwu fm_l fm_r split_key False = splitGT0 key elt vwu fm_l fm_r split_key otherwise; " "splitGT3 (Branch key elt vwu fm_l fm_r) split_key = splitGT2 key elt vwu fm_l fm_r split_key (split_key > key); " "splitGT4 EmptyFM split_key = emptyFM; splitGT4 xwu xwv = splitGT3 xwu xwv; " The following Function with conditions "splitLT EmptyFM split_key = emptyFM; splitLT (Branch key elt vwv fm_l fm_r) split_key|split_key < keysplitLT fm_l split_key|split_key > keymkVBalBranch key elt fm_l (splitLT fm_r split_key)|otherwisefm_l; " is transformed to "splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; splitLT (Branch key elt vwv fm_l fm_r) split_key = splitLT3 (Branch key elt vwv fm_l fm_r) split_key; " "splitLT0 key elt vwv fm_l fm_r split_key True = fm_l; " "splitLT1 key elt vwv fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); splitLT1 key elt vwv fm_l fm_r split_key False = splitLT0 key elt vwv fm_l fm_r split_key otherwise; " "splitLT2 key elt vwv fm_l fm_r split_key True = splitLT fm_l split_key; splitLT2 key elt vwv fm_l fm_r split_key False = splitLT1 key elt vwv fm_l fm_r split_key (split_key > key); " "splitLT3 (Branch key elt vwv fm_l fm_r) split_key = splitLT2 key elt vwv fm_l fm_r split_key (split_key < key); " "splitLT4 EmptyFM split_key = emptyFM; splitLT4 xwy xwz = splitLT3 xwy xwz; " The following Function with conditions "mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; " is transformed to "mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); " "mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = double_R fm_L fm_R; " "mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = single_R fm_L fm_R; mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; " "mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); " The following Function with conditions "mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; " is transformed to "mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); " "mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = double_L fm_L fm_R; " "mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = single_L fm_L fm_R; mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; " "mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); " The following Function with conditions "mkBalBranch key elt fm_L fm_R|size_l + size_r < 2mkBranch 1 key elt fm_L fm_R|size_r > sIZE_RATIO * size_lmkBalBranch0 fm_L fm_R fm_R|size_l > sIZE_RATIO * size_rmkBalBranch1 fm_L fm_R fm_L|otherwisemkBranch 2 key elt fm_L fm_R where { double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); ; double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); ; mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R; ; mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R; ; single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; ; single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); ; size_l = sizeFM fm_L; ; size_r = sizeFM fm_R; } ; " is transformed to "mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; " "mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); ; double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); ; mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); ; mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = double_L fm_L fm_R; ; mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = single_L fm_L fm_R; mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; ; mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); ; mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); ; mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = double_R fm_L fm_R; ; mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = single_R fm_L fm_R; mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; ; mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); ; mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; ; mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; ; mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); ; mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); ; single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; ; single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); ; size_l = sizeFM fm_L; ; size_r = sizeFM fm_R; } ; " The following Function with conditions "lookupFM EmptyFM key = Nothing; lookupFM (Branch key elt wvv fm_l fm_r) key_to_find|key_to_find < keylookupFM fm_l key_to_find|key_to_find > keylookupFM fm_r key_to_find|otherwiseJust elt; " is transformed to "lookupFM EmptyFM key = lookupFM4 EmptyFM key; lookupFM (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find; " "lookupFM0 key elt wvv fm_l fm_r key_to_find True = Just elt; " "lookupFM2 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; lookupFM2 key elt wvv fm_l fm_r key_to_find False = lookupFM1 key elt wvv fm_l fm_r key_to_find (key_to_find > key); " "lookupFM1 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; lookupFM1 key elt wvv fm_l fm_r key_to_find False = lookupFM0 key elt wvv fm_l fm_r key_to_find otherwise; " "lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM2 key elt wvv fm_l fm_r key_to_find (key_to_find < key); " "lookupFM4 EmptyFM key = Nothing; lookupFM4 xxy xxz = lookupFM3 xxy xxz; " ---------------------------------------- (10) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; instance (Eq a, Eq b) => Eq FiniteMap a b where { (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; } addToFM :: Ord b => FiniteMap b a -> b -> a -> FiniteMap b a; addToFM fm key elt = addToFM_C addToFM0 fm key elt; addToFM0 old new = new; addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); addToFM_C4 combiner EmptyFM key elt = unitFM key elt; addToFM_C4 wzu wzv wzw wzx = addToFM_C3 wzu wzv wzw wzx; emptyFM :: FiniteMap a b; emptyFM = EmptyFM; findMax :: FiniteMap a b -> (a,b); findMax (Branch key elt vxy vxz EmptyFM) = (key,elt); findMax (Branch key elt vyu vyv fm_r) = findMax fm_r; findMin :: FiniteMap a b -> (a,b); findMin (Branch key elt wvw EmptyFM wvx) = (key,elt); findMin (Branch key elt wvy fm_l wvz) = findMin fm_l; fmToList :: FiniteMap a b -> [(a,b)]; fmToList fm = foldFM fmToList0 [] fm; fmToList0 key elt rest = (key,elt) : rest; foldFM :: (b -> c -> a -> a) -> a -> FiniteMap b c -> a; foldFM k z EmptyFM = z; foldFM k z (Branch key elt wuw fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; lookupFM EmptyFM key = lookupFM4 EmptyFM key; lookupFM (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find; lookupFM0 key elt wvv fm_l fm_r key_to_find True = Just elt; lookupFM1 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; lookupFM1 key elt wvv fm_l fm_r key_to_find False = lookupFM0 key elt wvv fm_l fm_r key_to_find otherwise; lookupFM2 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; lookupFM2 key elt wvv fm_l fm_r key_to_find False = lookupFM1 key elt wvv fm_l fm_r key_to_find (key_to_find > key); lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM2 key elt wvv fm_l fm_r key_to_find (key_to_find < key); lookupFM4 EmptyFM key = Nothing; lookupFM4 xxy xxz = lookupFM3 xxy xxz; mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = double_L fm_L fm_R; mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = single_L fm_L fm_R; mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = double_R fm_L fm_R; mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = single_R fm_L fm_R; mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); size_l = sizeFM fm_L; size_r = sizeFM fm_R; }; mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkBranch which key elt fm_l fm_r = let { result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; } in result where { balance_ok = True; left_ok = left_ok0 fm_l key fm_l; left_ok0 fm_l key EmptyFM = True; left_ok0 fm_l key (Branch left_key vww vwx vwy vwz) = let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key; left_size = sizeFM fm_l; right_ok = right_ok0 fm_r key fm_r; right_ok0 fm_r key EmptyFM = True; right_ok0 fm_r key (Branch right_key vxu vxv vxw vxx) = let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key; right_size = sizeFM fm_r; unbox :: Int -> Int; unbox x = x; }; mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_l < size_r) where { mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_r < size_l); size_l = sizeFM (Branch vuv vuw vux vuy vuz); size_r = sizeFM (Branch vvv vvw vvx vvy vvz); }; mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch4 xuv xuw xux xuy = mkVBalBranch3 xuv xuw xux xuy; mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch5 xvu xvv xvw xvx = mkVBalBranch4 xvu xvv xvw xvx; plusFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; plusFM_C combiner EmptyFM fm2 = fm2; plusFM_C combiner fm1 EmptyFM = fm1; plusFM_C combiner fm1 (Branch split_key elt2 zz left right) = mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { gts = splitGT fm1 split_key; lts = splitLT fm1 split_key; new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); new_elt0 elt2 combiner Nothing = elt2; new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; }; sIZE_RATIO :: Int; sIZE_RATIO = 5; sizeFM :: FiniteMap a b -> Int; sizeFM EmptyFM = 0; sizeFM (Branch wux wuy size wuz wvu) = size; splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; splitGT (Branch key elt vwu fm_l fm_r) split_key = splitGT3 (Branch key elt vwu fm_l fm_r) split_key; splitGT0 key elt vwu fm_l fm_r split_key True = fm_r; splitGT1 key elt vwu fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; splitGT1 key elt vwu fm_l fm_r split_key False = splitGT0 key elt vwu fm_l fm_r split_key otherwise; splitGT2 key elt vwu fm_l fm_r split_key True = splitGT fm_r split_key; splitGT2 key elt vwu fm_l fm_r split_key False = splitGT1 key elt vwu fm_l fm_r split_key (split_key < key); splitGT3 (Branch key elt vwu fm_l fm_r) split_key = splitGT2 key elt vwu fm_l fm_r split_key (split_key > key); splitGT4 EmptyFM split_key = emptyFM; splitGT4 xwu xwv = splitGT3 xwu xwv; splitLT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; splitLT (Branch key elt vwv fm_l fm_r) split_key = splitLT3 (Branch key elt vwv fm_l fm_r) split_key; splitLT0 key elt vwv fm_l fm_r split_key True = fm_l; splitLT1 key elt vwv fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); splitLT1 key elt vwv fm_l fm_r split_key False = splitLT0 key elt vwv fm_l fm_r split_key otherwise; splitLT2 key elt vwv fm_l fm_r split_key True = splitLT fm_l split_key; splitLT2 key elt vwv fm_l fm_r split_key False = splitLT1 key elt vwv fm_l fm_r split_key (split_key > key); splitLT3 (Branch key elt vwv fm_l fm_r) split_key = splitLT2 key elt vwv fm_l fm_r split_key (split_key < key); splitLT4 EmptyFM split_key = emptyFM; splitLT4 xwy xwz = splitLT3 xwy xwz; unitFM :: a -> b -> FiniteMap a b; unitFM key elt = Branch key elt 1 emptyFM emptyFM; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (11) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "gcd' (abs x) (abs y) where { gcd' x wwu = gcd'2 x wwu; gcd' x y = gcd'0 x y; ; gcd'0 x y = gcd' y (x `rem` y); ; gcd'1 True x wwu = x; gcd'1 wwv www wwx = gcd'0 www wwx; ; gcd'2 x wwu = gcd'1 (wwu == 0) x wwu; gcd'2 wwy wwz = gcd'0 wwy wwz; } " are unpacked to the following functions on top level "gcd0Gcd'2 x wwu = gcd0Gcd'1 (wwu == 0) x wwu; gcd0Gcd'2 wwy wwz = gcd0Gcd'0 wwy wwz; " "gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y); " "gcd0Gcd' x wwu = gcd0Gcd'2 x wwu; gcd0Gcd' x y = gcd0Gcd'0 x y; " "gcd0Gcd'1 True x wwu = x; gcd0Gcd'1 wwv www wwx = gcd0Gcd'0 www wwx; " 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 "reduce2D xyu xyv = gcd xyu xyv; " "reduce2Reduce0 xyu xyv x y True = x `quot` reduce2D xyu xyv :% (y `quot` reduce2D xyu xyv); " "reduce2Reduce1 xyu xyv x y True = error []; reduce2Reduce1 xyu xyv x y False = reduce2Reduce0 xyu xyv x y otherwise; " The bindings of the following Let/Where expression "mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { double_L fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); ; double_R (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r); ; mkBalBranch0 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); ; mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = double_L fm_L fm_R; ; mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr True = single_L fm_L fm_R; mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; ; mkBalBranch02 fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); ; mkBalBranch1 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); ; mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = double_R fm_L fm_R; ; mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr True = single_R fm_L fm_R; mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; ; mkBalBranch12 fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); ; mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; ; mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L; mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise; ; mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R; mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r); ; mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l); ; single_L fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr; ; single_R (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r); ; size_l = sizeFM fm_L; ; size_r = sizeFM fm_R; } " are unpacked to the following functions on top level "mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_r xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_l xyw xyx xyy xyz); " "mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); " "mkBalBranch6Size_r xyw xyx xyy xyz = sizeFM xyw; " "mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; " "mkBalBranch6Size_l xyw xyx xyy xyz = sizeFM xyx; " "mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); " "mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Double_R xyw xyx xyy xyz fm_L fm_R; " "mkBalBranch6Single_R xyw xyx xyy xyz (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xyy xyz fm_lr fm_r); " "mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Single_L xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; " "mkBalBranch6Double_R xyw xyx xyy xyz (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xyy xyz fm_lrr fm_r); " "mkBalBranch6Single_L xyw xyx xyy xyz fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 xyy xyz fm_l fm_rl) fm_rr; " "mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Double_L xyw xyx xyy xyz fm_L fm_R; " "mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); " "mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R fm_R; mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_l xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_r xyw xyx xyy xyz); " "mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Single_R xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; " "mkBalBranch6Double_L xyw xyx xyy xyz fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 xyy xyz fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); " "mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); " "mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R fm_L; mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R otherwise; " The bindings of the following Let/Where expression "let { result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; } in result where { balance_ok = True; ; left_ok = left_ok0 fm_l key fm_l; ; left_ok0 fm_l key EmptyFM = True; left_ok0 fm_l key (Branch left_key vww vwx vwy vwz) = let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key; ; left_size = sizeFM fm_l; ; right_ok = right_ok0 fm_r key fm_r; ; right_ok0 fm_r key EmptyFM = True; right_ok0 fm_r key (Branch right_key vxu vxv vxw vxx) = let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key; ; right_size = sizeFM fm_r; ; unbox x = x; } " are unpacked to the following functions on top level "mkBranchBalance_ok xzu xzv xzw = True; " "mkBranchRight_ok xzu xzv xzw = mkBranchRight_ok0 xzu xzv xzw xzu xzv xzu; " "mkBranchLeft_ok xzu xzv xzw = mkBranchLeft_ok0 xzu xzv xzw xzw xzv xzw; " "mkBranchUnbox xzu xzv xzw x = x; " "mkBranchRight_size xzu xzv xzw = sizeFM xzu; " "mkBranchRight_ok0 xzu xzv xzw fm_r key EmptyFM = True; mkBranchRight_ok0 xzu xzv xzw fm_r key (Branch right_key vxu vxv vxw vxx) = key < mkBranchRight_ok0Smallest_right_key fm_r; " "mkBranchLeft_size xzu xzv xzw = sizeFM xzw; " "mkBranchLeft_ok0 xzu xzv xzw fm_l key EmptyFM = True; mkBranchLeft_ok0 xzu xzv xzw fm_l key (Branch left_key vww vwx vwy vwz) = mkBranchLeft_ok0Biggest_left_key fm_l < key; " The bindings of the following Let/Where expression "let { result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r; } in result" are unpacked to the following functions on top level "mkBranchResult xzx xzy xzz yuu = Branch xzx xzy (mkBranchUnbox xzz xzx yuu (1 + mkBranchLeft_size xzz xzx yuu + mkBranchRight_size xzz xzx yuu)) yuu xzz; " The bindings of the following Let/Where expression "mkVBalBranch split_key new_elt (plusFM_C combiner lts left) (plusFM_C combiner gts right) where { gts = splitGT fm1 split_key; ; lts = splitLT fm1 split_key; ; new_elt = new_elt0 elt2 combiner (lookupFM fm1 split_key); ; new_elt0 elt2 combiner Nothing = elt2; new_elt0 elt2 combiner (Just elt1) = combiner elt1 elt2; } " are unpacked to the following functions on top level "plusFM_CGts yuv yuw yux yuy = splitGT yuv yuw; " "plusFM_CNew_elt yuv yuw yux yuy = plusFM_CNew_elt0 yuv yuw yux yuy yux yuy (lookupFM yuv yuw); " "plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner Nothing = elt2; plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner (Just elt1) = combiner elt1 elt2; " "plusFM_CLts yuv yuw yux yuy = splitLT yuv yuw; " The bindings of the following Let/Where expression "mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_l < size_r) where { mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); ; mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch0 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; ; mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; mkVBalBranch2 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch1 key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * size_r < size_l); ; size_l = sizeFM (Branch vuv vuw vux vuy vuz); ; size_r = sizeFM (Branch vvv vvw vvx vvy vvz); } " are unpacked to the following functions on top level "mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; " "mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); " "mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww < mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww); " "mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yuz yvu yvv yvw yvx); " "mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yvy yvz ywu ywv yww); " The bindings of the following Let/Where expression "let { smallest_right_key = fst (findMin fm_r); } in key < smallest_right_key" are unpacked to the following functions on top level "mkBranchRight_ok0Smallest_right_key ywx = fst (findMin ywx); " The bindings of the following Let/Where expression "let { biggest_left_key = fst (findMax fm_l); } in biggest_left_key < key" are unpacked to the following functions on top level "mkBranchLeft_ok0Biggest_left_key ywy = fst (findMax ywy); " ---------------------------------------- (12) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap b a = EmptyFM | Branch b a Int (FiniteMap b a) (FiniteMap b a) ; instance (Eq a, Eq b) => Eq FiniteMap a b where { (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; } addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; addToFM fm key elt = addToFM_C addToFM0 fm key elt; addToFM0 old new = new; addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); addToFM_C4 combiner EmptyFM key elt = unitFM key elt; addToFM_C4 wzu wzv wzw wzx = addToFM_C3 wzu wzv wzw wzx; emptyFM :: FiniteMap b a; emptyFM = EmptyFM; findMax :: FiniteMap a b -> (a,b); findMax (Branch key elt vxy vxz EmptyFM) = (key,elt); findMax (Branch key elt vyu vyv fm_r) = findMax fm_r; findMin :: FiniteMap b a -> (b,a); findMin (Branch key elt wvw EmptyFM wvx) = (key,elt); findMin (Branch key elt wvy fm_l wvz) = findMin fm_l; fmToList :: FiniteMap a b -> [(a,b)]; fmToList fm = foldFM fmToList0 [] fm; fmToList0 key elt rest = (key,elt) : rest; foldFM :: (a -> c -> b -> b) -> b -> FiniteMap a c -> b; foldFM k z EmptyFM = z; foldFM k z (Branch key elt wuw fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; lookupFM :: Ord a => FiniteMap a b -> a -> Maybe b; lookupFM EmptyFM key = lookupFM4 EmptyFM key; lookupFM (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find; lookupFM0 key elt wvv fm_l fm_r key_to_find True = Just elt; lookupFM1 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; lookupFM1 key elt wvv fm_l fm_r key_to_find False = lookupFM0 key elt wvv fm_l fm_r key_to_find otherwise; lookupFM2 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; lookupFM2 key elt wvv fm_l fm_r key_to_find False = lookupFM1 key elt wvv fm_l fm_r key_to_find (key_to_find > key); lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM2 key elt wvv fm_l fm_r key_to_find (key_to_find < key); lookupFM4 EmptyFM key = Nothing; lookupFM4 xxy xxz = lookupFM3 xxy xxz; mkBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 fm_R fm_L key elt key elt fm_L fm_R (mkBalBranch6Size_l fm_R fm_L key elt + mkBalBranch6Size_r fm_R fm_L key elt < 2); mkBalBranch6Double_L xyw xyx xyy xyz fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 xyy xyz fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr); mkBalBranch6Double_R xyw xyx xyy xyz (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xyy xyz fm_lrr fm_r); mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Double_L xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Single_L xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr); mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Double_R xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Single_R xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll); mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R; mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R fm_L; mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R otherwise; mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R fm_R; mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_l xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_r xyw xyx xyy xyz); mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R; mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_r xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_l xyw xyx xyy xyz); mkBalBranch6Single_L xyw xyx xyy xyz fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 xyy xyz fm_l fm_rl) fm_rr; mkBalBranch6Single_R xyw xyx xyy xyz (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xyy xyz fm_lr fm_r); mkBalBranch6Size_l xyw xyx xyy xyz = sizeFM xyx; mkBalBranch6Size_r xyw xyx xyy xyz = sizeFM xyw; mkBranch :: Ord a => Int -> a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_r fm_l; mkBranchBalance_ok xzu xzv xzw = True; mkBranchLeft_ok xzu xzv xzw = mkBranchLeft_ok0 xzu xzv xzw xzw xzv xzw; mkBranchLeft_ok0 xzu xzv xzw fm_l key EmptyFM = True; mkBranchLeft_ok0 xzu xzv xzw fm_l key (Branch left_key vww vwx vwy vwz) = mkBranchLeft_ok0Biggest_left_key fm_l < key; mkBranchLeft_ok0Biggest_left_key ywy = fst (findMax ywy); mkBranchLeft_size xzu xzv xzw = sizeFM xzw; mkBranchResult xzx xzy xzz yuu = Branch xzx xzy (mkBranchUnbox xzz xzx yuu (1 + mkBranchLeft_size xzz xzx yuu + mkBranchRight_size xzz xzx yuu)) yuu xzz; mkBranchRight_ok xzu xzv xzw = mkBranchRight_ok0 xzu xzv xzw xzu xzv xzu; mkBranchRight_ok0 xzu xzv xzw fm_r key EmptyFM = True; mkBranchRight_ok0 xzu xzv xzw fm_r key (Branch right_key vxu vxv vxw vxx) = key < mkBranchRight_ok0Smallest_right_key fm_r; mkBranchRight_ok0Smallest_right_key ywx = fst (findMin ywx); mkBranchRight_size xzu xzv xzw = sizeFM xzu; mkBranchUnbox :: Ord a => -> (FiniteMap a b) ( -> a ( -> (FiniteMap a b) (Int -> Int))); mkBranchUnbox xzu xzv xzw x = x; mkVBalBranch :: Ord a => a -> b -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3MkVBalBranch2 vuv vuw vux vuy vuz vvv vvw vvx vvy vvz key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_l vuv vuw vux vuy vuz vvv vvw vvx vvy vvz < mkVBalBranch3Size_r vuv vuw vux vuy vuz vvv vvw vvx vvy vvz); mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch 13 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww < mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww); mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yuz yvu yvv yvw yvx); mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yvy yvz ywu ywv yww); mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch4 xuv xuw xux xuy = mkVBalBranch3 xuv xuw xux xuy; mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch5 xvu xvv xvw xvx = mkVBalBranch4 xvu xvv xvw xvx; plusFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; plusFM_C combiner EmptyFM fm2 = fm2; plusFM_C combiner fm1 EmptyFM = fm1; plusFM_C combiner fm1 (Branch split_key elt2 zz left right) = mkVBalBranch split_key (plusFM_CNew_elt fm1 split_key elt2 combiner) (plusFM_C combiner (plusFM_CLts fm1 split_key elt2 combiner) left) (plusFM_C combiner (plusFM_CGts fm1 split_key elt2 combiner) right); plusFM_CGts yuv yuw yux yuy = splitGT yuv yuw; plusFM_CLts yuv yuw yux yuy = splitLT yuv yuw; plusFM_CNew_elt yuv yuw yux yuy = plusFM_CNew_elt0 yuv yuw yux yuy yux yuy (lookupFM yuv yuw); plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner Nothing = elt2; plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner (Just elt1) = combiner elt1 elt2; sIZE_RATIO :: Int; sIZE_RATIO = 5; sizeFM :: FiniteMap b a -> Int; sizeFM EmptyFM = 0; sizeFM (Branch wux wuy size wuz wvu) = size; splitGT :: Ord b => FiniteMap b a -> b -> FiniteMap b a; splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; splitGT (Branch key elt vwu fm_l fm_r) split_key = splitGT3 (Branch key elt vwu fm_l fm_r) split_key; splitGT0 key elt vwu fm_l fm_r split_key True = fm_r; splitGT1 key elt vwu fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; splitGT1 key elt vwu fm_l fm_r split_key False = splitGT0 key elt vwu fm_l fm_r split_key otherwise; splitGT2 key elt vwu fm_l fm_r split_key True = splitGT fm_r split_key; splitGT2 key elt vwu fm_l fm_r split_key False = splitGT1 key elt vwu fm_l fm_r split_key (split_key < key); splitGT3 (Branch key elt vwu fm_l fm_r) split_key = splitGT2 key elt vwu fm_l fm_r split_key (split_key > key); splitGT4 EmptyFM split_key = emptyFM; splitGT4 xwu xwv = splitGT3 xwu xwv; splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; splitLT (Branch key elt vwv fm_l fm_r) split_key = splitLT3 (Branch key elt vwv fm_l fm_r) split_key; splitLT0 key elt vwv fm_l fm_r split_key True = fm_l; splitLT1 key elt vwv fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); splitLT1 key elt vwv fm_l fm_r split_key False = splitLT0 key elt vwv fm_l fm_r split_key otherwise; splitLT2 key elt vwv fm_l fm_r split_key True = splitLT fm_l split_key; splitLT2 key elt vwv fm_l fm_r split_key False = splitLT1 key elt vwv fm_l fm_r split_key (split_key > key); splitLT3 (Branch key elt vwv fm_l fm_r) split_key = splitLT2 key elt vwv fm_l fm_r split_key (split_key < key); splitLT4 EmptyFM split_key = emptyFM; splitLT4 xwy xwz = splitLT3 xwy xwz; unitFM :: a -> b -> FiniteMap a b; unitFM key elt = Branch key elt 1 emptyFM emptyFM; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (13) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (14) Obligation: mainModule Main module FiniteMap where { import qualified Main; import qualified Maybe; import qualified Prelude; data FiniteMap a b = EmptyFM | Branch a b Int (FiniteMap a b) (FiniteMap a b) ; instance (Eq a, Eq b) => Eq FiniteMap a b where { (==) fm_1 fm_2 = sizeFM fm_1 == sizeFM fm_2 && fmToList fm_1 == fmToList fm_2; } addToFM :: Ord a => FiniteMap a b -> a -> b -> FiniteMap a b; addToFM fm key elt = addToFM_C addToFM0 fm key elt; addToFM0 old new = new; addToFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> a -> b -> FiniteMap a b; addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt; addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt; addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r; addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt); addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise; addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r; addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key); addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key); addToFM_C4 combiner EmptyFM key elt = unitFM key elt; addToFM_C4 wzu wzv wzw wzx = addToFM_C3 wzu wzv wzw wzx; emptyFM :: FiniteMap a b; emptyFM = EmptyFM; findMax :: FiniteMap a b -> (a,b); findMax (Branch key elt vxy vxz EmptyFM) = (key,elt); findMax (Branch key elt vyu vyv fm_r) = findMax fm_r; findMin :: FiniteMap b a -> (b,a); findMin (Branch key elt wvw EmptyFM wvx) = (key,elt); findMin (Branch key elt wvy fm_l wvz) = findMin fm_l; fmToList :: FiniteMap b a -> [(b,a)]; fmToList fm = foldFM fmToList0 [] fm; fmToList0 key elt rest = (key,elt) : rest; foldFM :: (a -> b -> c -> c) -> c -> FiniteMap a b -> c; foldFM k z EmptyFM = z; foldFM k z (Branch key elt wuw fm_l fm_r) = foldFM k (k key elt (foldFM k z fm_r)) fm_l; lookupFM :: Ord b => FiniteMap b a -> b -> Maybe a; lookupFM EmptyFM key = lookupFM4 EmptyFM key; lookupFM (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find; lookupFM0 key elt wvv fm_l fm_r key_to_find True = Just elt; lookupFM1 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_r key_to_find; lookupFM1 key elt wvv fm_l fm_r key_to_find False = lookupFM0 key elt wvv fm_l fm_r key_to_find otherwise; lookupFM2 key elt wvv fm_l fm_r key_to_find True = lookupFM fm_l key_to_find; lookupFM2 key elt wvv fm_l fm_r key_to_find False = lookupFM1 key elt wvv fm_l fm_r key_to_find (key_to_find > key); lookupFM3 (Branch key elt wvv fm_l fm_r) key_to_find = lookupFM2 key elt wvv fm_l fm_r key_to_find (key_to_find < key); lookupFM4 EmptyFM key = Nothing; lookupFM4 xxy xxz = lookupFM3 xxy xxz; mkBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R; mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 fm_R fm_L key elt key elt fm_L fm_R (mkBalBranch6Size_l fm_R fm_L key elt + mkBalBranch6Size_r fm_R fm_L key elt < Pos (Succ (Succ Zero))); mkBalBranch6Double_L xyw xyx xyy xyz fm_l (Branch key_r elt_r vzw (Branch key_rl elt_rl vzx fm_rll fm_rlr) fm_rr) = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) xyy xyz fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr); mkBalBranch6Double_R xyw xyx xyy xyz (Branch key_l elt_l vyx fm_ll (Branch key_lr elt_lr vyy fm_lrl fm_lrr)) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) xyy xyz fm_lrr fm_r); mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr); mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Double_L xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr True = mkBalBranch6Single_L xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr otherwise; mkBalBranch6MkBalBranch02 xyw xyx xyy xyz fm_L fm_R (Branch vzy vzz wuu fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xyw xyx xyy xyz fm_L fm_R vzy vzz wuu fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr); mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr); mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Double_R xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr True = mkBalBranch6Single_R xyw xyx xyy xyz fm_L fm_R; mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr otherwise; mkBalBranch6MkBalBranch12 xyw xyx xyy xyz fm_L fm_R (Branch vyz vzu vzv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xyw xyx xyy xyz fm_L fm_R vyz vzu vzv fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll); mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R; mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xyw xyx xyy xyz fm_L fm_R fm_L; mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xyw xyx xyy xyz key elt fm_L fm_R otherwise; mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xyw xyx xyy xyz fm_L fm_R fm_R; mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_l xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_r xyw xyx xyy xyz); mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R; mkBalBranch6MkBalBranch5 xyw xyx xyy xyz key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xyw xyx xyy xyz key elt fm_L fm_R (mkBalBranch6Size_r xyw xyx xyy xyz > sIZE_RATIO * mkBalBranch6Size_l xyw xyx xyy xyz); mkBalBranch6Single_L xyw xyx xyy xyz fm_l (Branch key_r elt_r wuv fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) xyy xyz fm_l fm_rl) fm_rr; mkBalBranch6Single_R xyw xyx xyy xyz (Branch key_l elt_l vyw fm_ll fm_lr) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) xyy xyz fm_lr fm_r); mkBalBranch6Size_l xyw xyx xyy xyz = sizeFM xyx; mkBalBranch6Size_r xyw xyx xyy xyz = sizeFM xyw; mkBranch :: Ord b => Int -> b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_r fm_l; mkBranchBalance_ok xzu xzv xzw = True; mkBranchLeft_ok xzu xzv xzw = mkBranchLeft_ok0 xzu xzv xzw xzw xzv xzw; mkBranchLeft_ok0 xzu xzv xzw fm_l key EmptyFM = True; mkBranchLeft_ok0 xzu xzv xzw fm_l key (Branch left_key vww vwx vwy vwz) = mkBranchLeft_ok0Biggest_left_key fm_l < key; mkBranchLeft_ok0Biggest_left_key ywy = fst (findMax ywy); mkBranchLeft_size xzu xzv xzw = sizeFM xzw; mkBranchResult xzx xzy xzz yuu = Branch xzx xzy (mkBranchUnbox xzz xzx yuu (Pos (Succ Zero) + mkBranchLeft_size xzz xzx yuu + mkBranchRight_size xzz xzx yuu)) yuu xzz; mkBranchRight_ok xzu xzv xzw = mkBranchRight_ok0 xzu xzv xzw xzu xzv xzu; mkBranchRight_ok0 xzu xzv xzw fm_r key EmptyFM = True; mkBranchRight_ok0 xzu xzv xzw fm_r key (Branch right_key vxu vxv vxw vxx) = key < mkBranchRight_ok0Smallest_right_key fm_r; mkBranchRight_ok0Smallest_right_key ywx = fst (findMin ywx); mkBranchRight_size xzu xzv xzw = sizeFM xzu; mkBranchUnbox :: Ord a => -> (FiniteMap a b) ( -> a ( -> (FiniteMap a b) (Int -> Int))); mkBranchUnbox xzu xzv xzw x = x; mkVBalBranch :: Ord b => b -> a -> FiniteMap b a -> FiniteMap b a -> FiniteMap b a; mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r; mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM; mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); mkVBalBranch3 key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz) = mkVBalBranch3MkVBalBranch2 vuv vuw vux vuy vuz vvv vvw vvx vvy vvz key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_l vuv vuw vux vuy vuz vvv vvw vvx vvy vvz < mkVBalBranch3Size_r vuv vuw vux vuy vuz vvv vvw vvx vvy vvz); mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) key elt (Branch vuv vuw vux vuy vuz) (Branch vvv vvw vvx vvy vvz); mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vuv vuw vuy (mkVBalBranch key elt vuz (Branch vvv vvw vvx vvy vvz)); mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch0 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz otherwise; mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz True = mkBalBranch vvv vvw (mkVBalBranch key elt (Branch vuv vuw vux vuy vuz) vvy) vvz; mkVBalBranch3MkVBalBranch2 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz False = mkVBalBranch3MkVBalBranch1 yuz yvu yvv yvw yvx yvy yvz ywu ywv yww key elt vuv vuw vux vuy vuz vvv vvw vvx vvy vvz (sIZE_RATIO * mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww < mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww); mkVBalBranch3Size_l yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yuz yvu yvv yvw yvx); mkVBalBranch3Size_r yuz yvu yvv yvw yvx yvy yvz ywu ywv yww = sizeFM (Branch yvy yvz ywu ywv yww); mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt; mkVBalBranch4 xuv xuw xux xuy = mkVBalBranch3 xuv xuw xux xuy; mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt; mkVBalBranch5 xvu xvv xvw xvx = mkVBalBranch4 xvu xvv xvw xvx; plusFM_C :: Ord a => (b -> b -> b) -> FiniteMap a b -> FiniteMap a b -> FiniteMap a b; plusFM_C combiner EmptyFM fm2 = fm2; plusFM_C combiner fm1 EmptyFM = fm1; plusFM_C combiner fm1 (Branch split_key elt2 zz left right) = mkVBalBranch split_key (plusFM_CNew_elt fm1 split_key elt2 combiner) (plusFM_C combiner (plusFM_CLts fm1 split_key elt2 combiner) left) (plusFM_C combiner (plusFM_CGts fm1 split_key elt2 combiner) right); plusFM_CGts yuv yuw yux yuy = splitGT yuv yuw; plusFM_CLts yuv yuw yux yuy = splitLT yuv yuw; plusFM_CNew_elt yuv yuw yux yuy = plusFM_CNew_elt0 yuv yuw yux yuy yux yuy (lookupFM yuv yuw); plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner Nothing = elt2; plusFM_CNew_elt0 yuv yuw yux yuy elt2 combiner (Just elt1) = combiner elt1 elt2; sIZE_RATIO :: Int; sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero))))); sizeFM :: FiniteMap b a -> Int; sizeFM EmptyFM = Pos Zero; sizeFM (Branch wux wuy size wuz wvu) = size; splitGT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; splitGT EmptyFM split_key = splitGT4 EmptyFM split_key; splitGT (Branch key elt vwu fm_l fm_r) split_key = splitGT3 (Branch key elt vwu fm_l fm_r) split_key; splitGT0 key elt vwu fm_l fm_r split_key True = fm_r; splitGT1 key elt vwu fm_l fm_r split_key True = mkVBalBranch key elt (splitGT fm_l split_key) fm_r; splitGT1 key elt vwu fm_l fm_r split_key False = splitGT0 key elt vwu fm_l fm_r split_key otherwise; splitGT2 key elt vwu fm_l fm_r split_key True = splitGT fm_r split_key; splitGT2 key elt vwu fm_l fm_r split_key False = splitGT1 key elt vwu fm_l fm_r split_key (split_key < key); splitGT3 (Branch key elt vwu fm_l fm_r) split_key = splitGT2 key elt vwu fm_l fm_r split_key (split_key > key); splitGT4 EmptyFM split_key = emptyFM; splitGT4 xwu xwv = splitGT3 xwu xwv; splitLT :: Ord a => FiniteMap a b -> a -> FiniteMap a b; splitLT EmptyFM split_key = splitLT4 EmptyFM split_key; splitLT (Branch key elt vwv fm_l fm_r) split_key = splitLT3 (Branch key elt vwv fm_l fm_r) split_key; splitLT0 key elt vwv fm_l fm_r split_key True = fm_l; splitLT1 key elt vwv fm_l fm_r split_key True = mkVBalBranch key elt fm_l (splitLT fm_r split_key); splitLT1 key elt vwv fm_l fm_r split_key False = splitLT0 key elt vwv fm_l fm_r split_key otherwise; splitLT2 key elt vwv fm_l fm_r split_key True = splitLT fm_l split_key; splitLT2 key elt vwv fm_l fm_r split_key False = splitLT1 key elt vwv fm_l fm_r split_key (split_key > key); splitLT3 (Branch key elt vwv fm_l fm_r) split_key = splitLT2 key elt vwv fm_l fm_r split_key (split_key < key); splitLT4 EmptyFM split_key = emptyFM; splitLT4 xwy xwz = splitLT3 xwy xwz; unitFM :: b -> a -> FiniteMap b a; unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM; } module Maybe where { import qualified FiniteMap; import qualified Main; import qualified Prelude; } module Main where { import qualified FiniteMap; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (15) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="FiniteMap.plusFM_C",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="FiniteMap.plusFM_C ywz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="FiniteMap.plusFM_C ywz3 ywz4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 5[label="FiniteMap.plusFM_C ywz3 ywz4 ywz5",fontsize=16,color="burlywood",shape="triangle"];25315[label="ywz4/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 25315[label="",style="solid", color="burlywood", weight=9]; 25315 -> 6[label="",style="solid", color="burlywood", weight=3]; 25316[label="ywz4/FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 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13650[label="",style="dashed", color="magenta", weight=3]; 36 -> 13651[label="",style="dashed", color="magenta", weight=3]; 36 -> 13652[label="",style="dashed", color="magenta", weight=3]; 36 -> 13653[label="",style="dashed", color="magenta", weight=3]; 37[label="FiniteMap.splitLT2 ywz40 ywz41 ywz42 ywz43 ywz44 ywz50 (compare ywz50 ywz40 == LT)",fontsize=16,color="black",shape="box"];37 -> 43[label="",style="solid", color="black", weight=3]; 38[label="FiniteMap.splitGT2 ywz40 ywz41 ywz42 ywz43 ywz44 ywz50 (compare ywz50 ywz40 == GT)",fontsize=16,color="black",shape="box"];38 -> 44[label="",style="solid", color="black", weight=3]; 39[label="FiniteMap.addToFM_C FiniteMap.addToFM0 FiniteMap.EmptyFM ywz50 (FiniteMap.plusFM_CNew_elt (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3)",fontsize=16,color="black",shape="box"];39 -> 45[label="",style="solid", color="black", weight=3]; 40[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch ywz60 ywz61 ywz62 ywz63 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ywz3",fontsize=16,color="magenta"];13652 -> 10999[label="",style="dashed", color="red", weight=0]; 13652[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz70 ywz71 ywz72 ywz73 ywz74 ywz60 ywz61 ywz62 ywz63 ywz64 < FiniteMap.mkVBalBranch3Size_r ywz70 ywz71 ywz72 ywz73 ywz74 ywz60 ywz61 ywz62 ywz63 ywz64",fontsize=16,color="magenta"];13652 -> 14088[label="",style="dashed", color="magenta", weight=3]; 13652 -> 14089[label="",style="dashed", color="magenta", weight=3]; 13653[label="ywz63",fontsize=16,color="green",shape="box"];13641[label="FiniteMap.mkVBalBranch3MkVBalBranch2 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 ywz50 ywz9 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 ywz1167",fontsize=16,color="burlywood",shape="triangle"];25325[label="ywz1167/False",fontsize=10,color="white",style="solid",shape="box"];13641 -> 25325[label="",style="solid", color="burlywood", weight=9]; 25325 -> 14090[label="",style="solid", color="burlywood", weight=3]; 25326[label="ywz1167/True",fontsize=10,color="white",style="solid",shape="box"];13641 -> 25326[label="",style="solid", color="burlywood", weight=9]; 25326 -> 14091[label="",style="solid", color="burlywood", weight=3]; 43[label="FiniteMap.splitLT2 ywz40 ywz41 ywz42 ywz43 ywz44 ywz50 (primCmpInt ywz50 ywz40 == LT)",fontsize=16,color="burlywood",shape="box"];25327[label="ywz50/Pos ywz500",fontsize=10,color="white",style="solid",shape="box"];43 -> 25327[label="",style="solid", color="burlywood", weight=9]; 25327 -> 48[label="",style="solid", color="burlywood", weight=3]; 25328[label="ywz50/Neg ywz500",fontsize=10,color="white",style="solid",shape="box"];43 -> 25328[label="",style="solid", color="burlywood", weight=9]; 25328 -> 49[label="",style="solid", color="burlywood", weight=3]; 44[label="FiniteMap.splitGT2 ywz40 ywz41 ywz42 ywz43 ywz44 ywz50 (primCmpInt ywz50 ywz40 == GT)",fontsize=16,color="burlywood",shape="box"];25329[label="ywz50/Pos ywz500",fontsize=10,color="white",style="solid",shape="box"];44 -> 25329[label="",style="solid", color="burlywood", weight=9]; 25329 -> 50[label="",style="solid", color="burlywood", weight=3]; 25330[label="ywz50/Neg ywz500",fontsize=10,color="white",style="solid",shape="box"];44 -> 25330[label="",style="solid", color="burlywood", weight=9]; 25330 -> 51[label="",style="solid", color="burlywood", weight=3]; 45[label="FiniteMap.addToFM_C4 FiniteMap.addToFM0 FiniteMap.EmptyFM ywz50 (FiniteMap.plusFM_CNew_elt (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3)",fontsize=16,color="black",shape="box"];45 -> 52[label="",style="solid", color="black", weight=3]; 46[label="FiniteMap.addToFM_C3 FiniteMap.addToFM0 (FiniteMap.Branch ywz60 ywz61 ywz62 ywz63 ywz64) ywz50 (FiniteMap.plusFM_CNew_elt (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3)",fontsize=16,color="black",shape="box"];46 -> 53[label="",style="solid", color="black", weight=3]; 82[label="FiniteMap.plusFM_CNew_elt (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3",fontsize=16,color="black",shape="triangle"];82 -> 111[label="",style="solid", color="black", weight=3]; 14088 -> 12141[label="",style="dashed", color="red", weight=0]; 14088[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz70 ywz71 ywz72 ywz73 ywz74 ywz60 ywz61 ywz62 ywz63 ywz64",fontsize=16,color="magenta"];14088 -> 14138[label="",style="dashed", color="magenta", weight=3]; 14089[label="FiniteMap.mkVBalBranch3Size_r ywz70 ywz71 ywz72 ywz73 ywz74 ywz60 ywz61 ywz62 ywz63 ywz64",fontsize=16,color="black",shape="triangle"];14089 -> 14139[label="",style="solid", color="black", weight=3]; 10999[label="ywz821 < ywz811",fontsize=16,color="black",shape="triangle"];10999 -> 11367[label="",style="solid", color="black", weight=3]; 14090[label="FiniteMap.mkVBalBranch3MkVBalBranch2 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 ywz50 ywz9 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 False",fontsize=16,color="black",shape="box"];14090 -> 14140[label="",style="solid", color="black", weight=3]; 14091[label="FiniteMap.mkVBalBranch3MkVBalBranch2 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 ywz50 ywz9 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 True",fontsize=16,color="black",shape="box"];14091 -> 14141[label="",style="solid", color="black", weight=3]; 48[label="FiniteMap.splitLT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Pos ywz500) (primCmpInt (Pos ywz500) ywz40 == LT)",fontsize=16,color="burlywood",shape="box"];25331[label="ywz500/Succ ywz5000",fontsize=10,color="white",style="solid",shape="box"];48 -> 25331[label="",style="solid", color="burlywood", weight=9]; 25331 -> 55[label="",style="solid", color="burlywood", weight=3]; 25332[label="ywz500/Zero",fontsize=10,color="white",style="solid",shape="box"];48 -> 25332[label="",style="solid", color="burlywood", weight=9]; 25332 -> 56[label="",style="solid", color="burlywood", weight=3]; 49[label="FiniteMap.splitLT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Neg ywz500) (primCmpInt (Neg ywz500) ywz40 == LT)",fontsize=16,color="burlywood",shape="box"];25333[label="ywz500/Succ ywz5000",fontsize=10,color="white",style="solid",shape="box"];49 -> 25333[label="",style="solid", color="burlywood", weight=9]; 25333 -> 57[label="",style="solid", color="burlywood", weight=3]; 25334[label="ywz500/Zero",fontsize=10,color="white",style="solid",shape="box"];49 -> 25334[label="",style="solid", color="burlywood", weight=9]; 25334 -> 58[label="",style="solid", color="burlywood", weight=3]; 50[label="FiniteMap.splitGT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Pos ywz500) (primCmpInt (Pos ywz500) ywz40 == GT)",fontsize=16,color="burlywood",shape="box"];25335[label="ywz500/Succ ywz5000",fontsize=10,color="white",style="solid",shape="box"];50 -> 25335[label="",style="solid", color="burlywood", weight=9]; 25335 -> 59[label="",style="solid", color="burlywood", weight=3]; 25336[label="ywz500/Zero",fontsize=10,color="white",style="solid",shape="box"];50 -> 25336[label="",style="solid", color="burlywood", weight=9]; 25336 -> 60[label="",style="solid", color="burlywood", weight=3]; 51[label="FiniteMap.splitGT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Neg ywz500) (primCmpInt (Neg ywz500) ywz40 == GT)",fontsize=16,color="burlywood",shape="box"];25337[label="ywz500/Succ ywz5000",fontsize=10,color="white",style="solid",shape="box"];51 -> 25337[label="",style="solid", color="burlywood", weight=9]; 25337 -> 61[label="",style="solid", color="burlywood", weight=3]; 25338[label="ywz500/Zero",fontsize=10,color="white",style="solid",shape="box"];51 -> 25338[label="",style="solid", color="burlywood", weight=9]; 25338 -> 62[label="",style="solid", color="burlywood", weight=3]; 52[label="FiniteMap.unitFM ywz50 (FiniteMap.plusFM_CNew_elt (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3)",fontsize=16,color="black",shape="box"];52 -> 63[label="",style="solid", color="black", weight=3]; 53 -> 14543[label="",style="dashed", color="red", weight=0]; 53[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 ywz60 ywz61 ywz62 ywz63 ywz64 ywz50 (FiniteMap.plusFM_CNew_elt (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3) (ywz50 < ywz60)",fontsize=16,color="magenta"];53 -> 14544[label="",style="dashed", color="magenta", weight=3]; 53 -> 14545[label="",style="dashed", color="magenta", weight=3]; 53 -> 14546[label="",style="dashed", color="magenta", weight=3]; 53 -> 14547[label="",style="dashed", color="magenta", weight=3]; 53 -> 14548[label="",style="dashed", color="magenta", weight=3]; 53 -> 14549[label="",style="dashed", color="magenta", weight=3]; 53 -> 14550[label="",style="dashed", color="magenta", weight=3]; 111[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50)",fontsize=16,color="black",shape="box"];111 -> 145[label="",style="solid", color="black", weight=3]; 14138[label="FiniteMap.mkVBalBranch3Size_l ywz70 ywz71 ywz72 ywz73 ywz74 ywz60 ywz61 ywz62 ywz63 ywz64",fontsize=16,color="black",shape="triangle"];14138 -> 14199[label="",style="solid", color="black", weight=3]; 12141[label="FiniteMap.sIZE_RATIO * ywz1037",fontsize=16,color="black",shape="triangle"];12141 -> 12161[label="",style="solid", color="black", weight=3]; 14139 -> 3313[label="",style="dashed", color="red", weight=0]; 14139[label="FiniteMap.sizeFM (FiniteMap.Branch ywz60 ywz61 ywz62 ywz63 ywz64)",fontsize=16,color="magenta"];14139 -> 14200[label="",style="dashed", color="magenta", weight=3]; 11367[label="compare ywz821 ywz811 == LT",fontsize=16,color="black",shape="box"];11367 -> 12163[label="",style="solid", color="black", weight=3]; 14140 -> 14201[label="",style="dashed", color="red", weight=0]; 14140[label="FiniteMap.mkVBalBranch3MkVBalBranch1 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 ywz50 ywz9 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 < FiniteMap.mkVBalBranch3Size_l ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634)",fontsize=16,color="magenta"];14140 -> 14202[label="",style="dashed", color="magenta", weight=3]; 14141[label="FiniteMap.mkBalBranch ywz630 ywz631 (FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633) ywz634",fontsize=16,color="black",shape="box"];14141 -> 14203[label="",style="solid", color="black", weight=3]; 55[label="FiniteMap.splitLT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpInt (Pos (Succ ywz5000)) ywz40 == LT)",fontsize=16,color="burlywood",shape="box"];25339[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];55 -> 25339[label="",style="solid", color="burlywood", weight=9]; 25339 -> 66[label="",style="solid", color="burlywood", weight=3]; 25340[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];55 -> 25340[label="",style="solid", color="burlywood", weight=9]; 25340 -> 67[label="",style="solid", color="burlywood", weight=3]; 56[label="FiniteMap.splitLT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) ywz40 == LT)",fontsize=16,color="burlywood",shape="box"];25341[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];56 -> 25341[label="",style="solid", color="burlywood", weight=9]; 25341 -> 68[label="",style="solid", color="burlywood", weight=3]; 25342[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];56 -> 25342[label="",style="solid", color="burlywood", weight=9]; 25342 -> 69[label="",style="solid", color="burlywood", weight=3]; 57[label="FiniteMap.splitLT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpInt (Neg (Succ ywz5000)) ywz40 == LT)",fontsize=16,color="burlywood",shape="box"];25343[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];57 -> 25343[label="",style="solid", color="burlywood", weight=9]; 25343 -> 70[label="",style="solid", color="burlywood", weight=3]; 25344[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];57 -> 25344[label="",style="solid", color="burlywood", weight=9]; 25344 -> 71[label="",style="solid", color="burlywood", weight=3]; 58[label="FiniteMap.splitLT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) ywz40 == LT)",fontsize=16,color="burlywood",shape="box"];25345[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];58 -> 25345[label="",style="solid", color="burlywood", weight=9]; 25345 -> 72[label="",style="solid", color="burlywood", weight=3]; 25346[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];58 -> 25346[label="",style="solid", color="burlywood", weight=9]; 25346 -> 73[label="",style="solid", color="burlywood", weight=3]; 59[label="FiniteMap.splitGT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpInt (Pos (Succ ywz5000)) ywz40 == GT)",fontsize=16,color="burlywood",shape="box"];25347[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];59 -> 25347[label="",style="solid", color="burlywood", weight=9]; 25347 -> 74[label="",style="solid", color="burlywood", weight=3]; 25348[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];59 -> 25348[label="",style="solid", color="burlywood", weight=9]; 25348 -> 75[label="",style="solid", color="burlywood", weight=3]; 60[label="FiniteMap.splitGT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) ywz40 == GT)",fontsize=16,color="burlywood",shape="box"];25349[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];60 -> 25349[label="",style="solid", color="burlywood", weight=9]; 25349 -> 76[label="",style="solid", color="burlywood", weight=3]; 25350[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];60 -> 25350[label="",style="solid", color="burlywood", weight=9]; 25350 -> 77[label="",style="solid", color="burlywood", weight=3]; 61[label="FiniteMap.splitGT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpInt (Neg (Succ ywz5000)) ywz40 == GT)",fontsize=16,color="burlywood",shape="box"];25351[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];61 -> 25351[label="",style="solid", color="burlywood", weight=9]; 25351 -> 78[label="",style="solid", color="burlywood", weight=3]; 25352[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];61 -> 25352[label="",style="solid", color="burlywood", weight=9]; 25352 -> 79[label="",style="solid", color="burlywood", weight=3]; 62[label="FiniteMap.splitGT2 ywz40 ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) ywz40 == GT)",fontsize=16,color="burlywood",shape="box"];25353[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];62 -> 25353[label="",style="solid", color="burlywood", weight=9]; 25353 -> 80[label="",style="solid", color="burlywood", weight=3]; 25354[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];62 -> 25354[label="",style="solid", color="burlywood", weight=9]; 25354 -> 81[label="",style="solid", color="burlywood", weight=3]; 63[label="FiniteMap.Branch ywz50 (FiniteMap.plusFM_CNew_elt (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3) (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];63 -> 82[label="",style="dashed", color="green", weight=3]; 63 -> 83[label="",style="dashed", color="green", weight=3]; 63 -> 84[label="",style="dashed", color="green", weight=3]; 14544[label="ywz61",fontsize=16,color="green",shape="box"];14545[label="ywz63",fontsize=16,color="green",shape="box"];14546[label="ywz60",fontsize=16,color="green",shape="box"];14547[label="ywz62",fontsize=16,color="green",shape="box"];14548[label="ywz64",fontsize=16,color="green",shape="box"];14549 -> 82[label="",style="dashed", color="red", weight=0]; 14549[label="FiniteMap.plusFM_CNew_elt (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3",fontsize=16,color="magenta"];14550 -> 10999[label="",style="dashed", color="red", weight=0]; 14550[label="ywz50 < ywz60",fontsize=16,color="magenta"];14550 -> 14989[label="",style="dashed", color="magenta", weight=3]; 14550 -> 14990[label="",style="dashed", color="magenta", weight=3]; 14543[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 ywz50 ywz9 ywz1208",fontsize=16,color="burlywood",shape="triangle"];25355[label="ywz1208/False",fontsize=10,color="white",style="solid",shape="box"];14543 -> 25355[label="",style="solid", color="burlywood", weight=9]; 25355 -> 14991[label="",style="solid", color="burlywood", weight=3]; 25356[label="ywz1208/True",fontsize=10,color="white",style="solid",shape="box"];14543 -> 25356[label="",style="solid", color="burlywood", weight=9]; 25356 -> 14992[label="",style="solid", color="burlywood", weight=3]; 145[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50)",fontsize=16,color="black",shape="box"];145 -> 177[label="",style="solid", color="black", weight=3]; 14199 -> 3313[label="",style="dashed", color="red", weight=0]; 14199[label="FiniteMap.sizeFM (FiniteMap.Branch ywz70 ywz71 ywz72 ywz73 ywz74)",fontsize=16,color="magenta"];14199 -> 14204[label="",style="dashed", color="magenta", weight=3]; 12161[label="primMulInt FiniteMap.sIZE_RATIO ywz1037",fontsize=16,color="black",shape="box"];12161 -> 12607[label="",style="solid", color="black", weight=3]; 14200[label="FiniteMap.Branch ywz60 ywz61 ywz62 ywz63 ywz64",fontsize=16,color="green",shape="box"];3313[label="FiniteMap.sizeFM ywz63",fontsize=16,color="burlywood",shape="triangle"];25357[label="ywz63/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];3313 -> 25357[label="",style="solid", color="burlywood", weight=9]; 25357 -> 3719[label="",style="solid", color="burlywood", weight=3]; 25358[label="ywz63/FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634",fontsize=10,color="white",style="solid",shape="box"];3313 -> 25358[label="",style="solid", color="burlywood", weight=9]; 25358 -> 3720[label="",style="solid", color="burlywood", weight=3]; 12163[label="primCmpInt ywz821 ywz811 == LT",fontsize=16,color="burlywood",shape="triangle"];25359[label="ywz821/Pos ywz8210",fontsize=10,color="white",style="solid",shape="box"];12163 -> 25359[label="",style="solid", color="burlywood", weight=9]; 25359 -> 12608[label="",style="solid", color="burlywood", weight=3]; 25360[label="ywz821/Neg ywz8210",fontsize=10,color="white",style="solid",shape="box"];12163 -> 25360[label="",style="solid", color="burlywood", weight=9]; 25360 -> 12609[label="",style="solid", color="burlywood", weight=3]; 14202 -> 10999[label="",style="dashed", color="red", weight=0]; 14202[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 < FiniteMap.mkVBalBranch3Size_l ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634",fontsize=16,color="magenta"];14202 -> 14205[label="",style="dashed", color="magenta", weight=3]; 14202 -> 14206[label="",style="dashed", color="magenta", weight=3]; 14201[label="FiniteMap.mkVBalBranch3MkVBalBranch1 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 ywz50 ywz9 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 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67[label="FiniteMap.splitLT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpInt (Pos (Succ ywz5000)) (Neg ywz400) == LT)",fontsize=16,color="black",shape="box"];67 -> 88[label="",style="solid", color="black", weight=3]; 68[label="FiniteMap.splitLT2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos ywz400) == LT)",fontsize=16,color="burlywood",shape="box"];25363[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];68 -> 25363[label="",style="solid", color="burlywood", weight=9]; 25363 -> 89[label="",style="solid", color="burlywood", weight=3]; 25364[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];68 -> 25364[label="",style="solid", color="burlywood", weight=9]; 25364 -> 90[label="",style="solid", color="burlywood", weight=3]; 69[label="FiniteMap.splitLT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg ywz400) == 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25370[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];73 -> 25370[label="",style="solid", color="burlywood", weight=9]; 25370 -> 98[label="",style="solid", color="burlywood", weight=3]; 74[label="FiniteMap.splitGT2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpInt (Pos (Succ ywz5000)) (Pos ywz400) == GT)",fontsize=16,color="black",shape="box"];74 -> 99[label="",style="solid", color="black", weight=3]; 75[label="FiniteMap.splitGT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpInt (Pos (Succ ywz5000)) (Neg ywz400) == GT)",fontsize=16,color="black",shape="box"];75 -> 100[label="",style="solid", color="black", weight=3]; 76[label="FiniteMap.splitGT2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos ywz400) == GT)",fontsize=16,color="burlywood",shape="box"];25371[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];76 -> 25371[label="",style="solid", color="burlywood", weight=9]; 25371 -> 101[label="",style="solid", color="burlywood", weight=3]; 25372[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];76 -> 25372[label="",style="solid", color="burlywood", weight=9]; 25372 -> 102[label="",style="solid", color="burlywood", weight=3]; 77[label="FiniteMap.splitGT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg ywz400) == GT)",fontsize=16,color="burlywood",shape="box"];25373[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];77 -> 25373[label="",style="solid", color="burlywood", weight=9]; 25373 -> 103[label="",style="solid", color="burlywood", weight=3]; 25374[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];77 -> 25374[label="",style="solid", color="burlywood", weight=9]; 25374 -> 104[label="",style="solid", color="burlywood", weight=3]; 78[label="FiniteMap.splitGT2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpInt (Neg (Succ 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25382[label="ywz8210/Zero",fontsize=10,color="white",style="solid",shape="box"];12608 -> 25382[label="",style="solid", color="burlywood", weight=9]; 25382 -> 12630[label="",style="solid", color="burlywood", weight=3]; 12609[label="primCmpInt (Neg ywz8210) ywz811 == LT",fontsize=16,color="burlywood",shape="box"];25383[label="ywz8210/Succ ywz82100",fontsize=10,color="white",style="solid",shape="box"];12609 -> 25383[label="",style="solid", color="burlywood", weight=9]; 25383 -> 12631[label="",style="solid", color="burlywood", weight=3]; 25384[label="ywz8210/Zero",fontsize=10,color="white",style="solid",shape="box"];12609 -> 25384[label="",style="solid", color="burlywood", weight=9]; 25384 -> 12632[label="",style="solid", color="burlywood", weight=3]; 14205 -> 12141[label="",style="dashed", color="red", weight=0]; 14205[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_r ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634",fontsize=16,color="magenta"];14205 -> 14290[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14138[label="",style="dashed", color="red", weight=0]; 14206[label="FiniteMap.mkVBalBranch3Size_l ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634",fontsize=16,color="magenta"];14206 -> 14291[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14292[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14293[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14294[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14295[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14296[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14297[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14298[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14299[label="",style="dashed", color="magenta", weight=3]; 14206 -> 14300[label="",style="dashed", color="magenta", weight=3]; 14207[label="FiniteMap.mkVBalBranch3MkVBalBranch1 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color="burlywood", weight=9]; 25385 -> 117[label="",style="solid", color="burlywood", weight=3]; 25386[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];87 -> 25386[label="",style="solid", color="burlywood", weight=9]; 25386 -> 118[label="",style="solid", color="burlywood", weight=3]; 88[label="FiniteMap.splitLT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (GT == LT)",fontsize=16,color="black",shape="box"];88 -> 119[label="",style="solid", color="black", weight=3]; 89[label="FiniteMap.splitLT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ ywz4000)) == LT)",fontsize=16,color="black",shape="box"];89 -> 120[label="",style="solid", color="black", weight=3]; 90[label="FiniteMap.splitLT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];90 -> 121[label="",style="solid", color="black", weight=3]; 91[label="FiniteMap.splitLT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ ywz4000)) == LT)",fontsize=16,color="black",shape="box"];91 -> 122[label="",style="solid", color="black", weight=3]; 92[label="FiniteMap.splitLT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];92 -> 123[label="",style="solid", color="black", weight=3]; 93[label="FiniteMap.splitLT2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (LT == LT)",fontsize=16,color="black",shape="box"];93 -> 124[label="",style="solid", color="black", weight=3]; 94[label="FiniteMap.splitLT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat ywz400 (Succ ywz5000) == LT)",fontsize=16,color="burlywood",shape="box"];25387[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];94 -> 25387[label="",style="solid", color="burlywood", weight=9]; 25387 -> 125[label="",style="solid", color="burlywood", weight=3]; 25388[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];94 -> 25388[label="",style="solid", color="burlywood", weight=9]; 25388 -> 126[label="",style="solid", color="burlywood", weight=3]; 95[label="FiniteMap.splitLT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ ywz4000)) == LT)",fontsize=16,color="black",shape="box"];95 -> 127[label="",style="solid", color="black", weight=3]; 96[label="FiniteMap.splitLT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];96 -> 128[label="",style="solid", color="black", weight=3]; 97[label="FiniteMap.splitLT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ ywz4000)) == LT)",fontsize=16,color="black",shape="box"];97 -> 129[label="",style="solid", color="black", weight=3]; 98[label="FiniteMap.splitLT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];98 -> 130[label="",style="solid", color="black", weight=3]; 99[label="FiniteMap.splitGT2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat (Succ ywz5000) ywz400 == GT)",fontsize=16,color="burlywood",shape="box"];25389[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];99 -> 25389[label="",style="solid", color="burlywood", weight=9]; 25389 -> 131[label="",style="solid", color="burlywood", weight=3]; 25390[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];99 -> 25390[label="",style="solid", color="burlywood", weight=9]; 25390 -> 132[label="",style="solid", color="burlywood", weight=3]; 100[label="FiniteMap.splitGT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (GT == GT)",fontsize=16,color="black",shape="box"];100 -> 133[label="",style="solid", color="black", weight=3]; 101[label="FiniteMap.splitGT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ ywz4000)) == GT)",fontsize=16,color="black",shape="box"];101 -> 134[label="",style="solid", color="black", weight=3]; 102[label="FiniteMap.splitGT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];102 -> 135[label="",style="solid", color="black", weight=3]; 103[label="FiniteMap.splitGT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ ywz4000)) == GT)",fontsize=16,color="black",shape="box"];103 -> 136[label="",style="solid", color="black", weight=3]; 104[label="FiniteMap.splitGT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];104 -> 137[label="",style="solid", color="black", weight=3]; 105[label="FiniteMap.splitGT2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (LT == GT)",fontsize=16,color="black",shape="box"];105 -> 138[label="",style="solid", color="black", weight=3]; 106[label="FiniteMap.splitGT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat ywz400 (Succ ywz5000) == GT)",fontsize=16,color="burlywood",shape="box"];25391[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];106 -> 25391[label="",style="solid", color="burlywood", weight=9]; 25391 -> 139[label="",style="solid", color="burlywood", weight=3]; 25392[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];106 -> 25392[label="",style="solid", color="burlywood", weight=9]; 25392 -> 140[label="",style="solid", color="burlywood", weight=3]; 107[label="FiniteMap.splitGT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ ywz4000)) == GT)",fontsize=16,color="black",shape="box"];107 -> 141[label="",style="solid", color="black", weight=3]; 108[label="FiniteMap.splitGT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];108 -> 142[label="",style="solid", color="black", weight=3]; 109[label="FiniteMap.splitGT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ ywz4000)) == GT)",fontsize=16,color="black",shape="box"];109 -> 143[label="",style="solid", color="black", weight=3]; 110[label="FiniteMap.splitGT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];110 -> 144[label="",style="solid", color="black", weight=3]; 112[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];15019[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 ywz50 ywz9 (ywz50 > ywz740)",fontsize=16,color="black",shape="box"];15019 -> 15074[label="",style="solid", color="black", weight=3]; 15020[label="FiniteMap.mkBalBranch ywz740 ywz741 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz744",fontsize=16,color="black",shape="box"];15020 -> 15075[label="",style="solid", color="black", weight=3]; 218[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 ywz40 ywz41 ywz42 ywz43 ywz44 ywz50 (compare ywz50 ywz40 == LT))",fontsize=16,color="black",shape="box"];218 -> 273[label="",style="solid", color="black", weight=3]; 12627[label="primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Pos ywz10370)",fontsize=16,color="black",shape="box"];12627 -> 12765[label="",style="solid", color="black", weight=3]; 12628[label="primMulInt (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) (Neg ywz10370)",fontsize=16,color="black",shape="box"];12628 -> 12766[label="",style="solid", color="black", weight=3]; 4126[label="Pos Zero",fontsize=16,color="green",shape="box"];4127[label="ywz632",fontsize=16,color="green",shape="box"];12629[label="primCmpInt (Pos (Succ ywz82100)) ywz811 == LT",fontsize=16,color="burlywood",shape="box"];25393[label="ywz811/Pos ywz8110",fontsize=10,color="white",style="solid",shape="box"];12629 -> 25393[label="",style="solid", color="burlywood", weight=9]; 25393 -> 12666[label="",style="solid", color="burlywood", weight=3]; 25394[label="ywz811/Neg ywz8110",fontsize=10,color="white",style="solid",shape="box"];12629 -> 25394[label="",style="solid", color="burlywood", weight=9]; 25394 -> 12667[label="",style="solid", color="burlywood", weight=3]; 12630[label="primCmpInt (Pos Zero) ywz811 == LT",fontsize=16,color="burlywood",shape="box"];25395[label="ywz811/Pos ywz8110",fontsize=10,color="white",style="solid",shape="box"];12630 -> 25395[label="",style="solid", color="burlywood", weight=9]; 25395 -> 12668[label="",style="solid", color="burlywood", weight=3]; 25396[label="ywz811/Neg ywz8110",fontsize=10,color="white",style="solid",shape="box"];12630 -> 25396[label="",style="solid", color="burlywood", weight=9]; 25396 -> 12669[label="",style="solid", color="burlywood", weight=3]; 12631[label="primCmpInt (Neg (Succ ywz82100)) ywz811 == LT",fontsize=16,color="burlywood",shape="box"];25397[label="ywz811/Pos ywz8110",fontsize=10,color="white",style="solid",shape="box"];12631 -> 25397[label="",style="solid", color="burlywood", weight=9]; 25397 -> 12670[label="",style="solid", color="burlywood", weight=3]; 25398[label="ywz811/Neg ywz8110",fontsize=10,color="white",style="solid",shape="box"];12631 -> 25398[label="",style="solid", color="burlywood", weight=9]; 25398 -> 12671[label="",style="solid", color="burlywood", weight=3]; 12632[label="primCmpInt (Neg Zero) ywz811 == LT",fontsize=16,color="burlywood",shape="box"];25399[label="ywz811/Pos ywz8110",fontsize=10,color="white",style="solid",shape="box"];12632 -> 25399[label="",style="solid", color="burlywood", weight=9]; 25399 -> 12672[label="",style="solid", color="burlywood", weight=3]; 25400[label="ywz811/Neg ywz8110",fontsize=10,color="white",style="solid",shape="box"];12632 -> 25400[label="",style="solid", color="burlywood", weight=9]; 25400 -> 12673[label="",style="solid", color="burlywood", weight=3]; 14290 -> 14089[label="",style="dashed", color="red", weight=0]; 14290[label="FiniteMap.mkVBalBranch3Size_r ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634",fontsize=16,color="magenta"];14290 -> 14352[label="",style="dashed", color="magenta", weight=3]; 14290 -> 14353[label="",style="dashed", color="magenta", weight=3]; 14290 -> 14354[label="",style="dashed", color="magenta", weight=3]; 14290 -> 14355[label="",style="dashed", color="magenta", weight=3]; 14290 -> 14356[label="",style="dashed", color="magenta", weight=3]; 14290 -> 14357[label="",style="dashed", color="magenta", weight=3]; 14290 -> 14358[label="",style="dashed", color="magenta", weight=3]; 14290 -> 14359[label="",style="dashed", color="magenta", weight=3]; 14290 -> 14360[label="",style="dashed", color="magenta", weight=3]; 14290 -> 14361[label="",style="dashed", color="magenta", weight=3]; 14291[label="ywz743",fontsize=16,color="green",shape="box"];14292[label="ywz630",fontsize=16,color="green",shape="box"];14293[label="ywz632",fontsize=16,color="green",shape="box"];14294[label="ywz631",fontsize=16,color="green",shape="box"];14295[label="ywz634",fontsize=16,color="green",shape="box"];14296[label="ywz633",fontsize=16,color="green",shape="box"];14297[label="ywz744",fontsize=16,color="green",shape="box"];14298[label="ywz740",fontsize=16,color="green",shape="box"];14299[label="ywz741",fontsize=16,color="green",shape="box"];14300[label="ywz742",fontsize=16,color="green",shape="box"];14301[label="FiniteMap.mkVBalBranch3MkVBalBranch0 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 ywz50 ywz9 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 otherwise",fontsize=16,color="black",shape="box"];14301 -> 14362[label="",style="solid", color="black", weight=3]; 14302[label="FiniteMap.mkBalBranch ywz740 ywz741 ywz743 (FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634))",fontsize=16,color="black",shape="box"];14302 -> 14363[label="",style="solid", color="black", weight=3]; 14346[label="FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633",fontsize=16,color="burlywood",shape="triangle"];25401[label="ywz633/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];14346 -> 25401[label="",style="solid", color="burlywood", weight=9]; 25401 -> 14371[label="",style="solid", color="burlywood", weight=3]; 25402[label="ywz633/FiniteMap.Branch ywz6330 ywz6331 ywz6332 ywz6333 ywz6334",fontsize=10,color="white",style="solid",shape="box"];14346 -> 25402[label="",style="solid", color="burlywood", weight=9]; 25402 -> 14372[label="",style="solid", color="burlywood", weight=3]; 14347[label="ywz634",fontsize=16,color="green",shape="box"];14348[label="ywz634",fontsize=16,color="green",shape="box"];14349[label="ywz630",fontsize=16,color="green",shape="box"];14350[label="ywz631",fontsize=16,color="green",shape="box"];14351 -> 10999[label="",style="dashed", color="red", weight=0]; 14351[label="FiniteMap.mkBalBranch6Size_l ywz634 (FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633) ywz630 ywz631 + FiniteMap.mkBalBranch6Size_r ywz634 (FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633) ywz630 ywz631 < Pos (Succ (Succ Zero))",fontsize=16,color="magenta"];14351 -> 14373[label="",style="dashed", color="magenta", weight=3]; 14351 -> 14374[label="",style="dashed", color="magenta", weight=3]; 13158[label="FiniteMap.mkBalBranch6MkBalBranch5 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 ywz1143",fontsize=16,color="burlywood",shape="triangle"];25403[label="ywz1143/False",fontsize=10,color="white",style="solid",shape="box"];13158 -> 25403[label="",style="solid", color="burlywood", weight=9]; 25403 -> 13330[label="",style="solid", color="burlywood", weight=3]; 25404[label="ywz1143/True",fontsize=10,color="white",style="solid",shape="box"];13158 -> 25404[label="",style="solid", color="burlywood", weight=9]; 25404 -> 13331[label="",style="solid", color="burlywood", weight=3]; 117[label="FiniteMap.splitLT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat (Succ ywz5000) (Succ ywz4000) == LT)",fontsize=16,color="black",shape="box"];117 -> 149[label="",style="solid", color="black", weight=3]; 118[label="FiniteMap.splitLT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat (Succ ywz5000) Zero == LT)",fontsize=16,color="black",shape="box"];118 -> 150[label="",style="solid", color="black", weight=3]; 119[label="FiniteMap.splitLT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) False",fontsize=16,color="black",shape="box"];119 -> 151[label="",style="solid", color="black", weight=3]; 120[label="FiniteMap.splitLT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpNat Zero (Succ ywz4000) == LT)",fontsize=16,color="black",shape="box"];120 -> 152[label="",style="solid", color="black", weight=3]; 121[label="FiniteMap.splitLT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];121 -> 153[label="",style="solid", color="black", weight=3]; 122[label="FiniteMap.splitLT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (GT == LT)",fontsize=16,color="black",shape="box"];122 -> 154[label="",style="solid", color="black", weight=3]; 123[label="FiniteMap.splitLT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];123 -> 155[label="",style="solid", color="black", weight=3]; 124[label="FiniteMap.splitLT2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) True",fontsize=16,color="black",shape="box"];124 -> 156[label="",style="solid", color="black", weight=3]; 125[label="FiniteMap.splitLT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat (Succ ywz4000) (Succ ywz5000) == LT)",fontsize=16,color="black",shape="box"];125 -> 157[label="",style="solid", color="black", weight=3]; 126[label="FiniteMap.splitLT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat Zero (Succ ywz5000) == LT)",fontsize=16,color="black",shape="box"];126 -> 158[label="",style="solid", color="black", weight=3]; 127[label="FiniteMap.splitLT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (LT == LT)",fontsize=16,color="black",shape="box"];127 -> 159[label="",style="solid", color="black", weight=3]; 128[label="FiniteMap.splitLT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];128 -> 160[label="",style="solid", color="black", weight=3]; 129[label="FiniteMap.splitLT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpNat (Succ ywz4000) Zero == LT)",fontsize=16,color="black",shape="box"];129 -> 161[label="",style="solid", color="black", weight=3]; 130[label="FiniteMap.splitLT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];130 -> 162[label="",style="solid", color="black", weight=3]; 131[label="FiniteMap.splitGT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat (Succ ywz5000) (Succ ywz4000) == GT)",fontsize=16,color="black",shape="box"];131 -> 163[label="",style="solid", color="black", weight=3]; 132[label="FiniteMap.splitGT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat (Succ ywz5000) Zero == GT)",fontsize=16,color="black",shape="box"];132 -> 164[label="",style="solid", color="black", weight=3]; 133[label="FiniteMap.splitGT2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) True",fontsize=16,color="black",shape="box"];133 -> 165[label="",style="solid", color="black", weight=3]; 134[label="FiniteMap.splitGT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpNat Zero (Succ ywz4000) == GT)",fontsize=16,color="black",shape="box"];134 -> 166[label="",style="solid", color="black", weight=3]; 135[label="FiniteMap.splitGT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];135 -> 167[label="",style="solid", color="black", weight=3]; 136[label="FiniteMap.splitGT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (GT == GT)",fontsize=16,color="black",shape="box"];136 -> 168[label="",style="solid", color="black", weight=3]; 137[label="FiniteMap.splitGT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];137 -> 169[label="",style="solid", color="black", weight=3]; 138[label="FiniteMap.splitGT2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) False",fontsize=16,color="black",shape="box"];138 -> 170[label="",style="solid", color="black", weight=3]; 139[label="FiniteMap.splitGT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat (Succ ywz4000) (Succ ywz5000) == GT)",fontsize=16,color="black",shape="box"];139 -> 171[label="",style="solid", color="black", weight=3]; 140[label="FiniteMap.splitGT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat Zero (Succ ywz5000) == GT)",fontsize=16,color="black",shape="box"];140 -> 172[label="",style="solid", color="black", weight=3]; 141[label="FiniteMap.splitGT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (LT == GT)",fontsize=16,color="black",shape="box"];141 -> 173[label="",style="solid", color="black", weight=3]; 142[label="FiniteMap.splitGT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];142 -> 174[label="",style="solid", color="black", weight=3]; 143[label="FiniteMap.splitGT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpNat (Succ ywz4000) Zero == GT)",fontsize=16,color="black",shape="box"];143 -> 175[label="",style="solid", color="black", weight=3]; 144[label="FiniteMap.splitGT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];144 -> 176[label="",style="solid", color="black", weight=3]; 15074[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 ywz50 ywz9 (compare ywz50 ywz740 == GT)",fontsize=16,color="black",shape="box"];15074 -> 15122[label="",style="solid", color="black", weight=3]; 15075[label="FiniteMap.mkBalBranch6 ywz740 ywz741 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz744",fontsize=16,color="black",shape="box"];15075 -> 15123[label="",style="solid", color="black", weight=3]; 273[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) ywz50 ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 ywz40 ywz41 ywz42 ywz43 ywz44 ywz50 (primCmpInt ywz50 ywz40 == LT))",fontsize=16,color="burlywood",shape="box"];25405[label="ywz50/Pos ywz500",fontsize=10,color="white",style="solid",shape="box"];273 -> 25405[label="",style="solid", color="burlywood", weight=9]; 25405 -> 344[label="",style="solid", color="burlywood", weight=3]; 25406[label="ywz50/Neg ywz500",fontsize=10,color="white",style="solid",shape="box"];273 -> 25406[label="",style="solid", color="burlywood", weight=9]; 25406 -> 345[label="",style="solid", color="burlywood", weight=3]; 12765[label="Pos (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) ywz10370)",fontsize=16,color="green",shape="box"];12765 -> 12842[label="",style="dashed", color="green", weight=3]; 12766[label="Neg (primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) ywz10370)",fontsize=16,color="green",shape="box"];12766 -> 12843[label="",style="dashed", color="green", weight=3]; 12666[label="primCmpInt (Pos (Succ ywz82100)) (Pos ywz8110) == LT",fontsize=16,color="black",shape="box"];12666 -> 12696[label="",style="solid", color="black", weight=3]; 12667[label="primCmpInt (Pos (Succ ywz82100)) (Neg ywz8110) == LT",fontsize=16,color="black",shape="box"];12667 -> 12697[label="",style="solid", color="black", weight=3]; 12668[label="primCmpInt (Pos Zero) (Pos ywz8110) == LT",fontsize=16,color="burlywood",shape="box"];25407[label="ywz8110/Succ ywz81100",fontsize=10,color="white",style="solid",shape="box"];12668 -> 25407[label="",style="solid", color="burlywood", weight=9]; 25407 -> 12698[label="",style="solid", color="burlywood", weight=3]; 25408[label="ywz8110/Zero",fontsize=10,color="white",style="solid",shape="box"];12668 -> 25408[label="",style="solid", color="burlywood", weight=9]; 25408 -> 12699[label="",style="solid", color="burlywood", weight=3]; 12669[label="primCmpInt (Pos Zero) (Neg ywz8110) == LT",fontsize=16,color="burlywood",shape="box"];25409[label="ywz8110/Succ ywz81100",fontsize=10,color="white",style="solid",shape="box"];12669 -> 25409[label="",style="solid", color="burlywood", weight=9]; 25409 -> 12700[label="",style="solid", color="burlywood", weight=3]; 25410[label="ywz8110/Zero",fontsize=10,color="white",style="solid",shape="box"];12669 -> 25410[label="",style="solid", color="burlywood", weight=9]; 25410 -> 12701[label="",style="solid", color="burlywood", weight=3]; 12670[label="primCmpInt (Neg (Succ ywz82100)) (Pos ywz8110) == LT",fontsize=16,color="black",shape="box"];12670 -> 12702[label="",style="solid", color="black", weight=3]; 12671[label="primCmpInt (Neg (Succ ywz82100)) (Neg ywz8110) == LT",fontsize=16,color="black",shape="box"];12671 -> 12703[label="",style="solid", color="black", weight=3]; 12672[label="primCmpInt (Neg Zero) (Pos ywz8110) == LT",fontsize=16,color="burlywood",shape="box"];25411[label="ywz8110/Succ ywz81100",fontsize=10,color="white",style="solid",shape="box"];12672 -> 25411[label="",style="solid", color="burlywood", weight=9]; 25411 -> 12704[label="",style="solid", color="burlywood", weight=3]; 25412[label="ywz8110/Zero",fontsize=10,color="white",style="solid",shape="box"];12672 -> 25412[label="",style="solid", color="burlywood", weight=9]; 25412 -> 12705[label="",style="solid", color="burlywood", weight=3]; 12673[label="primCmpInt (Neg Zero) (Neg ywz8110) == LT",fontsize=16,color="burlywood",shape="box"];25413[label="ywz8110/Succ ywz81100",fontsize=10,color="white",style="solid",shape="box"];12673 -> 25413[label="",style="solid", color="burlywood", weight=9]; 25413 -> 12706[label="",style="solid", color="burlywood", weight=3]; 25414[label="ywz8110/Zero",fontsize=10,color="white",style="solid",shape="box"];12673 -> 25414[label="",style="solid", color="burlywood", weight=9]; 25414 -> 12707[label="",style="solid", color="burlywood", weight=3]; 14352[label="ywz743",fontsize=16,color="green",shape="box"];14353[label="ywz630",fontsize=16,color="green",shape="box"];14354[label="ywz632",fontsize=16,color="green",shape="box"];14355[label="ywz631",fontsize=16,color="green",shape="box"];14356[label="ywz634",fontsize=16,color="green",shape="box"];14357[label="ywz633",fontsize=16,color="green",shape="box"];14358[label="ywz744",fontsize=16,color="green",shape="box"];14359[label="ywz740",fontsize=16,color="green",shape="box"];14360[label="ywz741",fontsize=16,color="green",shape="box"];14361[label="ywz742",fontsize=16,color="green",shape="box"];14362[label="FiniteMap.mkVBalBranch3MkVBalBranch0 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 ywz50 ywz9 ywz740 ywz741 ywz742 ywz743 ywz744 ywz630 ywz631 ywz632 ywz633 ywz634 True",fontsize=16,color="black",shape="box"];14362 -> 14375[label="",style="solid", color="black", weight=3]; 14363[label="FiniteMap.mkBalBranch6 ywz740 ywz741 ywz743 (FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634))",fontsize=16,color="black",shape="box"];14363 -> 14376[label="",style="solid", color="black", weight=3]; 14371[label="FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];14371 -> 14414[label="",style="solid", color="black", weight=3]; 14372[label="FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) (FiniteMap.Branch ywz6330 ywz6331 ywz6332 ywz6333 ywz6334)",fontsize=16,color="black",shape="box"];14372 -> 14415[label="",style="solid", color="black", weight=3]; 14373 -> 12612[label="",style="dashed", color="red", weight=0]; 14373[label="FiniteMap.mkBalBranch6Size_l ywz634 (FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633) ywz630 ywz631 + FiniteMap.mkBalBranch6Size_r ywz634 (FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633) ywz630 ywz631",fontsize=16,color="magenta"];14373 -> 14416[label="",style="dashed", color="magenta", weight=3]; 14373 -> 14417[label="",style="dashed", color="magenta", weight=3]; 14374[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];13330[label="FiniteMap.mkBalBranch6MkBalBranch5 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 False",fontsize=16,color="black",shape="box"];13330 -> 13391[label="",style="solid", color="black", weight=3]; 13331[label="FiniteMap.mkBalBranch6MkBalBranch5 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 True",fontsize=16,color="black",shape="box"];13331 -> 13392[label="",style="solid", color="black", weight=3]; 149 -> 5977[label="",style="dashed", color="red", weight=0]; 149[label="FiniteMap.splitLT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat ywz5000 ywz4000 == LT)",fontsize=16,color="magenta"];149 -> 5978[label="",style="dashed", color="magenta", weight=3]; 149 -> 5979[label="",style="dashed", color="magenta", weight=3]; 149 -> 5980[label="",style="dashed", color="magenta", weight=3]; 149 -> 5981[label="",style="dashed", color="magenta", weight=3]; 149 -> 5982[label="",style="dashed", color="magenta", weight=3]; 149 -> 5983[label="",style="dashed", color="magenta", weight=3]; 149 -> 5984[label="",style="dashed", color="magenta", weight=3]; 149 -> 5985[label="",style="dashed", color="magenta", weight=3]; 150[label="FiniteMap.splitLT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (GT == LT)",fontsize=16,color="black",shape="box"];150 -> 186[label="",style="solid", color="black", weight=3]; 151[label="FiniteMap.splitLT1 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (Pos (Succ ywz5000) > Neg ywz400)",fontsize=16,color="black",shape="box"];151 -> 187[label="",style="solid", color="black", weight=3]; 152[label="FiniteMap.splitLT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (LT == LT)",fontsize=16,color="black",shape="box"];152 -> 188[label="",style="solid", color="black", weight=3]; 153[label="FiniteMap.splitLT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];153 -> 189[label="",style="solid", color="black", weight=3]; 154[label="FiniteMap.splitLT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];154 -> 190[label="",style="solid", color="black", weight=3]; 155[label="FiniteMap.splitLT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];155 -> 191[label="",style="solid", color="black", weight=3]; 156[label="FiniteMap.splitLT ywz43 (Neg (Succ ywz5000))",fontsize=16,color="burlywood",shape="triangle"];25415[label="ywz43/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];156 -> 25415[label="",style="solid", color="burlywood", weight=9]; 25415 -> 192[label="",style="solid", color="burlywood", weight=3]; 25416[label="ywz43/FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434",fontsize=10,color="white",style="solid",shape="box"];156 -> 25416[label="",style="solid", color="burlywood", weight=9]; 25416 -> 193[label="",style="solid", color="burlywood", weight=3]; 157 -> 6079[label="",style="dashed", color="red", weight=0]; 157[label="FiniteMap.splitLT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat ywz4000 ywz5000 == LT)",fontsize=16,color="magenta"];157 -> 6080[label="",style="dashed", color="magenta", weight=3]; 157 -> 6081[label="",style="dashed", color="magenta", weight=3]; 157 -> 6082[label="",style="dashed", color="magenta", weight=3]; 157 -> 6083[label="",style="dashed", color="magenta", weight=3]; 157 -> 6084[label="",style="dashed", color="magenta", weight=3]; 157 -> 6085[label="",style="dashed", color="magenta", weight=3]; 157 -> 6086[label="",style="dashed", color="magenta", weight=3]; 157 -> 6087[label="",style="dashed", color="magenta", weight=3]; 158[label="FiniteMap.splitLT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (LT == LT)",fontsize=16,color="black",shape="box"];158 -> 196[label="",style="solid", color="black", weight=3]; 159[label="FiniteMap.splitLT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True",fontsize=16,color="black",shape="box"];159 -> 197[label="",style="solid", color="black", weight=3]; 160[label="FiniteMap.splitLT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];160 -> 198[label="",style="solid", color="black", weight=3]; 161[label="FiniteMap.splitLT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (GT == LT)",fontsize=16,color="black",shape="box"];161 -> 199[label="",style="solid", color="black", weight=3]; 162[label="FiniteMap.splitLT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];162 -> 200[label="",style="solid", color="black", weight=3]; 163 -> 6182[label="",style="dashed", color="red", weight=0]; 163[label="FiniteMap.splitGT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat ywz5000 ywz4000 == GT)",fontsize=16,color="magenta"];163 -> 6183[label="",style="dashed", color="magenta", weight=3]; 163 -> 6184[label="",style="dashed", color="magenta", weight=3]; 163 -> 6185[label="",style="dashed", color="magenta", weight=3]; 163 -> 6186[label="",style="dashed", color="magenta", weight=3]; 163 -> 6187[label="",style="dashed", color="magenta", weight=3]; 163 -> 6188[label="",style="dashed", color="magenta", weight=3]; 163 -> 6189[label="",style="dashed", color="magenta", weight=3]; 163 -> 6190[label="",style="dashed", color="magenta", weight=3]; 164[label="FiniteMap.splitGT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (GT == GT)",fontsize=16,color="black",shape="box"];164 -> 203[label="",style="solid", color="black", weight=3]; 165[label="FiniteMap.splitGT ywz44 (Pos (Succ ywz5000))",fontsize=16,color="burlywood",shape="triangle"];25417[label="ywz44/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];165 -> 25417[label="",style="solid", color="burlywood", weight=9]; 25417 -> 204[label="",style="solid", color="burlywood", weight=3]; 25418[label="ywz44/FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=10,color="white",style="solid",shape="box"];165 -> 25418[label="",style="solid", color="burlywood", weight=9]; 25418 -> 205[label="",style="solid", color="burlywood", weight=3]; 166[label="FiniteMap.splitGT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (LT == GT)",fontsize=16,color="black",shape="box"];166 -> 206[label="",style="solid", color="black", weight=3]; 167[label="FiniteMap.splitGT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];167 -> 207[label="",style="solid", color="black", weight=3]; 168[label="FiniteMap.splitGT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True",fontsize=16,color="black",shape="box"];168 -> 208[label="",style="solid", color="black", weight=3]; 169[label="FiniteMap.splitGT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];169 -> 209[label="",style="solid", color="black", weight=3]; 170[label="FiniteMap.splitGT1 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (Neg (Succ ywz5000) < Pos ywz400)",fontsize=16,color="black",shape="box"];170 -> 210[label="",style="solid", color="black", weight=3]; 171 -> 6283[label="",style="dashed", color="red", weight=0]; 171[label="FiniteMap.splitGT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat ywz4000 ywz5000 == GT)",fontsize=16,color="magenta"];171 -> 6284[label="",style="dashed", color="magenta", weight=3]; 171 -> 6285[label="",style="dashed", color="magenta", weight=3]; 171 -> 6286[label="",style="dashed", color="magenta", weight=3]; 171 -> 6287[label="",style="dashed", color="magenta", weight=3]; 171 -> 6288[label="",style="dashed", color="magenta", weight=3]; 171 -> 6289[label="",style="dashed", color="magenta", weight=3]; 171 -> 6290[label="",style="dashed", color="magenta", weight=3]; 171 -> 6291[label="",style="dashed", color="magenta", weight=3]; 172[label="FiniteMap.splitGT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (LT == GT)",fontsize=16,color="black",shape="box"];172 -> 213[label="",style="solid", color="black", weight=3]; 173[label="FiniteMap.splitGT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];173 -> 214[label="",style="solid", color="black", weight=3]; 174[label="FiniteMap.splitGT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];174 -> 215[label="",style="solid", color="black", weight=3]; 175[label="FiniteMap.splitGT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (GT == GT)",fontsize=16,color="black",shape="box"];175 -> 216[label="",style="solid", color="black", weight=3]; 176[label="FiniteMap.splitGT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];176 -> 217[label="",style="solid", color="black", weight=3]; 15122[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 ywz50 ywz9 (primCmpInt ywz50 ywz740 == GT)",fontsize=16,color="burlywood",shape="box"];25419[label="ywz50/Pos ywz500",fontsize=10,color="white",style="solid",shape="box"];15122 -> 25419[label="",style="solid", color="burlywood", weight=9]; 25419 -> 15165[label="",style="solid", color="burlywood", weight=3]; 25420[label="ywz50/Neg ywz500",fontsize=10,color="white",style="solid",shape="box"];15122 -> 25420[label="",style="solid", color="burlywood", weight=9]; 25420 -> 15166[label="",style="solid", color="burlywood", weight=3]; 15123 -> 13158[label="",style="dashed", color="red", weight=0]; 15123[label="FiniteMap.mkBalBranch6MkBalBranch5 ywz744 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz740 ywz741 ywz740 ywz741 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz744 (FiniteMap.mkBalBranch6Size_l ywz744 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz740 ywz741 + FiniteMap.mkBalBranch6Size_r ywz744 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz740 ywz741 < Pos (Succ (Succ Zero)))",fontsize=16,color="magenta"];15123 -> 15167[label="",style="dashed", color="magenta", weight=3]; 15123 -> 15168[label="",style="dashed", color="magenta", weight=3]; 15123 -> 15169[label="",style="dashed", color="magenta", weight=3]; 15123 -> 15170[label="",style="dashed", color="magenta", weight=3]; 15123 -> 15171[label="",style="dashed", color="magenta", weight=3]; 15123 -> 15172[label="",style="dashed", color="magenta", weight=3]; 344[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) (Pos ywz500) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 ywz40 ywz41 ywz42 ywz43 ywz44 (Pos ywz500) (primCmpInt (Pos ywz500) ywz40 == LT))",fontsize=16,color="burlywood",shape="box"];25421[label="ywz500/Succ ywz5000",fontsize=10,color="white",style="solid",shape="box"];344 -> 25421[label="",style="solid", color="burlywood", weight=9]; 25421 -> 418[label="",style="solid", color="burlywood", weight=3]; 25422[label="ywz500/Zero",fontsize=10,color="white",style="solid",shape="box"];344 -> 25422[label="",style="solid", color="burlywood", weight=9]; 25422 -> 419[label="",style="solid", color="burlywood", weight=3]; 345[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) (Neg ywz500) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 ywz40 ywz41 ywz42 ywz43 ywz44 (Neg ywz500) (primCmpInt (Neg ywz500) ywz40 == LT))",fontsize=16,color="burlywood",shape="box"];25423[label="ywz500/Succ ywz5000",fontsize=10,color="white",style="solid",shape="box"];345 -> 25423[label="",style="solid", color="burlywood", weight=9]; 25423 -> 420[label="",style="solid", color="burlywood", weight=3]; 25424[label="ywz500/Zero",fontsize=10,color="white",style="solid",shape="box"];345 -> 25424[label="",style="solid", color="burlywood", weight=9]; 25424 -> 421[label="",style="solid", color="burlywood", weight=3]; 12842[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) ywz10370",fontsize=16,color="burlywood",shape="triangle"];25425[label="ywz10370/Succ ywz103700",fontsize=10,color="white",style="solid",shape="box"];12842 -> 25425[label="",style="solid", color="burlywood", weight=9]; 25425 -> 12911[label="",style="solid", color="burlywood", weight=3]; 25426[label="ywz10370/Zero",fontsize=10,color="white",style="solid",shape="box"];12842 -> 25426[label="",style="solid", color="burlywood", weight=9]; 25426 -> 12912[label="",style="solid", color="burlywood", weight=3]; 12843 -> 12842[label="",style="dashed", color="red", weight=0]; 12843[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) ywz10370",fontsize=16,color="magenta"];12843 -> 12913[label="",style="dashed", color="magenta", weight=3]; 12696[label="primCmpNat (Succ ywz82100) ywz8110 == LT",fontsize=16,color="burlywood",shape="triangle"];25427[label="ywz8110/Succ ywz81100",fontsize=10,color="white",style="solid",shape="box"];12696 -> 25427[label="",style="solid", color="burlywood", weight=9]; 25427 -> 12814[label="",style="solid", color="burlywood", weight=3]; 25428[label="ywz8110/Zero",fontsize=10,color="white",style="solid",shape="box"];12696 -> 25428[label="",style="solid", color="burlywood", weight=9]; 25428 -> 12815[label="",style="solid", color="burlywood", weight=3]; 12697 -> 12118[label="",style="dashed", color="red", weight=0]; 12697[label="GT == LT",fontsize=16,color="magenta"];12698[label="primCmpInt (Pos Zero) (Pos (Succ ywz81100)) == LT",fontsize=16,color="black",shape="box"];12698 -> 12816[label="",style="solid", color="black", weight=3]; 12699[label="primCmpInt (Pos Zero) (Pos Zero) == LT",fontsize=16,color="black",shape="box"];12699 -> 12817[label="",style="solid", color="black", weight=3]; 12700[label="primCmpInt (Pos Zero) (Neg (Succ ywz81100)) == LT",fontsize=16,color="black",shape="box"];12700 -> 12818[label="",style="solid", color="black", weight=3]; 12701[label="primCmpInt (Pos Zero) (Neg Zero) == LT",fontsize=16,color="black",shape="box"];12701 -> 12819[label="",style="solid", color="black", weight=3]; 12702 -> 12125[label="",style="dashed", color="red", weight=0]; 12702[label="LT == LT",fontsize=16,color="magenta"];12703[label="primCmpNat ywz8110 (Succ ywz82100) == LT",fontsize=16,color="burlywood",shape="triangle"];25429[label="ywz8110/Succ ywz81100",fontsize=10,color="white",style="solid",shape="box"];12703 -> 25429[label="",style="solid", color="burlywood", weight=9]; 25429 -> 12820[label="",style="solid", color="burlywood", weight=3]; 25430[label="ywz8110/Zero",fontsize=10,color="white",style="solid",shape="box"];12703 -> 25430[label="",style="solid", color="burlywood", weight=9]; 25430 -> 12821[label="",style="solid", color="burlywood", weight=3]; 12704[label="primCmpInt (Neg Zero) (Pos (Succ ywz81100)) == LT",fontsize=16,color="black",shape="box"];12704 -> 12822[label="",style="solid", color="black", weight=3]; 12705[label="primCmpInt (Neg Zero) (Pos Zero) == LT",fontsize=16,color="black",shape="box"];12705 -> 12823[label="",style="solid", color="black", weight=3]; 12706[label="primCmpInt (Neg Zero) (Neg (Succ ywz81100)) == LT",fontsize=16,color="black",shape="box"];12706 -> 12824[label="",style="solid", color="black", weight=3]; 12707[label="primCmpInt (Neg Zero) (Neg Zero) == LT",fontsize=16,color="black",shape="box"];12707 -> 12825[label="",style="solid", color="black", weight=3]; 14375 -> 15392[label="",style="dashed", color="red", weight=0]; 14375[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) (FiniteMap.Branch ywz630 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ywz632 ywz633 ywz634)) ywz743 ywz740 ywz741 < Pos (Succ (Succ Zero)))",fontsize=16,color="magenta"];14376 -> 14432[label="",style="dashed", color="magenta", weight=3]; 14376 -> 14433[label="",style="dashed", color="magenta", weight=3]; 14376 -> 14434[label="",style="dashed", color="magenta", weight=3]; 14376 -> 14435[label="",style="dashed", color="magenta", weight=3]; 14376 -> 14436[label="",style="dashed", color="magenta", weight=3]; 14376 -> 14437[label="",style="dashed", color="magenta", weight=3]; 14414[label="FiniteMap.mkVBalBranch4 ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];14414 -> 14438[label="",style="solid", color="black", weight=3]; 14415[label="FiniteMap.mkVBalBranch3 ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) (FiniteMap.Branch ywz6330 ywz6331 ywz6332 ywz6333 ywz6334)",fontsize=16,color="black",shape="triangle"];14415 -> 14439[label="",style="solid", color="black", weight=3]; 14416 -> 13476[label="",style="dashed", color="red", weight=0]; 14416[label="FiniteMap.mkBalBranch6Size_l ywz634 (FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633) ywz630 ywz631",fontsize=16,color="magenta"];14416 -> 14440[label="",style="dashed", color="magenta", weight=3]; 14417 -> 13515[label="",style="dashed", color="red", weight=0]; 14417[label="FiniteMap.mkBalBranch6Size_r ywz634 (FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633) ywz630 ywz631",fontsize=16,color="magenta"];14417 -> 14441[label="",style="dashed", color="magenta", weight=3]; 12612[label="ywz1049 + ywz1048",fontsize=16,color="black",shape="triangle"];12612 -> 12682[label="",style="solid", color="black", weight=3]; 13391 -> 13461[label="",style="dashed", color="red", weight=0]; 13391[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (FiniteMap.mkBalBranch6Size_r ywz1007 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5978[label="ywz41",fontsize=16,color="green",shape="box"];5979[label="ywz42",fontsize=16,color="green",shape="box"];5980[label="ywz5000",fontsize=16,color="green",shape="box"];5981[label="ywz43",fontsize=16,color="green",shape="box"];5982[label="ywz4000",fontsize=16,color="green",shape="box"];5983[label="ywz4000",fontsize=16,color="green",shape="box"];5984[label="ywz44",fontsize=16,color="green",shape="box"];5985[label="ywz5000",fontsize=16,color="green",shape="box"];5977[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpNat ywz433 ywz434 == LT)",fontsize=16,color="burlywood",shape="triangle"];25431[label="ywz433/Succ ywz4330",fontsize=10,color="white",style="solid",shape="box"];5977 -> 25431[label="",style="solid", color="burlywood", weight=9]; 25431 -> 6058[label="",style="solid", color="burlywood", weight=3]; 25432[label="ywz433/Zero",fontsize=10,color="white",style="solid",shape="box"];5977 -> 25432[label="",style="solid", color="burlywood", weight=9]; 25432 -> 6059[label="",style="solid", color="burlywood", weight=3]; 186[label="FiniteMap.splitLT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) False",fontsize=16,color="black",shape="box"];186 -> 233[label="",style="solid", color="black", weight=3]; 187[label="FiniteMap.splitLT1 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (compare (Pos (Succ ywz5000)) (Neg ywz400) == GT)",fontsize=16,color="black",shape="box"];187 -> 234[label="",style="solid", color="black", weight=3]; 188[label="FiniteMap.splitLT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True",fontsize=16,color="black",shape="box"];188 -> 235[label="",style="solid", color="black", weight=3]; 189[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (Pos Zero > Pos Zero)",fontsize=16,color="black",shape="box"];189 -> 236[label="",style="solid", color="black", weight=3]; 190[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (Pos Zero > Neg (Succ ywz4000))",fontsize=16,color="black",shape="box"];190 -> 237[label="",style="solid", color="black", weight=3]; 191[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (Pos Zero > Neg Zero)",fontsize=16,color="black",shape="box"];191 -> 238[label="",style="solid", color="black", weight=3]; 192[label="FiniteMap.splitLT FiniteMap.EmptyFM (Neg (Succ ywz5000))",fontsize=16,color="black",shape="box"];192 -> 239[label="",style="solid", color="black", weight=3]; 193[label="FiniteMap.splitLT (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Neg (Succ ywz5000))",fontsize=16,color="black",shape="box"];193 -> 240[label="",style="solid", color="black", weight=3]; 6080[label="ywz4000",fontsize=16,color="green",shape="box"];6081[label="ywz41",fontsize=16,color="green",shape="box"];6082[label="ywz42",fontsize=16,color="green",shape="box"];6083[label="ywz4000",fontsize=16,color="green",shape="box"];6084[label="ywz44",fontsize=16,color="green",shape="box"];6085[label="ywz5000",fontsize=16,color="green",shape="box"];6086[label="ywz43",fontsize=16,color="green",shape="box"];6087[label="ywz5000",fontsize=16,color="green",shape="box"];6079[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpNat ywz442 ywz443 == LT)",fontsize=16,color="burlywood",shape="triangle"];25433[label="ywz442/Succ ywz4420",fontsize=10,color="white",style="solid",shape="box"];6079 -> 25433[label="",style="solid", color="burlywood", weight=9]; 25433 -> 6160[label="",style="solid", color="burlywood", weight=3]; 25434[label="ywz442/Zero",fontsize=10,color="white",style="solid",shape="box"];6079 -> 25434[label="",style="solid", color="burlywood", weight=9]; 25434 -> 6161[label="",style="solid", color="burlywood", weight=3]; 196[label="FiniteMap.splitLT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) True",fontsize=16,color="black",shape="box"];196 -> 245[label="",style="solid", color="black", weight=3]; 197[label="FiniteMap.splitLT ywz43 (Neg Zero)",fontsize=16,color="burlywood",shape="triangle"];25435[label="ywz43/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];197 -> 25435[label="",style="solid", color="burlywood", weight=9]; 25435 -> 246[label="",style="solid", color="burlywood", weight=3]; 25436[label="ywz43/FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434",fontsize=10,color="white",style="solid",shape="box"];197 -> 25436[label="",style="solid", color="burlywood", weight=9]; 25436 -> 247[label="",style="solid", color="burlywood", weight=3]; 198[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (Neg Zero > Pos Zero)",fontsize=16,color="black",shape="box"];198 -> 248[label="",style="solid", color="black", weight=3]; 199[label="FiniteMap.splitLT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];199 -> 249[label="",style="solid", color="black", weight=3]; 200[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (Neg Zero > Neg Zero)",fontsize=16,color="black",shape="box"];200 -> 250[label="",style="solid", color="black", weight=3]; 6183[label="ywz4000",fontsize=16,color="green",shape="box"];6184[label="ywz5000",fontsize=16,color="green",shape="box"];6185[label="ywz41",fontsize=16,color="green",shape="box"];6186[label="ywz43",fontsize=16,color="green",shape="box"];6187[label="ywz42",fontsize=16,color="green",shape="box"];6188[label="ywz44",fontsize=16,color="green",shape="box"];6189[label="ywz5000",fontsize=16,color="green",shape="box"];6190[label="ywz4000",fontsize=16,color="green",shape="box"];6182[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (primCmpNat ywz451 ywz452 == GT)",fontsize=16,color="burlywood",shape="triangle"];25437[label="ywz451/Succ ywz4510",fontsize=10,color="white",style="solid",shape="box"];6182 -> 25437[label="",style="solid", color="burlywood", weight=9]; 25437 -> 6263[label="",style="solid", color="burlywood", weight=3]; 25438[label="ywz451/Zero",fontsize=10,color="white",style="solid",shape="box"];6182 -> 25438[label="",style="solid", color="burlywood", weight=9]; 25438 -> 6264[label="",style="solid", color="burlywood", weight=3]; 203[label="FiniteMap.splitGT2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) True",fontsize=16,color="black",shape="box"];203 -> 255[label="",style="solid", color="black", weight=3]; 204[label="FiniteMap.splitGT FiniteMap.EmptyFM (Pos (Succ ywz5000))",fontsize=16,color="black",shape="box"];204 -> 256[label="",style="solid", color="black", weight=3]; 205[label="FiniteMap.splitGT (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos (Succ ywz5000))",fontsize=16,color="black",shape="box"];205 -> 257[label="",style="solid", color="black", weight=3]; 206[label="FiniteMap.splitGT2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];206 -> 258[label="",style="solid", color="black", weight=3]; 207[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (Pos Zero < Pos Zero)",fontsize=16,color="black",shape="box"];207 -> 259[label="",style="solid", color="black", weight=3]; 208[label="FiniteMap.splitGT ywz44 (Pos Zero)",fontsize=16,color="burlywood",shape="triangle"];25439[label="ywz44/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];208 -> 25439[label="",style="solid", color="burlywood", weight=9]; 25439 -> 260[label="",style="solid", color="burlywood", weight=3]; 25440[label="ywz44/FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=10,color="white",style="solid",shape="box"];208 -> 25440[label="",style="solid", color="burlywood", weight=9]; 25440 -> 261[label="",style="solid", color="burlywood", weight=3]; 209[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (Pos Zero < Neg Zero)",fontsize=16,color="black",shape="box"];209 -> 262[label="",style="solid", color="black", weight=3]; 210[label="FiniteMap.splitGT1 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (compare (Neg (Succ ywz5000)) (Pos ywz400) == LT)",fontsize=16,color="black",shape="box"];210 -> 263[label="",style="solid", color="black", weight=3]; 6284[label="ywz41",fontsize=16,color="green",shape="box"];6285[label="ywz42",fontsize=16,color="green",shape="box"];6286[label="ywz43",fontsize=16,color="green",shape="box"];6287[label="ywz5000",fontsize=16,color="green",shape="box"];6288[label="ywz44",fontsize=16,color="green",shape="box"];6289[label="ywz4000",fontsize=16,color="green",shape="box"];6290[label="ywz4000",fontsize=16,color="green",shape="box"];6291[label="ywz5000",fontsize=16,color="green",shape="box"];6283[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (primCmpNat ywz460 ywz461 == GT)",fontsize=16,color="burlywood",shape="triangle"];25441[label="ywz460/Succ ywz4600",fontsize=10,color="white",style="solid",shape="box"];6283 -> 25441[label="",style="solid", color="burlywood", weight=9]; 25441 -> 6364[label="",style="solid", color="burlywood", weight=3]; 25442[label="ywz460/Zero",fontsize=10,color="white",style="solid",shape="box"];6283 -> 25442[label="",style="solid", color="burlywood", weight=9]; 25442 -> 6365[label="",style="solid", color="burlywood", weight=3]; 213[label="FiniteMap.splitGT2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) False",fontsize=16,color="black",shape="box"];213 -> 268[label="",style="solid", color="black", weight=3]; 214[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (Neg Zero < Pos (Succ ywz4000))",fontsize=16,color="black",shape="box"];214 -> 269[label="",style="solid", color="black", weight=3]; 215[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (Neg Zero < Pos Zero)",fontsize=16,color="black",shape="box"];215 -> 270[label="",style="solid", color="black", weight=3]; 216[label="FiniteMap.splitGT2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True",fontsize=16,color="black",shape="box"];216 -> 271[label="",style="solid", color="black", weight=3]; 217[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (Neg Zero < Neg Zero)",fontsize=16,color="black",shape="box"];217 -> 272[label="",style="solid", color="black", weight=3]; 15165[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 (Pos ywz500) ywz9 (primCmpInt (Pos ywz500) ywz740 == GT)",fontsize=16,color="burlywood",shape="box"];25443[label="ywz500/Succ ywz5000",fontsize=10,color="white",style="solid",shape="box"];15165 -> 25443[label="",style="solid", color="burlywood", weight=9]; 25443 -> 15204[label="",style="solid", color="burlywood", weight=3]; 25444[label="ywz500/Zero",fontsize=10,color="white",style="solid",shape="box"];15165 -> 25444[label="",style="solid", color="burlywood", weight=9]; 25444 -> 15205[label="",style="solid", color="burlywood", weight=3]; 15166[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 (Neg ywz500) ywz9 (primCmpInt (Neg ywz500) ywz740 == GT)",fontsize=16,color="burlywood",shape="box"];25445[label="ywz500/Succ ywz5000",fontsize=10,color="white",style="solid",shape="box"];15166 -> 25445[label="",style="solid", color="burlywood", weight=9]; 25445 -> 15206[label="",style="solid", color="burlywood", weight=3]; 25446[label="ywz500/Zero",fontsize=10,color="white",style="solid",shape="box"];15166 -> 25446[label="",style="solid", color="burlywood", weight=9]; 25446 -> 15207[label="",style="solid", color="burlywood", weight=3]; 15167[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9",fontsize=16,color="burlywood",shape="triangle"];25447[label="ywz743/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];15167 -> 25447[label="",style="solid", color="burlywood", weight=9]; 25447 -> 15208[label="",style="solid", color="burlywood", weight=3]; 25448[label="ywz743/FiniteMap.Branch ywz7430 ywz7431 ywz7432 ywz7433 ywz7434",fontsize=10,color="white",style="solid",shape="box"];15167 -> 25448[label="",style="solid", color="burlywood", weight=9]; 25448 -> 15209[label="",style="solid", color="burlywood", weight=3]; 15168[label="ywz744",fontsize=16,color="green",shape="box"];15169[label="ywz744",fontsize=16,color="green",shape="box"];15170[label="ywz740",fontsize=16,color="green",shape="box"];15171[label="ywz741",fontsize=16,color="green",shape="box"];15172 -> 10999[label="",style="dashed", color="red", weight=0]; 15172[label="FiniteMap.mkBalBranch6Size_l ywz744 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz740 ywz741 + FiniteMap.mkBalBranch6Size_r ywz744 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz740 ywz741 < Pos (Succ (Succ Zero))",fontsize=16,color="magenta"];15172 -> 15210[label="",style="dashed", color="magenta", weight=3]; 15172 -> 15211[label="",style="dashed", color="magenta", weight=3]; 418[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) (Pos (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 ywz40 ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpInt (Pos (Succ ywz5000)) ywz40 == LT))",fontsize=16,color="burlywood",shape="box"];25449[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];418 -> 25449[label="",style="solid", color="burlywood", weight=9]; 25449 -> 498[label="",style="solid", color="burlywood", weight=3]; 25450[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];418 -> 25450[label="",style="solid", color="burlywood", weight=9]; 25450 -> 499[label="",style="solid", color="burlywood", weight=3]; 419[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 ywz40 ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) ywz40 == LT))",fontsize=16,color="burlywood",shape="box"];25451[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];419 -> 25451[label="",style="solid", color="burlywood", weight=9]; 25451 -> 500[label="",style="solid", color="burlywood", weight=3]; 25452[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];419 -> 25452[label="",style="solid", color="burlywood", weight=9]; 25452 -> 501[label="",style="solid", color="burlywood", weight=3]; 420[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) (Neg (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 ywz40 ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpInt (Neg (Succ ywz5000)) ywz40 == LT))",fontsize=16,color="burlywood",shape="box"];25453[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];420 -> 25453[label="",style="solid", color="burlywood", weight=9]; 25453 -> 502[label="",style="solid", color="burlywood", weight=3]; 25454[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];420 -> 25454[label="",style="solid", color="burlywood", weight=9]; 25454 -> 503[label="",style="solid", color="burlywood", weight=3]; 421[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch ywz40 ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 ywz40 ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) ywz40 == LT))",fontsize=16,color="burlywood",shape="box"];25455[label="ywz40/Pos ywz400",fontsize=10,color="white",style="solid",shape="box"];421 -> 25455[label="",style="solid", color="burlywood", weight=9]; 25455 -> 504[label="",style="solid", color="burlywood", weight=3]; 25456[label="ywz40/Neg ywz400",fontsize=10,color="white",style="solid",shape="box"];421 -> 25456[label="",style="solid", color="burlywood", weight=9]; 25456 -> 505[label="",style="solid", color="burlywood", weight=3]; 12911[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) (Succ ywz103700)",fontsize=16,color="black",shape="box"];12911 -> 12985[label="",style="solid", color="black", weight=3]; 12912[label="primMulNat (Succ (Succ (Succ (Succ (Succ Zero))))) Zero",fontsize=16,color="black",shape="box"];12912 -> 12986[label="",style="solid", color="black", weight=3]; 12913[label="ywz10370",fontsize=16,color="green",shape="box"];12814[label="primCmpNat (Succ ywz82100) (Succ ywz81100) == LT",fontsize=16,color="black",shape="box"];12814 -> 12889[label="",style="solid", color="black", weight=3]; 12815[label="primCmpNat (Succ ywz82100) Zero == LT",fontsize=16,color="black",shape="box"];12815 -> 12890[label="",style="solid", color="black", weight=3]; 12118[label="GT == LT",fontsize=16,color="black",shape="triangle"];12118 -> 12140[label="",style="solid", color="black", weight=3]; 12816 -> 12703[label="",style="dashed", color="red", weight=0]; 12816[label="primCmpNat Zero (Succ ywz81100) == LT",fontsize=16,color="magenta"];12816 -> 12891[label="",style="dashed", color="magenta", weight=3]; 12816 -> 12892[label="",style="dashed", color="magenta", weight=3]; 12817 -> 12117[label="",style="dashed", color="red", weight=0]; 12817[label="EQ == LT",fontsize=16,color="magenta"];12818 -> 12118[label="",style="dashed", color="red", weight=0]; 12818[label="GT == LT",fontsize=16,color="magenta"];12819 -> 12117[label="",style="dashed", color="red", weight=0]; 12819[label="EQ == LT",fontsize=16,color="magenta"];12125[label="LT == LT",fontsize=16,color="black",shape="triangle"];12125 -> 12149[label="",style="solid", color="black", weight=3]; 12820[label="primCmpNat (Succ ywz81100) (Succ ywz82100) == LT",fontsize=16,color="black",shape="box"];12820 -> 12893[label="",style="solid", color="black", weight=3]; 12821[label="primCmpNat Zero (Succ ywz82100) == LT",fontsize=16,color="black",shape="box"];12821 -> 12894[label="",style="solid", color="black", weight=3]; 12822 -> 12125[label="",style="dashed", color="red", weight=0]; 12822[label="LT == LT",fontsize=16,color="magenta"];12823 -> 12117[label="",style="dashed", color="red", weight=0]; 12823[label="EQ == LT",fontsize=16,color="magenta"];12824 -> 12696[label="",style="dashed", color="red", weight=0]; 12824[label="primCmpNat (Succ ywz81100) Zero == LT",fontsize=16,color="magenta"];12824 -> 12895[label="",style="dashed", color="magenta", weight=3]; 12824 -> 12896[label="",style="dashed", color="magenta", weight=3]; 12825 -> 12117[label="",style="dashed", color="red", weight=0]; 12825[label="EQ == LT",fontsize=16,color="magenta"];15393[label="ywz50",fontsize=16,color="green",shape="box"];15394[label="ywz9",fontsize=16,color="green",shape="box"];15395[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="green",shape="box"];15396[label="FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744",fontsize=16,color="green",shape="box"];15397[label="FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634",fontsize=16,color="green",shape="box"];15392[label="FiniteMap.mkBranch (Pos (Succ ywz1234)) ywz1235 ywz1236 ywz1237 ywz1238",fontsize=16,color="black",shape="triangle"];15392 -> 15438[label="",style="solid", color="black", weight=3]; 14432[label="ywz743",fontsize=16,color="green",shape="box"];14433[label="FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)",fontsize=16,color="burlywood",shape="triangle"];25457[label="ywz744/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];14433 -> 25457[label="",style="solid", color="burlywood", weight=9]; 25457 -> 14470[label="",style="solid", color="burlywood", weight=3]; 25458[label="ywz744/FiniteMap.Branch ywz7440 ywz7441 ywz7442 ywz7443 ywz7444",fontsize=10,color="white",style="solid",shape="box"];14433 -> 25458[label="",style="solid", color="burlywood", weight=9]; 25458 -> 14471[label="",style="solid", color="burlywood", weight=3]; 14434 -> 14433[label="",style="dashed", color="red", weight=0]; 14434[label="FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)",fontsize=16,color="magenta"];14435[label="ywz740",fontsize=16,color="green",shape="box"];14436[label="ywz741",fontsize=16,color="green",shape="box"];14437 -> 10999[label="",style="dashed", color="red", weight=0]; 14437[label="FiniteMap.mkBalBranch6Size_l (FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)) ywz743 ywz740 ywz741 + FiniteMap.mkBalBranch6Size_r (FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)) ywz743 ywz740 ywz741 < Pos (Succ (Succ Zero))",fontsize=16,color="magenta"];14437 -> 14472[label="",style="dashed", color="magenta", weight=3]; 14437 -> 14473[label="",style="dashed", color="magenta", weight=3]; 14438[label="FiniteMap.addToFM (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz50 ywz9",fontsize=16,color="black",shape="triangle"];14438 -> 14474[label="",style="solid", color="black", weight=3]; 14439 -> 13641[label="",style="dashed", color="red", weight=0]; 14439[label="FiniteMap.mkVBalBranch3MkVBalBranch2 ywz740 ywz741 ywz742 ywz743 ywz744 ywz6330 ywz6331 ywz6332 ywz6333 ywz6334 ywz50 ywz9 ywz740 ywz741 ywz742 ywz743 ywz744 ywz6330 ywz6331 ywz6332 ywz6333 ywz6334 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz740 ywz741 ywz742 ywz743 ywz744 ywz6330 ywz6331 ywz6332 ywz6333 ywz6334 < FiniteMap.mkVBalBranch3Size_r ywz740 ywz741 ywz742 ywz743 ywz744 ywz6330 ywz6331 ywz6332 ywz6333 ywz6334)",fontsize=16,color="magenta"];14439 -> 14475[label="",style="dashed", color="magenta", weight=3]; 14439 -> 14476[label="",style="dashed", color="magenta", weight=3]; 14439 -> 14477[label="",style="dashed", color="magenta", weight=3]; 14439 -> 14478[label="",style="dashed", color="magenta", weight=3]; 14439 -> 14479[label="",style="dashed", color="magenta", weight=3]; 14439 -> 14480[label="",style="dashed", color="magenta", weight=3]; 14440 -> 14346[label="",style="dashed", color="red", weight=0]; 14440[label="FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633",fontsize=16,color="magenta"];13476[label="FiniteMap.mkBalBranch6Size_l ywz634 ywz1155 ywz630 ywz631",fontsize=16,color="black",shape="triangle"];13476 -> 13511[label="",style="solid", color="black", weight=3]; 14441 -> 14346[label="",style="dashed", color="red", weight=0]; 14441[label="FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz633",fontsize=16,color="magenta"];13515[label="FiniteMap.mkBalBranch6Size_r ywz634 ywz1156 ywz630 ywz631",fontsize=16,color="black",shape="triangle"];13515 -> 13546[label="",style="solid", color="black", weight=3]; 12682[label="primPlusInt ywz1049 ywz1048",fontsize=16,color="burlywood",shape="box"];25459[label="ywz1049/Pos ywz10490",fontsize=10,color="white",style="solid",shape="box"];12682 -> 25459[label="",style="solid", color="burlywood", weight=9]; 25459 -> 12774[label="",style="solid", color="burlywood", weight=3]; 25460[label="ywz1049/Neg ywz10490",fontsize=10,color="white",style="solid",shape="box"];12682 -> 25460[label="",style="solid", color="burlywood", weight=9]; 25460 -> 12775[label="",style="solid", color="burlywood", weight=3]; 13462 -> 12141[label="",style="dashed", color="red", weight=0]; 13462[label="FiniteMap.sIZE_RATIO * FiniteMap.mkBalBranch6Size_l ywz1007 ywz73 ywz70 ywz71",fontsize=16,color="magenta"];13462 -> 13472[label="",style="dashed", color="magenta", weight=3]; 13461[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (FiniteMap.mkBalBranch6Size_r ywz1007 ywz73 ywz70 ywz71 > ywz1154)",fontsize=16,color="black",shape="triangle"];13461 -> 13473[label="",style="solid", color="black", weight=3]; 15398[label="ywz70",fontsize=16,color="green",shape="box"];15399[label="ywz71",fontsize=16,color="green",shape="box"];15400[label="Zero",fontsize=16,color="green",shape="box"];15401[label="ywz73",fontsize=16,color="green",shape="box"];15402[label="ywz1006",fontsize=16,color="green",shape="box"];6058[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpNat (Succ ywz4330) ywz434 == LT)",fontsize=16,color="burlywood",shape="box"];25461[label="ywz434/Succ ywz4340",fontsize=10,color="white",style="solid",shape="box"];6058 -> 25461[label="",style="solid", color="burlywood", weight=9]; 25461 -> 6162[label="",style="solid", color="burlywood", weight=3]; 25462[label="ywz434/Zero",fontsize=10,color="white",style="solid",shape="box"];6058 -> 25462[label="",style="solid", color="burlywood", weight=9]; 25462 -> 6163[label="",style="solid", color="burlywood", weight=3]; 6059[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpNat Zero ywz434 == LT)",fontsize=16,color="burlywood",shape="box"];25463[label="ywz434/Succ ywz4340",fontsize=10,color="white",style="solid",shape="box"];6059 -> 25463[label="",style="solid", color="burlywood", weight=9]; 25463 -> 6164[label="",style="solid", color="burlywood", weight=3]; 25464[label="ywz434/Zero",fontsize=10,color="white",style="solid",shape="box"];6059 -> 25464[label="",style="solid", color="burlywood", weight=9]; 25464 -> 6165[label="",style="solid", color="burlywood", weight=3]; 233[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (Pos (Succ ywz5000) > Pos Zero)",fontsize=16,color="black",shape="box"];233 -> 294[label="",style="solid", color="black", weight=3]; 234[label="FiniteMap.splitLT1 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpInt (Pos (Succ ywz5000)) (Neg ywz400) == GT)",fontsize=16,color="black",shape="box"];234 -> 295[label="",style="solid", color="black", weight=3]; 235[label="FiniteMap.splitLT ywz43 (Pos Zero)",fontsize=16,color="burlywood",shape="triangle"];25465[label="ywz43/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];235 -> 25465[label="",style="solid", color="burlywood", weight=9]; 25465 -> 296[label="",style="solid", color="burlywood", weight=3]; 25466[label="ywz43/FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434",fontsize=10,color="white",style="solid",shape="box"];235 -> 25466[label="",style="solid", color="burlywood", weight=9]; 25466 -> 297[label="",style="solid", color="burlywood", weight=3]; 236[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (compare (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];236 -> 298[label="",style="solid", color="black", weight=3]; 237[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (compare (Pos Zero) (Neg (Succ ywz4000)) == GT)",fontsize=16,color="black",shape="box"];237 -> 299[label="",style="solid", color="black", weight=3]; 238[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (compare (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];238 -> 300[label="",style="solid", color="black", weight=3]; 239[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Neg (Succ ywz5000))",fontsize=16,color="black",shape="box"];239 -> 301[label="",style="solid", color="black", weight=3]; 240 -> 27[label="",style="dashed", color="red", weight=0]; 240[label="FiniteMap.splitLT3 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Neg (Succ ywz5000))",fontsize=16,color="magenta"];240 -> 302[label="",style="dashed", color="magenta", weight=3]; 240 -> 303[label="",style="dashed", color="magenta", weight=3]; 240 -> 304[label="",style="dashed", color="magenta", weight=3]; 240 -> 305[label="",style="dashed", color="magenta", weight=3]; 240 -> 306[label="",style="dashed", color="magenta", weight=3]; 240 -> 307[label="",style="dashed", color="magenta", weight=3]; 6160[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpNat (Succ ywz4420) ywz443 == LT)",fontsize=16,color="burlywood",shape="box"];25467[label="ywz443/Succ ywz4430",fontsize=10,color="white",style="solid",shape="box"];6160 -> 25467[label="",style="solid", color="burlywood", weight=9]; 25467 -> 6265[label="",style="solid", color="burlywood", weight=3]; 25468[label="ywz443/Zero",fontsize=10,color="white",style="solid",shape="box"];6160 -> 25468[label="",style="solid", color="burlywood", weight=9]; 25468 -> 6266[label="",style="solid", color="burlywood", weight=3]; 6161[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpNat Zero ywz443 == LT)",fontsize=16,color="burlywood",shape="box"];25469[label="ywz443/Succ ywz4430",fontsize=10,color="white",style="solid",shape="box"];6161 -> 25469[label="",style="solid", color="burlywood", weight=9]; 25469 -> 6267[label="",style="solid", color="burlywood", weight=3]; 25470[label="ywz443/Zero",fontsize=10,color="white",style="solid",shape="box"];6161 -> 25470[label="",style="solid", color="burlywood", weight=9]; 25470 -> 6268[label="",style="solid", color="burlywood", weight=3]; 245 -> 156[label="",style="dashed", color="red", weight=0]; 245[label="FiniteMap.splitLT ywz43 (Neg (Succ ywz5000))",fontsize=16,color="magenta"];246[label="FiniteMap.splitLT FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="black",shape="box"];246 -> 312[label="",style="solid", color="black", weight=3]; 247[label="FiniteMap.splitLT (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Neg Zero)",fontsize=16,color="black",shape="box"];247 -> 313[label="",style="solid", color="black", weight=3]; 248[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (compare (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];248 -> 314[label="",style="solid", color="black", weight=3]; 249[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (Neg Zero > Neg (Succ ywz4000))",fontsize=16,color="black",shape="box"];249 -> 315[label="",style="solid", color="black", weight=3]; 250[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (compare (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];250 -> 316[label="",style="solid", color="black", weight=3]; 6263[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (primCmpNat (Succ ywz4510) ywz452 == GT)",fontsize=16,color="burlywood",shape="box"];25471[label="ywz452/Succ ywz4520",fontsize=10,color="white",style="solid",shape="box"];6263 -> 25471[label="",style="solid", color="burlywood", weight=9]; 25471 -> 6366[label="",style="solid", color="burlywood", weight=3]; 25472[label="ywz452/Zero",fontsize=10,color="white",style="solid",shape="box"];6263 -> 25472[label="",style="solid", color="burlywood", weight=9]; 25472 -> 6367[label="",style="solid", color="burlywood", weight=3]; 6264[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (primCmpNat Zero ywz452 == GT)",fontsize=16,color="burlywood",shape="box"];25473[label="ywz452/Succ ywz4520",fontsize=10,color="white",style="solid",shape="box"];6264 -> 25473[label="",style="solid", color="burlywood", weight=9]; 25473 -> 6368[label="",style="solid", color="burlywood", weight=3]; 25474[label="ywz452/Zero",fontsize=10,color="white",style="solid",shape="box"];6264 -> 25474[label="",style="solid", color="burlywood", weight=9]; 25474 -> 6369[label="",style="solid", color="burlywood", weight=3]; 255 -> 165[label="",style="dashed", color="red", weight=0]; 255[label="FiniteMap.splitGT ywz44 (Pos (Succ ywz5000))",fontsize=16,color="magenta"];256[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Pos (Succ ywz5000))",fontsize=16,color="black",shape="box"];256 -> 321[label="",style="solid", color="black", weight=3]; 257 -> 28[label="",style="dashed", color="red", weight=0]; 257[label="FiniteMap.splitGT3 (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos (Succ ywz5000))",fontsize=16,color="magenta"];257 -> 322[label="",style="dashed", color="magenta", weight=3]; 257 -> 323[label="",style="dashed", color="magenta", weight=3]; 257 -> 324[label="",style="dashed", color="magenta", weight=3]; 257 -> 325[label="",style="dashed", color="magenta", weight=3]; 257 -> 326[label="",style="dashed", color="magenta", weight=3]; 257 -> 327[label="",style="dashed", color="magenta", weight=3]; 258[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (Pos Zero < Pos (Succ ywz4000))",fontsize=16,color="black",shape="box"];258 -> 328[label="",style="solid", color="black", weight=3]; 259[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (compare (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];259 -> 329[label="",style="solid", color="black", weight=3]; 260[label="FiniteMap.splitGT FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="box"];260 -> 330[label="",style="solid", color="black", weight=3]; 261[label="FiniteMap.splitGT (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos Zero)",fontsize=16,color="black",shape="box"];261 -> 331[label="",style="solid", color="black", weight=3]; 262[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (compare (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];262 -> 332[label="",style="solid", color="black", weight=3]; 263[label="FiniteMap.splitGT1 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpInt (Neg (Succ ywz5000)) (Pos ywz400) == LT)",fontsize=16,color="black",shape="box"];263 -> 333[label="",style="solid", color="black", weight=3]; 6364[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (primCmpNat (Succ ywz4600) ywz461 == GT)",fontsize=16,color="burlywood",shape="box"];25475[label="ywz461/Succ ywz4610",fontsize=10,color="white",style="solid",shape="box"];6364 -> 25475[label="",style="solid", color="burlywood", weight=9]; 25475 -> 6475[label="",style="solid", color="burlywood", weight=3]; 25476[label="ywz461/Zero",fontsize=10,color="white",style="solid",shape="box"];6364 -> 25476[label="",style="solid", color="burlywood", weight=9]; 25476 -> 6476[label="",style="solid", color="burlywood", weight=3]; 6365[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (primCmpNat Zero ywz461 == GT)",fontsize=16,color="burlywood",shape="box"];25477[label="ywz461/Succ ywz4610",fontsize=10,color="white",style="solid",shape="box"];6365 -> 25477[label="",style="solid", color="burlywood", weight=9]; 25477 -> 6477[label="",style="solid", color="burlywood", weight=3]; 25478[label="ywz461/Zero",fontsize=10,color="white",style="solid",shape="box"];6365 -> 25478[label="",style="solid", color="burlywood", weight=9]; 25478 -> 6478[label="",style="solid", color="burlywood", weight=3]; 268[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (Neg (Succ ywz5000) < Neg Zero)",fontsize=16,color="black",shape="box"];268 -> 338[label="",style="solid", color="black", weight=3]; 269[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (compare (Neg Zero) (Pos (Succ ywz4000)) == LT)",fontsize=16,color="black",shape="box"];269 -> 339[label="",style="solid", color="black", weight=3]; 270[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (compare (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];270 -> 340[label="",style="solid", color="black", weight=3]; 271[label="FiniteMap.splitGT ywz44 (Neg Zero)",fontsize=16,color="burlywood",shape="triangle"];25479[label="ywz44/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];271 -> 25479[label="",style="solid", color="burlywood", weight=9]; 25479 -> 341[label="",style="solid", color="burlywood", weight=3]; 25480[label="ywz44/FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=10,color="white",style="solid",shape="box"];271 -> 25480[label="",style="solid", color="burlywood", weight=9]; 25480 -> 342[label="",style="solid", color="burlywood", weight=3]; 272[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (compare (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];272 -> 343[label="",style="solid", color="black", weight=3]; 15204[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 (primCmpInt (Pos (Succ ywz5000)) ywz740 == GT)",fontsize=16,color="burlywood",shape="box"];25481[label="ywz740/Pos ywz7400",fontsize=10,color="white",style="solid",shape="box"];15204 -> 25481[label="",style="solid", color="burlywood", weight=9]; 25481 -> 15259[label="",style="solid", color="burlywood", weight=3]; 25482[label="ywz740/Neg ywz7400",fontsize=10,color="white",style="solid",shape="box"];15204 -> 25482[label="",style="solid", color="burlywood", weight=9]; 25482 -> 15260[label="",style="solid", color="burlywood", weight=3]; 15205[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 (primCmpInt (Pos Zero) ywz740 == GT)",fontsize=16,color="burlywood",shape="box"];25483[label="ywz740/Pos ywz7400",fontsize=10,color="white",style="solid",shape="box"];15205 -> 25483[label="",style="solid", color="burlywood", weight=9]; 25483 -> 15261[label="",style="solid", color="burlywood", weight=3]; 25484[label="ywz740/Neg ywz7400",fontsize=10,color="white",style="solid",shape="box"];15205 -> 25484[label="",style="solid", color="burlywood", weight=9]; 25484 -> 15262[label="",style="solid", color="burlywood", weight=3]; 15206[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 (primCmpInt (Neg (Succ ywz5000)) ywz740 == GT)",fontsize=16,color="burlywood",shape="box"];25485[label="ywz740/Pos ywz7400",fontsize=10,color="white",style="solid",shape="box"];15206 -> 25485[label="",style="solid", color="burlywood", weight=9]; 25485 -> 15263[label="",style="solid", color="burlywood", weight=3]; 25486[label="ywz740/Neg ywz7400",fontsize=10,color="white",style="solid",shape="box"];15206 -> 25486[label="",style="solid", color="burlywood", weight=9]; 25486 -> 15264[label="",style="solid", color="burlywood", weight=3]; 15207[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (primCmpInt (Neg Zero) ywz740 == GT)",fontsize=16,color="burlywood",shape="box"];25487[label="ywz740/Pos ywz7400",fontsize=10,color="white",style="solid",shape="box"];15207 -> 25487[label="",style="solid", color="burlywood", weight=9]; 25487 -> 15265[label="",style="solid", color="burlywood", weight=3]; 25488[label="ywz740/Neg ywz7400",fontsize=10,color="white",style="solid",shape="box"];15207 -> 25488[label="",style="solid", color="burlywood", weight=9]; 25488 -> 15266[label="",style="solid", color="burlywood", weight=3]; 15208[label="FiniteMap.addToFM_C FiniteMap.addToFM0 FiniteMap.EmptyFM ywz50 ywz9",fontsize=16,color="black",shape="box"];15208 -> 15267[label="",style="solid", color="black", weight=3]; 15209[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch ywz7430 ywz7431 ywz7432 ywz7433 ywz7434) ywz50 ywz9",fontsize=16,color="black",shape="box"];15209 -> 15268[label="",style="solid", color="black", weight=3]; 15210 -> 12612[label="",style="dashed", color="red", weight=0]; 15210[label="FiniteMap.mkBalBranch6Size_l ywz744 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz740 ywz741 + FiniteMap.mkBalBranch6Size_r ywz744 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz740 ywz741",fontsize=16,color="magenta"];15210 -> 15269[label="",style="dashed", color="magenta", weight=3]; 15210 -> 15270[label="",style="dashed", color="magenta", weight=3]; 15211[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];498[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz400) ywz41 ywz42 ywz43 ywz44) (Pos (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpInt (Pos (Succ ywz5000)) (Pos ywz400) == LT))",fontsize=16,color="black",shape="box"];498 -> 574[label="",style="solid", color="black", weight=3]; 499[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz400) ywz41 ywz42 ywz43 ywz44) (Pos (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpInt (Pos (Succ ywz5000)) (Neg ywz400) == LT))",fontsize=16,color="black",shape="box"];499 -> 575[label="",style="solid", color="black", weight=3]; 500[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz400) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos ywz400) == LT))",fontsize=16,color="burlywood",shape="box"];25489[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];500 -> 25489[label="",style="solid", color="burlywood", weight=9]; 25489 -> 576[label="",style="solid", color="burlywood", weight=3]; 25490[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];500 -> 25490[label="",style="solid", color="burlywood", weight=9]; 25490 -> 577[label="",style="solid", color="burlywood", weight=3]; 501[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz400) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg ywz400) == LT))",fontsize=16,color="burlywood",shape="box"];25491[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];501 -> 25491[label="",style="solid", color="burlywood", weight=9]; 25491 -> 578[label="",style="solid", color="burlywood", weight=3]; 25492[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];501 -> 25492[label="",style="solid", color="burlywood", weight=9]; 25492 -> 579[label="",style="solid", color="burlywood", weight=3]; 502[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz400) ywz41 ywz42 ywz43 ywz44) (Neg (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpInt (Neg (Succ ywz5000)) (Pos ywz400) == LT))",fontsize=16,color="black",shape="box"];502 -> 580[label="",style="solid", color="black", weight=3]; 503[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz400) ywz41 ywz42 ywz43 ywz44) (Neg (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpInt (Neg (Succ ywz5000)) (Neg ywz400) == LT))",fontsize=16,color="black",shape="box"];503 -> 581[label="",style="solid", color="black", weight=3]; 504[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz400) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Pos ywz400) == LT))",fontsize=16,color="burlywood",shape="box"];25493[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];504 -> 25493[label="",style="solid", color="burlywood", weight=9]; 25493 -> 582[label="",style="solid", color="burlywood", weight=3]; 25494[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];504 -> 25494[label="",style="solid", color="burlywood", weight=9]; 25494 -> 583[label="",style="solid", color="burlywood", weight=3]; 505[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz400) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Neg ywz400) == LT))",fontsize=16,color="burlywood",shape="box"];25495[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];505 -> 25495[label="",style="solid", color="burlywood", weight=9]; 25495 -> 584[label="",style="solid", color="burlywood", weight=3]; 25496[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];505 -> 25496[label="",style="solid", color="burlywood", weight=9]; 25496 -> 585[label="",style="solid", color="burlywood", weight=3]; 12985 -> 5537[label="",style="dashed", color="red", weight=0]; 12985[label="primPlusNat (primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ ywz103700)) (Succ ywz103700)",fontsize=16,color="magenta"];12985 -> 13037[label="",style="dashed", color="magenta", weight=3]; 12985 -> 13038[label="",style="dashed", color="magenta", weight=3]; 12986[label="Zero",fontsize=16,color="green",shape="box"];12889[label="primCmpNat ywz82100 ywz81100 == LT",fontsize=16,color="burlywood",shape="triangle"];25497[label="ywz82100/Succ ywz821000",fontsize=10,color="white",style="solid",shape="box"];12889 -> 25497[label="",style="solid", color="burlywood", weight=9]; 25497 -> 12975[label="",style="solid", color="burlywood", weight=3]; 25498[label="ywz82100/Zero",fontsize=10,color="white",style="solid",shape="box"];12889 -> 25498[label="",style="solid", color="burlywood", weight=9]; 25498 -> 12976[label="",style="solid", color="burlywood", weight=3]; 12890 -> 12118[label="",style="dashed", color="red", weight=0]; 12890[label="GT == LT",fontsize=16,color="magenta"];12140[label="False",fontsize=16,color="green",shape="box"];12891[label="ywz81100",fontsize=16,color="green",shape="box"];12892[label="Zero",fontsize=16,color="green",shape="box"];12117[label="EQ == LT",fontsize=16,color="black",shape="triangle"];12117 -> 12139[label="",style="solid", color="black", weight=3]; 12149[label="True",fontsize=16,color="green",shape="box"];12893 -> 12889[label="",style="dashed", color="red", weight=0]; 12893[label="primCmpNat ywz81100 ywz82100 == LT",fontsize=16,color="magenta"];12893 -> 12977[label="",style="dashed", color="magenta", weight=3]; 12893 -> 12978[label="",style="dashed", color="magenta", weight=3]; 12894 -> 12125[label="",style="dashed", color="red", weight=0]; 12894[label="LT == LT",fontsize=16,color="magenta"];12895[label="ywz81100",fontsize=16,color="green",shape="box"];12896[label="Zero",fontsize=16,color="green",shape="box"];15438[label="FiniteMap.mkBranchResult ywz1235 ywz1236 ywz1238 ywz1237",fontsize=16,color="black",shape="box"];15438 -> 15474[label="",style="solid", color="black", weight=3]; 14470[label="FiniteMap.mkVBalBranch ywz50 ywz9 FiniteMap.EmptyFM (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)",fontsize=16,color="black",shape="box"];14470 -> 14486[label="",style="solid", color="black", weight=3]; 14471[label="FiniteMap.mkVBalBranch ywz50 ywz9 (FiniteMap.Branch ywz7440 ywz7441 ywz7442 ywz7443 ywz7444) (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)",fontsize=16,color="black",shape="box"];14471 -> 14487[label="",style="solid", color="black", weight=3]; 14472 -> 12612[label="",style="dashed", color="red", weight=0]; 14472[label="FiniteMap.mkBalBranch6Size_l (FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)) ywz743 ywz740 ywz741 + FiniteMap.mkBalBranch6Size_r (FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)) ywz743 ywz740 ywz741",fontsize=16,color="magenta"];14472 -> 14488[label="",style="dashed", color="magenta", weight=3]; 14472 -> 14489[label="",style="dashed", color="magenta", weight=3]; 14473[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];14474[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz50 ywz9",fontsize=16,color="black",shape="box"];14474 -> 14490[label="",style="solid", color="black", weight=3]; 14475[label="ywz6332",fontsize=16,color="green",shape="box"];14476[label="ywz6331",fontsize=16,color="green",shape="box"];14477[label="ywz6330",fontsize=16,color="green",shape="box"];14478[label="ywz6334",fontsize=16,color="green",shape="box"];14479 -> 10999[label="",style="dashed", color="red", weight=0]; 14479[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz740 ywz741 ywz742 ywz743 ywz744 ywz6330 ywz6331 ywz6332 ywz6333 ywz6334 < FiniteMap.mkVBalBranch3Size_r ywz740 ywz741 ywz742 ywz743 ywz744 ywz6330 ywz6331 ywz6332 ywz6333 ywz6334",fontsize=16,color="magenta"];14479 -> 14491[label="",style="dashed", color="magenta", weight=3]; 14479 -> 14492[label="",style="dashed", color="magenta", weight=3]; 14480[label="ywz6333",fontsize=16,color="green",shape="box"];13511 -> 3313[label="",style="dashed", color="red", weight=0]; 13511[label="FiniteMap.sizeFM ywz1155",fontsize=16,color="magenta"];13511 -> 13547[label="",style="dashed", color="magenta", weight=3]; 13546 -> 3313[label="",style="dashed", color="red", weight=0]; 13546[label="FiniteMap.sizeFM ywz634",fontsize=16,color="magenta"];13546 -> 13555[label="",style="dashed", color="magenta", weight=3]; 12774[label="primPlusInt (Pos ywz10490) ywz1048",fontsize=16,color="burlywood",shape="box"];25499[label="ywz1048/Pos ywz10480",fontsize=10,color="white",style="solid",shape="box"];12774 -> 25499[label="",style="solid", color="burlywood", weight=9]; 25499 -> 12851[label="",style="solid", color="burlywood", weight=3]; 25500[label="ywz1048/Neg ywz10480",fontsize=10,color="white",style="solid",shape="box"];12774 -> 25500[label="",style="solid", color="burlywood", weight=9]; 25500 -> 12852[label="",style="solid", color="burlywood", weight=3]; 12775[label="primPlusInt (Neg ywz10490) ywz1048",fontsize=16,color="burlywood",shape="box"];25501[label="ywz1048/Pos ywz10480",fontsize=10,color="white",style="solid",shape="box"];12775 -> 25501[label="",style="solid", color="burlywood", weight=9]; 25501 -> 12853[label="",style="solid", color="burlywood", weight=3]; 25502[label="ywz1048/Neg ywz10480",fontsize=10,color="white",style="solid",shape="box"];12775 -> 25502[label="",style="solid", color="burlywood", weight=9]; 25502 -> 12854[label="",style="solid", color="burlywood", weight=3]; 13472 -> 13476[label="",style="dashed", color="red", weight=0]; 13472[label="FiniteMap.mkBalBranch6Size_l ywz1007 ywz73 ywz70 ywz71",fontsize=16,color="magenta"];13472 -> 13485[label="",style="dashed", color="magenta", weight=3]; 13472 -> 13486[label="",style="dashed", color="magenta", weight=3]; 13472 -> 13487[label="",style="dashed", color="magenta", weight=3]; 13472 -> 13488[label="",style="dashed", color="magenta", weight=3]; 13473[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (compare (FiniteMap.mkBalBranch6Size_r ywz1007 ywz73 ywz70 ywz71) ywz1154 == GT)",fontsize=16,color="black",shape="box"];13473 -> 13514[label="",style="solid", color="black", weight=3]; 6162[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpNat (Succ ywz4330) (Succ ywz4340) == LT)",fontsize=16,color="black",shape="box"];6162 -> 6269[label="",style="solid", color="black", weight=3]; 6163[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpNat (Succ ywz4330) Zero == LT)",fontsize=16,color="black",shape="box"];6163 -> 6270[label="",style="solid", color="black", weight=3]; 6164[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpNat Zero (Succ ywz4340) == LT)",fontsize=16,color="black",shape="box"];6164 -> 6271[label="",style="solid", color="black", weight=3]; 6165[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];6165 -> 6272[label="",style="solid", color="black", weight=3]; 294[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (compare (Pos (Succ ywz5000)) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];294 -> 369[label="",style="solid", color="black", weight=3]; 295[label="FiniteMap.splitLT1 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (GT == GT)",fontsize=16,color="black",shape="box"];295 -> 370[label="",style="solid", color="black", weight=3]; 296[label="FiniteMap.splitLT FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="box"];296 -> 371[label="",style="solid", color="black", weight=3]; 297[label="FiniteMap.splitLT (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Pos Zero)",fontsize=16,color="black",shape="box"];297 -> 372[label="",style="solid", color="black", weight=3]; 298[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];298 -> 373[label="",style="solid", color="black", weight=3]; 299[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ ywz4000)) == GT)",fontsize=16,color="black",shape="box"];299 -> 374[label="",style="solid", color="black", weight=3]; 300[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];300 -> 375[label="",style="solid", color="black", weight=3]; 301 -> 83[label="",style="dashed", color="red", weight=0]; 301[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];302[label="ywz434",fontsize=16,color="green",shape="box"];303[label="ywz432",fontsize=16,color="green",shape="box"];304[label="ywz431",fontsize=16,color="green",shape="box"];305[label="ywz433",fontsize=16,color="green",shape="box"];306[label="ywz430",fontsize=16,color="green",shape="box"];307[label="Neg (Succ ywz5000)",fontsize=16,color="green",shape="box"];6265[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpNat (Succ ywz4420) (Succ ywz4430) == LT)",fontsize=16,color="black",shape="box"];6265 -> 6370[label="",style="solid", color="black", weight=3]; 6266[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpNat (Succ ywz4420) Zero == LT)",fontsize=16,color="black",shape="box"];6266 -> 6371[label="",style="solid", color="black", weight=3]; 6267[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpNat Zero (Succ ywz4430) == LT)",fontsize=16,color="black",shape="box"];6267 -> 6372[label="",style="solid", color="black", weight=3]; 6268[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpNat Zero Zero == LT)",fontsize=16,color="black",shape="box"];6268 -> 6373[label="",style="solid", color="black", weight=3]; 312[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="black",shape="box"];312 -> 381[label="",style="solid", color="black", weight=3]; 313 -> 27[label="",style="dashed", color="red", weight=0]; 313[label="FiniteMap.splitLT3 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Neg Zero)",fontsize=16,color="magenta"];313 -> 382[label="",style="dashed", color="magenta", weight=3]; 313 -> 383[label="",style="dashed", color="magenta", weight=3]; 313 -> 384[label="",style="dashed", color="magenta", weight=3]; 313 -> 385[label="",style="dashed", color="magenta", weight=3]; 313 -> 386[label="",style="dashed", color="magenta", weight=3]; 313 -> 387[label="",style="dashed", color="magenta", weight=3]; 314[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];314 -> 388[label="",style="solid", color="black", weight=3]; 315[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (compare (Neg Zero) (Neg (Succ ywz4000)) == GT)",fontsize=16,color="black",shape="box"];315 -> 389[label="",style="solid", color="black", weight=3]; 316[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];316 -> 390[label="",style="solid", color="black", weight=3]; 6366[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (primCmpNat (Succ ywz4510) (Succ ywz4520) == GT)",fontsize=16,color="black",shape="box"];6366 -> 6479[label="",style="solid", color="black", weight=3]; 6367[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (primCmpNat (Succ ywz4510) Zero == GT)",fontsize=16,color="black",shape="box"];6367 -> 6480[label="",style="solid", color="black", weight=3]; 6368[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (primCmpNat Zero (Succ ywz4520) == GT)",fontsize=16,color="black",shape="box"];6368 -> 6481[label="",style="solid", color="black", weight=3]; 6369[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];6369 -> 6482[label="",style="solid", color="black", weight=3]; 321 -> 83[label="",style="dashed", color="red", weight=0]; 321[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];322[label="ywz444",fontsize=16,color="green",shape="box"];323[label="ywz442",fontsize=16,color="green",shape="box"];324[label="ywz441",fontsize=16,color="green",shape="box"];325[label="ywz443",fontsize=16,color="green",shape="box"];326[label="ywz440",fontsize=16,color="green",shape="box"];327[label="Pos (Succ ywz5000)",fontsize=16,color="green",shape="box"];328[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (compare (Pos Zero) (Pos (Succ ywz4000)) == LT)",fontsize=16,color="black",shape="box"];328 -> 396[label="",style="solid", color="black", weight=3]; 329[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];329 -> 397[label="",style="solid", color="black", weight=3]; 330[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="box"];330 -> 398[label="",style="solid", color="black", weight=3]; 331 -> 28[label="",style="dashed", color="red", weight=0]; 331[label="FiniteMap.splitGT3 (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos Zero)",fontsize=16,color="magenta"];331 -> 399[label="",style="dashed", color="magenta", weight=3]; 331 -> 400[label="",style="dashed", color="magenta", weight=3]; 331 -> 401[label="",style="dashed", color="magenta", weight=3]; 331 -> 402[label="",style="dashed", color="magenta", weight=3]; 331 -> 403[label="",style="dashed", color="magenta", weight=3]; 331 -> 404[label="",style="dashed", color="magenta", weight=3]; 332[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];332 -> 405[label="",style="solid", color="black", weight=3]; 333[label="FiniteMap.splitGT1 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (LT == LT)",fontsize=16,color="black",shape="box"];333 -> 406[label="",style="solid", color="black", weight=3]; 6475[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (primCmpNat (Succ ywz4600) (Succ ywz4610) == GT)",fontsize=16,color="black",shape="box"];6475 -> 6516[label="",style="solid", color="black", weight=3]; 6476[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (primCmpNat (Succ ywz4600) Zero == GT)",fontsize=16,color="black",shape="box"];6476 -> 6517[label="",style="solid", color="black", weight=3]; 6477[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (primCmpNat Zero (Succ ywz4610) == GT)",fontsize=16,color="black",shape="box"];6477 -> 6518[label="",style="solid", color="black", weight=3]; 6478[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];6478 -> 6519[label="",style="solid", color="black", weight=3]; 338[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (compare (Neg (Succ ywz5000)) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];338 -> 412[label="",style="solid", color="black", weight=3]; 339[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ ywz4000)) == LT)",fontsize=16,color="black",shape="box"];339 -> 413[label="",style="solid", color="black", weight=3]; 340[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == LT)",fontsize=16,color="black",shape="box"];340 -> 414[label="",style="solid", color="black", weight=3]; 341[label="FiniteMap.splitGT FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="black",shape="box"];341 -> 415[label="",style="solid", color="black", weight=3]; 342[label="FiniteMap.splitGT (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Neg Zero)",fontsize=16,color="black",shape="box"];342 -> 416[label="",style="solid", color="black", weight=3]; 343[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];343 -> 417[label="",style="solid", color="black", weight=3]; 15259[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos ywz7400) ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 (primCmpInt (Pos (Succ ywz5000)) (Pos ywz7400) == GT)",fontsize=16,color="black",shape="box"];15259 -> 15291[label="",style="solid", color="black", weight=3]; 15260[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg ywz7400) ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 (primCmpInt (Pos (Succ ywz5000)) (Neg ywz7400) == GT)",fontsize=16,color="black",shape="box"];15260 -> 15292[label="",style="solid", color="black", weight=3]; 15261[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos ywz7400) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 (primCmpInt (Pos Zero) (Pos ywz7400) == GT)",fontsize=16,color="burlywood",shape="box"];25503[label="ywz7400/Succ ywz74000",fontsize=10,color="white",style="solid",shape="box"];15261 -> 25503[label="",style="solid", color="burlywood", weight=9]; 25503 -> 15293[label="",style="solid", color="burlywood", weight=3]; 25504[label="ywz7400/Zero",fontsize=10,color="white",style="solid",shape="box"];15261 -> 25504[label="",style="solid", color="burlywood", weight=9]; 25504 -> 15294[label="",style="solid", color="burlywood", weight=3]; 15262[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg ywz7400) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 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GT)",fontsize=16,color="black",shape="box"];15264 -> 15298[label="",style="solid", color="black", weight=3]; 15265[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos ywz7400) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (primCmpInt (Neg Zero) (Pos ywz7400) == GT)",fontsize=16,color="burlywood",shape="box"];25507[label="ywz7400/Succ ywz74000",fontsize=10,color="white",style="solid",shape="box"];15265 -> 25507[label="",style="solid", color="burlywood", weight=9]; 25507 -> 15299[label="",style="solid", color="burlywood", weight=3]; 25508[label="ywz7400/Zero",fontsize=10,color="white",style="solid",shape="box"];15265 -> 25508[label="",style="solid", color="burlywood", weight=9]; 25508 -> 15300[label="",style="solid", color="burlywood", weight=3]; 15266[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg ywz7400) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (primCmpInt (Neg Zero) (Neg ywz7400) == GT)",fontsize=16,color="burlywood",shape="box"];25509[label="ywz7400/Succ ywz74000",fontsize=10,color="white",style="solid",shape="box"];15266 -> 25509[label="",style="solid", color="burlywood", weight=9]; 25509 -> 15301[label="",style="solid", color="burlywood", weight=3]; 25510[label="ywz7400/Zero",fontsize=10,color="white",style="solid",shape="box"];15266 -> 25510[label="",style="solid", color="burlywood", weight=9]; 25510 -> 15302[label="",style="solid", color="burlywood", weight=3]; 15267[label="FiniteMap.addToFM_C4 FiniteMap.addToFM0 FiniteMap.EmptyFM ywz50 ywz9",fontsize=16,color="black",shape="box"];15267 -> 15303[label="",style="solid", color="black", weight=3]; 15268 -> 14490[label="",style="dashed", color="red", weight=0]; 15268[label="FiniteMap.addToFM_C3 FiniteMap.addToFM0 (FiniteMap.Branch ywz7430 ywz7431 ywz7432 ywz7433 ywz7434) ywz50 ywz9",fontsize=16,color="magenta"];15268 -> 15304[label="",style="dashed", color="magenta", weight=3]; 15268 -> 15305[label="",style="dashed", color="magenta", weight=3]; 15268 -> 15306[label="",style="dashed", color="magenta", weight=3]; 15268 -> 15307[label="",style="dashed", color="magenta", weight=3]; 15268 -> 15308[label="",style="dashed", color="magenta", weight=3]; 15269 -> 13476[label="",style="dashed", color="red", weight=0]; 15269[label="FiniteMap.mkBalBranch6Size_l ywz744 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz740 ywz741",fontsize=16,color="magenta"];15269 -> 15309[label="",style="dashed", color="magenta", weight=3]; 15269 -> 15310[label="",style="dashed", color="magenta", weight=3]; 15269 -> 15311[label="",style="dashed", color="magenta", weight=3]; 15269 -> 15312[label="",style="dashed", color="magenta", weight=3]; 15270 -> 13515[label="",style="dashed", color="red", weight=0]; 15270[label="FiniteMap.mkBalBranch6Size_r ywz744 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9) ywz740 ywz741",fontsize=16,color="magenta"];15270 -> 15313[label="",style="dashed", color="magenta", weight=3]; 15270 -> 15314[label="",style="dashed", color="magenta", weight=3]; 15270 -> 15315[label="",style="dashed", color="magenta", weight=3]; 15270 -> 15316[label="",style="dashed", color="magenta", weight=3]; 574[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz400) ywz41 ywz42 ywz43 ywz44) (Pos (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat (Succ ywz5000) ywz400 == LT))",fontsize=16,color="burlywood",shape="box"];25511[label="ywz400/Succ ywz4000",fontsize=10,color="white",style="solid",shape="box"];574 -> 25511[label="",style="solid", color="burlywood", weight=9]; 25511 -> 665[label="",style="solid", color="burlywood", weight=3]; 25512[label="ywz400/Zero",fontsize=10,color="white",style="solid",shape="box"];574 -> 25512[label="",style="solid", color="burlywood", weight=9]; 25512 -> 666[label="",style="solid", color="burlywood", weight=3]; 575 -> 21630[label="",style="dashed", color="red", weight=0]; 575[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch 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19817[label="",style="dashed", color="magenta", weight=3]; 580 -> 19818[label="",style="dashed", color="magenta", weight=3]; 580 -> 19819[label="",style="dashed", color="magenta", weight=3]; 580 -> 19820[label="",style="dashed", color="magenta", weight=3]; 580 -> 19821[label="",style="dashed", color="magenta", weight=3]; 580 -> 19822[label="",style="dashed", color="magenta", weight=3]; 580 -> 19823[label="",style="dashed", color="magenta", weight=3]; 580 -> 19824[label="",style="dashed", color="magenta", weight=3]; 580 -> 19825[label="",style="dashed", color="magenta", weight=3]; 580 -> 19826[label="",style="dashed", color="magenta", weight=3]; 580 -> 19827[label="",style="dashed", color="magenta", weight=3]; 580 -> 19828[label="",style="dashed", color="magenta", weight=3]; 581[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz400) ywz41 ywz42 ywz43 ywz44) (Neg (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) 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13037[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ ywz103700)",fontsize=16,color="magenta"];13037 -> 13111[label="",style="dashed", color="magenta", weight=3]; 13038[label="Succ ywz103700",fontsize=16,color="green",shape="box"];5537[label="primPlusNat ywz25000 ywz37200",fontsize=16,color="burlywood",shape="triangle"];25515[label="ywz25000/Succ ywz250000",fontsize=10,color="white",style="solid",shape="box"];5537 -> 25515[label="",style="solid", color="burlywood", weight=9]; 25515 -> 5654[label="",style="solid", color="burlywood", weight=3]; 25516[label="ywz25000/Zero",fontsize=10,color="white",style="solid",shape="box"];5537 -> 25516[label="",style="solid", color="burlywood", weight=9]; 25516 -> 5655[label="",style="solid", color="burlywood", weight=3]; 12975[label="primCmpNat (Succ ywz821000) ywz81100 == LT",fontsize=16,color="burlywood",shape="box"];25517[label="ywz81100/Succ ywz811000",fontsize=10,color="white",style="solid",shape="box"];12975 -> 25517[label="",style="solid", color="burlywood", weight=9]; 25517 -> 13015[label="",style="solid", color="burlywood", weight=3]; 25518[label="ywz81100/Zero",fontsize=10,color="white",style="solid",shape="box"];12975 -> 25518[label="",style="solid", color="burlywood", weight=9]; 25518 -> 13016[label="",style="solid", color="burlywood", weight=3]; 12976[label="primCmpNat Zero ywz81100 == LT",fontsize=16,color="burlywood",shape="box"];25519[label="ywz81100/Succ ywz811000",fontsize=10,color="white",style="solid",shape="box"];12976 -> 25519[label="",style="solid", color="burlywood", weight=9]; 25519 -> 13017[label="",style="solid", color="burlywood", weight=3]; 25520[label="ywz81100/Zero",fontsize=10,color="white",style="solid",shape="box"];12976 -> 25520[label="",style="solid", color="burlywood", weight=9]; 25520 -> 13018[label="",style="solid", color="burlywood", weight=3]; 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14516[label="",style="dashed", color="magenta", weight=3]; 14488 -> 14517[label="",style="dashed", color="magenta", weight=3]; 14488 -> 14518[label="",style="dashed", color="magenta", weight=3]; 14488 -> 14519[label="",style="dashed", color="magenta", weight=3]; 14489 -> 13515[label="",style="dashed", color="red", weight=0]; 14489[label="FiniteMap.mkBalBranch6Size_r (FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)) ywz743 ywz740 ywz741",fontsize=16,color="magenta"];14489 -> 14520[label="",style="dashed", color="magenta", weight=3]; 14489 -> 14521[label="",style="dashed", color="magenta", weight=3]; 14489 -> 14522[label="",style="dashed", color="magenta", weight=3]; 14489 -> 14523[label="",style="dashed", color="magenta", weight=3]; 14490[label="FiniteMap.addToFM_C3 FiniteMap.addToFM0 (FiniteMap.Branch ywz740 ywz741 ywz742 ywz743 ywz744) ywz50 ywz9",fontsize=16,color="black",shape="triangle"];14490 -> 14524[label="",style="solid", 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color="magenta", weight=3]; 14492 -> 14533[label="",style="dashed", color="magenta", weight=3]; 14492 -> 14534[label="",style="dashed", color="magenta", weight=3]; 14492 -> 14535[label="",style="dashed", color="magenta", weight=3]; 13547[label="ywz1155",fontsize=16,color="green",shape="box"];13555[label="ywz634",fontsize=16,color="green",shape="box"];12851[label="primPlusInt (Pos ywz10490) (Pos ywz10480)",fontsize=16,color="black",shape="box"];12851 -> 12933[label="",style="solid", color="black", weight=3]; 12852[label="primPlusInt (Pos ywz10490) (Neg ywz10480)",fontsize=16,color="black",shape="box"];12852 -> 12934[label="",style="solid", color="black", weight=3]; 12853[label="primPlusInt (Neg ywz10490) (Pos ywz10480)",fontsize=16,color="black",shape="box"];12853 -> 12935[label="",style="solid", color="black", weight=3]; 12854[label="primPlusInt (Neg ywz10490) (Neg ywz10480)",fontsize=16,color="black",shape="box"];12854 -> 12936[label="",style="solid", color="black", weight=3]; 13485[label="ywz1007",fontsize=16,color="green",shape="box"];13486[label="ywz70",fontsize=16,color="green",shape="box"];13487[label="ywz71",fontsize=16,color="green",shape="box"];13488[label="ywz73",fontsize=16,color="green",shape="box"];13514 -> 13553[label="",style="dashed", color="red", weight=0]; 13514[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (FiniteMap.mkBalBranch6Size_r ywz1007 ywz73 ywz70 ywz71) ywz1154 == GT)",fontsize=16,color="magenta"];13514 -> 13554[label="",style="dashed", color="magenta", weight=3]; 6269 -> 5977[label="",style="dashed", color="red", weight=0]; 6269[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpNat ywz4330 ywz4340 == LT)",fontsize=16,color="magenta"];6269 -> 6374[label="",style="dashed", color="magenta", weight=3]; 6269 -> 6375[label="",style="dashed", color="magenta", weight=3]; 6270[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 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color="black", weight=3]; 371[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos Zero)",fontsize=16,color="black",shape="box"];371 -> 449[label="",style="solid", color="black", weight=3]; 372 -> 27[label="",style="dashed", color="red", weight=0]; 372[label="FiniteMap.splitLT3 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Pos Zero)",fontsize=16,color="magenta"];372 -> 450[label="",style="dashed", color="magenta", weight=3]; 372 -> 451[label="",style="dashed", color="magenta", weight=3]; 372 -> 452[label="",style="dashed", color="magenta", weight=3]; 372 -> 453[label="",style="dashed", color="magenta", weight=3]; 372 -> 454[label="",style="dashed", color="magenta", weight=3]; 372 -> 455[label="",style="dashed", color="magenta", weight=3]; 373[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];373 -> 456[label="",style="solid", color="black", weight=3]; 374[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (GT == GT)",fontsize=16,color="black",shape="box"];374 -> 457[label="",style="solid", color="black", weight=3]; 375[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];375 -> 458[label="",style="solid", color="black", weight=3]; 6370 -> 6079[label="",style="dashed", color="red", weight=0]; 6370[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpNat ywz4420 ywz4430 == LT)",fontsize=16,color="magenta"];6370 -> 6483[label="",style="dashed", color="magenta", weight=3]; 6370 -> 6484[label="",style="dashed", color="magenta", weight=3]; 6371[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (GT == LT)",fontsize=16,color="black",shape="box"];6371 -> 6485[label="",style="solid", color="black", weight=3]; 6372[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) 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389[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ ywz4000)) == GT)",fontsize=16,color="black",shape="box"];389 -> 467[label="",style="solid", color="black", weight=3]; 390[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == GT)",fontsize=16,color="black",shape="box"];390 -> 468[label="",style="solid", color="black", weight=3]; 6479 -> 6182[label="",style="dashed", color="red", weight=0]; 6479[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (primCmpNat ywz4510 ywz4520 == GT)",fontsize=16,color="magenta"];6479 -> 6520[label="",style="dashed", color="magenta", weight=3]; 6479 -> 6521[label="",style="dashed", color="magenta", weight=3]; 6480[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (GT == GT)",fontsize=16,color="black",shape="box"];6480 -> 6522[label="",style="solid", color="black", weight=3]; 6481[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (LT == GT)",fontsize=16,color="black",shape="box"];6481 -> 6523[label="",style="solid", color="black", weight=3]; 6482[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (EQ == GT)",fontsize=16,color="black",shape="box"];6482 -> 6524[label="",style="solid", color="black", weight=3]; 396[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ ywz4000)) == LT)",fontsize=16,color="black",shape="box"];396 -> 476[label="",style="solid", color="black", weight=3]; 397[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];397 -> 477[label="",style="solid", color="black", weight=3]; 398 -> 83[label="",style="dashed", color="red", weight=0]; 398[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];399[label="ywz444",fontsize=16,color="green",shape="box"];400[label="ywz442",fontsize=16,color="green",shape="box"];401[label="ywz441",fontsize=16,color="green",shape="box"];402[label="ywz443",fontsize=16,color="green",shape="box"];403[label="ywz440",fontsize=16,color="green",shape="box"];404[label="Pos Zero",fontsize=16,color="green",shape="box"];405[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];405 -> 478[label="",style="solid", color="black", weight=3]; 406[label="FiniteMap.splitGT1 (Pos ywz400) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) True",fontsize=16,color="black",shape="box"];406 -> 479[label="",style="solid", color="black", weight=3]; 6516 -> 6283[label="",style="dashed", color="red", weight=0]; 6516[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (primCmpNat ywz4600 ywz4610 == GT)",fontsize=16,color="magenta"];6516 -> 6594[label="",style="dashed", color="magenta", weight=3]; 6516 -> 6595[label="",style="dashed", color="magenta", weight=3]; 6517[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (GT == GT)",fontsize=16,color="black",shape="box"];6517 -> 6596[label="",style="solid", color="black", weight=3]; 6518[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (LT == GT)",fontsize=16,color="black",shape="box"];6518 -> 6597[label="",style="solid", color="black", weight=3]; 6519[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (EQ == GT)",fontsize=16,color="black",shape="box"];6519 -> 6598[label="",style="solid", color="black", weight=3]; 412[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpInt (Neg (Succ ywz5000)) (Neg Zero) == LT)",fontsize=16,color="black",shape="box"];412 -> 487[label="",style="solid", color="black", weight=3]; 413[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (LT == LT)",fontsize=16,color="black",shape="box"];413 -> 488[label="",style="solid", color="black", weight=3]; 414[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];414 -> 489[label="",style="solid", color="black", weight=3]; 415[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Neg Zero)",fontsize=16,color="black",shape="box"];415 -> 490[label="",style="solid", color="black", weight=3]; 416 -> 28[label="",style="dashed", color="red", weight=0]; 416[label="FiniteMap.splitGT3 (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Neg Zero)",fontsize=16,color="magenta"];416 -> 491[label="",style="dashed", color="magenta", weight=3]; 416 -> 492[label="",style="dashed", color="magenta", weight=3]; 416 -> 493[label="",style="dashed", color="magenta", weight=3]; 416 -> 494[label="",style="dashed", color="magenta", weight=3]; 416 -> 495[label="",style="dashed", color="magenta", weight=3]; 416 -> 496[label="",style="dashed", color="magenta", weight=3]; 417[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == LT)",fontsize=16,color="black",shape="box"];417 -> 497[label="",style="solid", color="black", weight=3]; 15291[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos ywz7400) ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 (primCmpNat (Succ ywz5000) ywz7400 == GT)",fontsize=16,color="burlywood",shape="box"];25521[label="ywz7400/Succ ywz74000",fontsize=10,color="white",style="solid",shape="box"];15291 -> 25521[label="",style="solid", color="burlywood", weight=9]; 25521 -> 15376[label="",style="solid", color="burlywood", weight=3]; 25522[label="ywz7400/Zero",fontsize=10,color="white",style="solid",shape="box"];15291 -> 25522[label="",style="solid", color="burlywood", weight=9]; 25522 -> 15377[label="",style="solid", color="burlywood", weight=3]; 15292[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg ywz7400) ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 (GT == GT)",fontsize=16,color="black",shape="box"];15292 -> 15378[label="",style="solid", color="black", weight=3]; 15293[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 (primCmpInt (Pos Zero) (Pos (Succ ywz74000)) == GT)",fontsize=16,color="black",shape="box"];15293 -> 15379[label="",style="solid", color="black", weight=3]; 15294[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];15294 -> 15380[label="",style="solid", color="black", weight=3]; 15295[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 (primCmpInt (Pos Zero) (Neg (Succ ywz74000)) == GT)",fontsize=16,color="black",shape="box"];15295 -> 15381[label="",style="solid", color="black", weight=3]; 15296[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];15296 -> 15382[label="",style="solid", color="black", weight=3]; 15297[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos ywz7400) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 (LT == GT)",fontsize=16,color="black",shape="box"];15297 -> 15383[label="",style="solid", color="black", weight=3]; 15298[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg ywz7400) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 (primCmpNat ywz7400 (Succ ywz5000) == GT)",fontsize=16,color="burlywood",shape="box"];25523[label="ywz7400/Succ ywz74000",fontsize=10,color="white",style="solid",shape="box"];15298 -> 25523[label="",style="solid", color="burlywood", weight=9]; 25523 -> 15384[label="",style="solid", color="burlywood", weight=3]; 25524[label="ywz7400/Zero",fontsize=10,color="white",style="solid",shape="box"];15298 -> 25524[label="",style="solid", color="burlywood", weight=9]; 25524 -> 15385[label="",style="solid", color="burlywood", weight=3]; 15299[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (primCmpInt (Neg Zero) (Pos (Succ ywz74000)) == GT)",fontsize=16,color="black",shape="box"];15299 -> 15386[label="",style="solid", color="black", weight=3]; 15300[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];15300 -> 15387[label="",style="solid", color="black", weight=3]; 15301[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (primCmpInt (Neg Zero) (Neg (Succ ywz74000)) == GT)",fontsize=16,color="black",shape="box"];15301 -> 15388[label="",style="solid", color="black", weight=3]; 15302[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];15302 -> 15389[label="",style="solid", color="black", weight=3]; 15303[label="FiniteMap.unitFM ywz50 ywz9",fontsize=16,color="black",shape="box"];15303 -> 15390[label="",style="solid", color="black", weight=3]; 15304[label="ywz7431",fontsize=16,color="green",shape="box"];15305[label="ywz7433",fontsize=16,color="green",shape="box"];15306[label="ywz7430",fontsize=16,color="green",shape="box"];15307[label="ywz7432",fontsize=16,color="green",shape="box"];15308[label="ywz7434",fontsize=16,color="green",shape="box"];15309[label="ywz744",fontsize=16,color="green",shape="box"];15310[label="ywz740",fontsize=16,color="green",shape="box"];15311[label="ywz741",fontsize=16,color="green",shape="box"];15312 -> 15167[label="",style="dashed", color="red", weight=0]; 15312[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9",fontsize=16,color="magenta"];15313[label="ywz744",fontsize=16,color="green",shape="box"];15314[label="ywz740",fontsize=16,color="green",shape="box"];15315[label="ywz741",fontsize=16,color="green",shape="box"];15316 -> 15167[label="",style="dashed", color="red", weight=0]; 15316[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz743 ywz50 ywz9",fontsize=16,color="magenta"];665[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44) (Pos (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat (Succ ywz5000) (Succ ywz4000) == LT))",fontsize=16,color="black",shape="box"];665 -> 797[label="",style="solid", color="black", weight=3]; 666[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat (Succ ywz5000) Zero == LT))",fontsize=16,color="black",shape="box"];666 -> 798[label="",style="solid", color="black", weight=3]; 21631[label="ywz43",fontsize=16,color="green",shape="box"];21632[label="ywz5000",fontsize=16,color="green",shape="box"];21633[label="ywz42",fontsize=16,color="green",shape="box"];21634[label="ywz3",fontsize=16,color="green",shape="box"];21635 -> 12118[label="",style="dashed", color="red", weight=0]; 21635[label="GT == LT",fontsize=16,color="magenta"];21636[label="Neg ywz400",fontsize=16,color="green",shape="box"];21637[label="ywz400",fontsize=16,color="green",shape="box"];21638[label="ywz51",fontsize=16,color="green",shape="box"];21639[label="ywz42",fontsize=16,color="green",shape="box"];21640[label="ywz43",fontsize=16,color="green",shape="box"];21641[label="ywz41",fontsize=16,color="green",shape="box"];21642[label="ywz44",fontsize=16,color="green",shape="box"];21643[label="ywz41",fontsize=16,color="green",shape="box"];21644[label="ywz44",fontsize=16,color="green",shape="box"];21630[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM2 ywz1894 ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) ywz1900)",fontsize=16,color="burlywood",shape="triangle"];25525[label="ywz1900/False",fontsize=10,color="white",style="solid",shape="box"];21630 -> 25525[label="",style="solid", color="burlywood", weight=9]; 25525 -> 21660[label="",style="solid", color="burlywood", weight=3]; 25526[label="ywz1900/True",fontsize=10,color="white",style="solid",shape="box"];21630 -> 25526[label="",style="solid", color="burlywood", weight=9]; 25526 -> 21661[label="",style="solid", color="burlywood", weight=3]; 668 -> 22575[label="",style="dashed", color="red", weight=0]; 668[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpNat Zero (Succ ywz4000) == LT))",fontsize=16,color="magenta"];668 -> 22576[label="",style="dashed", color="magenta", weight=3]; 668 -> 22577[label="",style="dashed", color="magenta", weight=3]; 668 -> 22578[label="",style="dashed", color="magenta", weight=3]; 668 -> 22579[label="",style="dashed", color="magenta", weight=3]; 668 -> 22580[label="",style="dashed", color="magenta", weight=3]; 668 -> 22581[label="",style="dashed", color="magenta", weight=3]; 668 -> 22582[label="",style="dashed", color="magenta", weight=3]; 668 -> 22583[label="",style="dashed", color="magenta", weight=3]; 668 -> 22584[label="",style="dashed", color="magenta", weight=3]; 668 -> 22585[label="",style="dashed", color="magenta", weight=3]; 668 -> 22586[label="",style="dashed", color="magenta", weight=3]; 668 -> 22587[label="",style="dashed", color="magenta", weight=3]; 668 -> 22588[label="",style="dashed", color="magenta", weight=3]; 669[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == LT))",fontsize=16,color="black",shape="box"];669 -> 801[label="",style="solid", color="black", weight=3]; 670 -> 21916[label="",style="dashed", color="red", weight=0]; 670[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (GT == LT))",fontsize=16,color="magenta"];670 -> 21917[label="",style="dashed", color="magenta", weight=3]; 670 -> 21918[label="",style="dashed", color="magenta", weight=3]; 670 -> 21919[label="",style="dashed", color="magenta", weight=3]; 670 -> 21920[label="",style="dashed", color="magenta", weight=3]; 670 -> 21921[label="",style="dashed", color="magenta", weight=3]; 670 -> 21922[label="",style="dashed", color="magenta", weight=3]; 670 -> 21923[label="",style="dashed", color="magenta", weight=3]; 670 -> 21924[label="",style="dashed", color="magenta", weight=3]; 670 -> 21925[label="",style="dashed", color="magenta", weight=3]; 670 -> 21926[label="",style="dashed", color="magenta", weight=3]; 670 -> 21927[label="",style="dashed", color="magenta", weight=3]; 670 -> 21928[label="",style="dashed", color="magenta", weight=3]; 670 -> 21929[label="",style="dashed", color="magenta", weight=3]; 671[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == LT))",fontsize=16,color="black",shape="box"];671 -> 803[label="",style="solid", color="black", weight=3]; 19815[label="ywz42",fontsize=16,color="green",shape="box"];19816[label="ywz44",fontsize=16,color="green",shape="box"];19817[label="ywz3",fontsize=16,color="green",shape="box"];19818[label="ywz43",fontsize=16,color="green",shape="box"];19819 -> 12125[label="",style="dashed", color="red", weight=0]; 19819[label="LT == LT",fontsize=16,color="magenta"];19820[label="Pos ywz400",fontsize=16,color="green",shape="box"];19821[label="ywz43",fontsize=16,color="green",shape="box"];19822[label="ywz41",fontsize=16,color="green",shape="box"];19823[label="ywz400",fontsize=16,color="green",shape="box"];19824[label="ywz51",fontsize=16,color="green",shape="box"];19825[label="ywz41",fontsize=16,color="green",shape="box"];19826[label="ywz42",fontsize=16,color="green",shape="box"];19827[label="ywz44",fontsize=16,color="green",shape="box"];19828[label="ywz5000",fontsize=16,color="green",shape="box"];19814[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM2 ywz1702 ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) ywz1708)",fontsize=16,color="burlywood",shape="triangle"];25527[label="ywz1708/False",fontsize=10,color="white",style="solid",shape="box"];19814 -> 25527[label="",style="solid", color="burlywood", weight=9]; 25527 -> 19844[label="",style="solid", color="burlywood", weight=3]; 25528[label="ywz1708/True",fontsize=10,color="white",style="solid",shape="box"];19814 -> 25528[label="",style="solid", color="burlywood", weight=9]; 25528 -> 19845[label="",style="solid", color="burlywood", weight=3]; 673[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44) (Neg (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat (Succ ywz4000) (Succ ywz5000) == LT))",fontsize=16,color="black",shape="box"];673 -> 805[label="",style="solid", color="black", weight=3]; 674[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat Zero (Succ ywz5000) == LT))",fontsize=16,color="black",shape="box"];674 -> 806[label="",style="solid", color="black", weight=3]; 675 -> 22320[label="",style="dashed", color="red", weight=0]; 675[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (LT == LT))",fontsize=16,color="magenta"];675 -> 22321[label="",style="dashed", color="magenta", weight=3]; 675 -> 22322[label="",style="dashed", color="magenta", weight=3]; 675 -> 22323[label="",style="dashed", color="magenta", weight=3]; 675 -> 22324[label="",style="dashed", color="magenta", weight=3]; 675 -> 22325[label="",style="dashed", color="magenta", weight=3]; 675 -> 22326[label="",style="dashed", color="magenta", weight=3]; 675 -> 22327[label="",style="dashed", color="magenta", weight=3]; 675 -> 22328[label="",style="dashed", color="magenta", weight=3]; 675 -> 22329[label="",style="dashed", color="magenta", weight=3]; 675 -> 22330[label="",style="dashed", color="magenta", weight=3]; 675 -> 22331[label="",style="dashed", color="magenta", weight=3]; 675 -> 22332[label="",style="dashed", color="magenta", weight=3]; 675 -> 22333[label="",style="dashed", color="magenta", weight=3]; 676[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == LT))",fontsize=16,color="black",shape="box"];676 -> 808[label="",style="solid", color="black", weight=3]; 677 -> 24654[label="",style="dashed", color="red", weight=0]; 677[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpNat (Succ ywz4000) Zero == LT))",fontsize=16,color="magenta"];677 -> 24655[label="",style="dashed", color="magenta", weight=3]; 677 -> 24656[label="",style="dashed", color="magenta", weight=3]; 677 -> 24657[label="",style="dashed", color="magenta", weight=3]; 677 -> 24658[label="",style="dashed", color="magenta", weight=3]; 677 -> 24659[label="",style="dashed", color="magenta", weight=3]; 677 -> 24660[label="",style="dashed", color="magenta", weight=3]; 677 -> 24661[label="",style="dashed", color="magenta", weight=3]; 677 -> 24662[label="",style="dashed", color="magenta", weight=3]; 677 -> 24663[label="",style="dashed", color="magenta", weight=3]; 677 -> 24664[label="",style="dashed", color="magenta", weight=3]; 677 -> 24665[label="",style="dashed", color="magenta", weight=3]; 677 -> 24666[label="",style="dashed", color="magenta", weight=3]; 677 -> 24667[label="",style="dashed", color="magenta", weight=3]; 678[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == LT))",fontsize=16,color="black",shape="box"];678 -> 810[label="",style="solid", color="black", weight=3]; 13111[label="ywz103700",fontsize=16,color="green",shape="box"];1424[label="primMulNat (Succ (Succ (Succ (Succ Zero)))) (Succ ywz7200)",fontsize=16,color="black",shape="triangle"];1424 -> 1536[label="",style="solid", color="black", weight=3]; 5654[label="primPlusNat (Succ ywz250000) ywz37200",fontsize=16,color="burlywood",shape="box"];25529[label="ywz37200/Succ ywz372000",fontsize=10,color="white",style="solid",shape="box"];5654 -> 25529[label="",style="solid", color="burlywood", weight=9]; 25529 -> 5813[label="",style="solid", color="burlywood", weight=3]; 25530[label="ywz37200/Zero",fontsize=10,color="white",style="solid",shape="box"];5654 -> 25530[label="",style="solid", color="burlywood", weight=9]; 25530 -> 5814[label="",style="solid", color="burlywood", weight=3]; 5655[label="primPlusNat Zero ywz37200",fontsize=16,color="burlywood",shape="box"];25531[label="ywz37200/Succ ywz372000",fontsize=10,color="white",style="solid",shape="box"];5655 -> 25531[label="",style="solid", color="burlywood", weight=9]; 25531 -> 5815[label="",style="solid", color="burlywood", weight=3]; 25532[label="ywz37200/Zero",fontsize=10,color="white",style="solid",shape="box"];5655 -> 25532[label="",style="solid", color="burlywood", weight=9]; 25532 -> 5816[label="",style="solid", color="burlywood", weight=3]; 13015[label="primCmpNat (Succ ywz821000) (Succ ywz811000) == LT",fontsize=16,color="black",shape="box"];13015 -> 13070[label="",style="solid", color="black", weight=3]; 13016[label="primCmpNat (Succ ywz821000) Zero == LT",fontsize=16,color="black",shape="box"];13016 -> 13071[label="",style="solid", color="black", weight=3]; 13017[label="primCmpNat Zero (Succ ywz811000) == LT",fontsize=16,color="black",shape="box"];13017 -> 13072[label="",style="solid", color="black", weight=3]; 13018[label="primCmpNat Zero Zero == LT",fontsize=16,color="black",shape="box"];13018 -> 13073[label="",style="solid", color="black", weight=3]; 15480 -> 15508[label="",style="dashed", color="red", weight=0]; 15480[label="FiniteMap.mkBranchUnbox ywz1238 ywz1235 ywz1237 (Pos (Succ Zero) + FiniteMap.mkBranchLeft_size ywz1238 ywz1235 ywz1237 + FiniteMap.mkBranchRight_size ywz1238 ywz1235 ywz1237)",fontsize=16,color="magenta"];15480 -> 15509[label="",style="dashed", color="magenta", weight=3]; 14505 -> 14438[label="",style="dashed", color="red", weight=0]; 14505[label="FiniteMap.addToFM (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634) ywz50 ywz9",fontsize=16,color="magenta"];14505 -> 14538[label="",style="dashed", color="magenta", weight=3]; 14505 -> 14539[label="",style="dashed", color="magenta", weight=3]; 14505 -> 14540[label="",style="dashed", color="magenta", weight=3]; 14505 -> 14541[label="",style="dashed", color="magenta", weight=3]; 14505 -> 14542[label="",style="dashed", color="magenta", weight=3]; 14506[label="ywz632",fontsize=16,color="green",shape="box"];14507[label="ywz7441",fontsize=16,color="green",shape="box"];14508[label="ywz630",fontsize=16,color="green",shape="box"];14509[label="ywz631",fontsize=16,color="green",shape="box"];14510[label="ywz7443",fontsize=16,color="green",shape="box"];14511[label="ywz7440",fontsize=16,color="green",shape="box"];14512[label="ywz634",fontsize=16,color="green",shape="box"];14513[label="ywz7442",fontsize=16,color="green",shape="box"];14514[label="ywz7444",fontsize=16,color="green",shape="box"];14515[label="ywz633",fontsize=16,color="green",shape="box"];14516 -> 14433[label="",style="dashed", color="red", weight=0]; 14516[label="FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)",fontsize=16,color="magenta"];14517[label="ywz740",fontsize=16,color="green",shape="box"];14518[label="ywz741",fontsize=16,color="green",shape="box"];14519[label="ywz743",fontsize=16,color="green",shape="box"];14520 -> 14433[label="",style="dashed", color="red", weight=0]; 14520[label="FiniteMap.mkVBalBranch ywz50 ywz9 ywz744 (FiniteMap.Branch ywz630 ywz631 ywz632 ywz633 ywz634)",fontsize=16,color="magenta"];14521[label="ywz740",fontsize=16,color="green",shape="box"];14522[label="ywz741",fontsize=16,color="green",shape="box"];14523[label="ywz743",fontsize=16,color="green",shape="box"];14524 -> 14543[label="",style="dashed", color="red", weight=0]; 14524[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 ywz740 ywz741 ywz742 ywz743 ywz744 ywz50 ywz9 (ywz50 < ywz740)",fontsize=16,color="magenta"];14524 -> 14780[label="",style="dashed", color="magenta", weight=3]; 14525 -> 14138[label="",style="dashed", color="red", weight=0]; 14525[label="FiniteMap.mkVBalBranch3Size_l ywz740 ywz741 ywz742 ywz743 ywz744 ywz6330 ywz6331 ywz6332 ywz6333 ywz6334",fontsize=16,color="magenta"];14525 -> 14993[label="",style="dashed", color="magenta", weight=3]; 14525 -> 14994[label="",style="dashed", color="magenta", weight=3]; 14525 -> 14995[label="",style="dashed", color="magenta", weight=3]; 14525 -> 14996[label="",style="dashed", color="magenta", weight=3]; 14525 -> 14997[label="",style="dashed", color="magenta", weight=3]; 14525 -> 14998[label="",style="dashed", color="magenta", weight=3]; 14525 -> 14999[label="",style="dashed", color="magenta", weight=3]; 14525 -> 15000[label="",style="dashed", color="magenta", weight=3]; 14525 -> 15001[label="",style="dashed", color="magenta", weight=3]; 14525 -> 15002[label="",style="dashed", color="magenta", weight=3]; 14526[label="ywz743",fontsize=16,color="green",shape="box"];14527[label="ywz6330",fontsize=16,color="green",shape="box"];14528[label="ywz6332",fontsize=16,color="green",shape="box"];14529[label="ywz6331",fontsize=16,color="green",shape="box"];14530[label="ywz6334",fontsize=16,color="green",shape="box"];14531[label="ywz6333",fontsize=16,color="green",shape="box"];14532[label="ywz744",fontsize=16,color="green",shape="box"];14533[label="ywz740",fontsize=16,color="green",shape="box"];14534[label="ywz741",fontsize=16,color="green",shape="box"];14535[label="ywz742",fontsize=16,color="green",shape="box"];12933[label="Pos (primPlusNat ywz10490 ywz10480)",fontsize=16,color="green",shape="box"];12933 -> 13003[label="",style="dashed", color="green", weight=3]; 12934[label="primMinusNat ywz10490 ywz10480",fontsize=16,color="burlywood",shape="triangle"];25533[label="ywz10490/Succ ywz104900",fontsize=10,color="white",style="solid",shape="box"];12934 -> 25533[label="",style="solid", color="burlywood", weight=9]; 25533 -> 13004[label="",style="solid", color="burlywood", weight=3]; 25534[label="ywz10490/Zero",fontsize=10,color="white",style="solid",shape="box"];12934 -> 25534[label="",style="solid", color="burlywood", weight=9]; 25534 -> 13005[label="",style="solid", color="burlywood", weight=3]; 12935 -> 12934[label="",style="dashed", color="red", weight=0]; 12935[label="primMinusNat ywz10480 ywz10490",fontsize=16,color="magenta"];12935 -> 13006[label="",style="dashed", color="magenta", weight=3]; 12935 -> 13007[label="",style="dashed", color="magenta", weight=3]; 12936[label="Neg (primPlusNat ywz10490 ywz10480)",fontsize=16,color="green",shape="box"];12936 -> 13008[label="",style="dashed", color="green", weight=3]; 13554 -> 13515[label="",style="dashed", color="red", weight=0]; 13554[label="FiniteMap.mkBalBranch6Size_r ywz1007 ywz73 ywz70 ywz71",fontsize=16,color="magenta"];13554 -> 13579[label="",style="dashed", color="magenta", weight=3]; 13554 -> 13580[label="",style="dashed", color="magenta", weight=3]; 13554 -> 13581[label="",style="dashed", color="magenta", weight=3]; 13554 -> 13582[label="",style="dashed", color="magenta", weight=3]; 13553[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt ywz1157 ywz1154 == GT)",fontsize=16,color="burlywood",shape="triangle"];25535[label="ywz1157/Pos ywz11570",fontsize=10,color="white",style="solid",shape="box"];13553 -> 25535[label="",style="solid", color="burlywood", weight=9]; 25535 -> 13583[label="",style="solid", color="burlywood", weight=3]; 25536[label="ywz1157/Neg ywz11570",fontsize=10,color="white",style="solid",shape="box"];13553 -> 25536[label="",style="solid", color="burlywood", weight=9]; 25536 -> 13584[label="",style="solid", color="burlywood", weight=3]; 6374[label="ywz4330",fontsize=16,color="green",shape="box"];6375[label="ywz4340",fontsize=16,color="green",shape="box"];6376[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) False",fontsize=16,color="black",shape="triangle"];6376 -> 6488[label="",style="solid", color="black", weight=3]; 6377[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) True",fontsize=16,color="black",shape="box"];6377 -> 6489[label="",style="solid", color="black", weight=3]; 6378 -> 6376[label="",style="dashed", color="red", weight=0]; 6378[label="FiniteMap.splitLT2 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) False",fontsize=16,color="magenta"];447[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat (Succ ywz5000) Zero == GT)",fontsize=16,color="black",shape="box"];447 -> 534[label="",style="solid", color="black", weight=3]; 448[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 ywz43 (FiniteMap.splitLT ywz44 (Pos (Succ ywz5000)))",fontsize=16,color="burlywood",shape="box"];25537[label="ywz43/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];448 -> 25537[label="",style="solid", color="burlywood", weight=9]; 25537 -> 535[label="",style="solid", color="burlywood", weight=3]; 25538[label="ywz43/FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434",fontsize=10,color="white",style="solid",shape="box"];448 -> 25538[label="",style="solid", color="burlywood", weight=9]; 25538 -> 536[label="",style="solid", color="burlywood", weight=3]; 449 -> 83[label="",style="dashed", color="red", weight=0]; 449[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];450[label="ywz434",fontsize=16,color="green",shape="box"];451[label="ywz432",fontsize=16,color="green",shape="box"];452[label="ywz431",fontsize=16,color="green",shape="box"];453[label="ywz433",fontsize=16,color="green",shape="box"];454[label="ywz430",fontsize=16,color="green",shape="box"];455[label="Pos Zero",fontsize=16,color="green",shape="box"];456[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];456 -> 537[label="",style="solid", color="black", weight=3]; 457[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True",fontsize=16,color="black",shape="box"];457 -> 538[label="",style="solid", color="black", weight=3]; 458[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];458 -> 539[label="",style="solid", color="black", weight=3]; 6483[label="ywz4420",fontsize=16,color="green",shape="box"];6484[label="ywz4430",fontsize=16,color="green",shape="box"];6485[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) False",fontsize=16,color="black",shape="triangle"];6485 -> 6525[label="",style="solid", color="black", weight=3]; 6486[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) True",fontsize=16,color="black",shape="box"];6486 -> 6526[label="",style="solid", color="black", weight=3]; 6487 -> 6485[label="",style="dashed", color="red", weight=0]; 6487[label="FiniteMap.splitLT2 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) False",fontsize=16,color="magenta"];466[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];466 -> 547[label="",style="solid", color="black", weight=3]; 467[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpNat (Succ ywz4000) Zero == GT)",fontsize=16,color="black",shape="box"];467 -> 548[label="",style="solid", color="black", weight=3]; 468[label="FiniteMap.splitLT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];468 -> 549[label="",style="solid", color="black", weight=3]; 6520[label="ywz4510",fontsize=16,color="green",shape="box"];6521[label="ywz4520",fontsize=16,color="green",shape="box"];6522[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) True",fontsize=16,color="black",shape="box"];6522 -> 6599[label="",style="solid", color="black", weight=3]; 6523[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) False",fontsize=16,color="black",shape="triangle"];6523 -> 6600[label="",style="solid", color="black", weight=3]; 6524 -> 6523[label="",style="dashed", color="red", weight=0]; 6524[label="FiniteMap.splitGT2 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) False",fontsize=16,color="magenta"];476[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpNat Zero (Succ ywz4000) == LT)",fontsize=16,color="black",shape="box"];476 -> 557[label="",style="solid", color="black", weight=3]; 477[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];477 -> 558[label="",style="solid", color="black", weight=3]; 478[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False",fontsize=16,color="black",shape="box"];478 -> 559[label="",style="solid", color="black", weight=3]; 479 -> 759[label="",style="dashed", color="red", weight=0]; 479[label="FiniteMap.mkVBalBranch (Pos ywz400) ywz41 (FiniteMap.splitGT ywz43 (Neg (Succ ywz5000))) ywz44",fontsize=16,color="magenta"];479 -> 760[label="",style="dashed", color="magenta", weight=3]; 6594[label="ywz4610",fontsize=16,color="green",shape="box"];6595[label="ywz4600",fontsize=16,color="green",shape="box"];6596[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) True",fontsize=16,color="black",shape="box"];6596 -> 6697[label="",style="solid", color="black", weight=3]; 6597[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) False",fontsize=16,color="black",shape="triangle"];6597 -> 6698[label="",style="solid", color="black", weight=3]; 6598 -> 6597[label="",style="dashed", color="red", weight=0]; 6598[label="FiniteMap.splitGT2 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) False",fontsize=16,color="magenta"];487[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat Zero (Succ ywz5000) == LT)",fontsize=16,color="black",shape="box"];487 -> 570[label="",style="solid", color="black", weight=3]; 488[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True",fontsize=16,color="black",shape="box"];488 -> 571[label="",style="solid", color="black", weight=3]; 489[label="FiniteMap.splitGT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];489 -> 572[label="",style="solid", color="black", weight=3]; 490 -> 83[label="",style="dashed", color="red", weight=0]; 490[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];491[label="ywz444",fontsize=16,color="green",shape="box"];492[label="ywz442",fontsize=16,color="green",shape="box"];493[label="ywz441",fontsize=16,color="green",shape="box"];494[label="ywz443",fontsize=16,color="green",shape="box"];495[label="ywz440",fontsize=16,color="green",shape="box"];496[label="Neg Zero",fontsize=16,color="green",shape="box"];497[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False",fontsize=16,color="black",shape="box"];497 -> 573[label="",style="solid", color="black", weight=3]; 15376[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 (primCmpNat (Succ ywz5000) (Succ ywz74000) == GT)",fontsize=16,color="black",shape="box"];15376 -> 15439[label="",style="solid", color="black", weight=3]; 15377[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 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GT)",fontsize=16,color="black",shape="box"];15381 -> 15444[label="",style="solid", color="black", weight=3]; 15382[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 (EQ == GT)",fontsize=16,color="black",shape="box"];15382 -> 15445[label="",style="solid", color="black", weight=3]; 15383[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos ywz7400) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 False",fontsize=16,color="black",shape="box"];15383 -> 15446[label="",style="solid", color="black", weight=3]; 15384[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 (primCmpNat (Succ ywz74000) (Succ ywz5000) == GT)",fontsize=16,color="black",shape="box"];15384 -> 15447[label="",style="solid", color="black", weight=3]; 15385[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 (primCmpNat Zero (Succ ywz5000) == GT)",fontsize=16,color="black",shape="box"];15385 -> 15448[label="",style="solid", color="black", weight=3]; 15386[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (LT == GT)",fontsize=16,color="black",shape="box"];15386 -> 15449[label="",style="solid", color="black", weight=3]; 15387[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (EQ == GT)",fontsize=16,color="black",shape="box"];15387 -> 15450[label="",style="solid", color="black", weight=3]; 15388[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (primCmpNat (Succ ywz74000) Zero == GT)",fontsize=16,color="black",shape="box"];15388 -> 15451[label="",style="solid", color="black", weight=3]; 15389[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (EQ == GT)",fontsize=16,color="black",shape="box"];15389 -> 15452[label="",style="solid", color="black", weight=3]; 15390[label="FiniteMap.Branch ywz50 ywz9 (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];15390 -> 15453[label="",style="dashed", color="green", weight=3]; 15390 -> 15454[label="",style="dashed", color="green", weight=3]; 797 -> 17540[label="",style="dashed", color="red", weight=0]; 797[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44) (Pos (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (primCmpNat ywz5000 ywz4000 == LT))",fontsize=16,color="magenta"];797 -> 17541[label="",style="dashed", color="magenta", weight=3]; 797 -> 17542[label="",style="dashed", color="magenta", weight=3]; 797 -> 17543[label="",style="dashed", color="magenta", weight=3]; 797 -> 17544[label="",style="dashed", color="magenta", weight=3]; 797 -> 17545[label="",style="dashed", color="magenta", weight=3]; 797 -> 17546[label="",style="dashed", color="magenta", weight=3]; 797 -> 17547[label="",style="dashed", color="magenta", weight=3]; 797 -> 17548[label="",style="dashed", color="magenta", weight=3]; 797 -> 17549[label="",style="dashed", color="magenta", weight=3]; 797 -> 17550[label="",style="dashed", color="magenta", weight=3]; 797 -> 17551[label="",style="dashed", color="magenta", weight=3]; 797 -> 17552[label="",style="dashed", color="magenta", weight=3]; 797 -> 17553[label="",style="dashed", color="magenta", weight=3]; 797 -> 17554[label="",style="dashed", color="magenta", weight=3]; 798 -> 21600[label="",style="dashed", color="red", weight=0]; 798[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (GT == LT))",fontsize=16,color="magenta"];798 -> 21601[label="",style="dashed", color="magenta", weight=3]; 798 -> 21602[label="",style="dashed", color="magenta", weight=3]; 798 -> 21603[label="",style="dashed", color="magenta", weight=3]; 798 -> 21604[label="",style="dashed", color="magenta", weight=3]; 798 -> 21605[label="",style="dashed", color="magenta", weight=3]; 798 -> 21606[label="",style="dashed", color="magenta", weight=3]; 798 -> 21607[label="",style="dashed", color="magenta", weight=3]; 798 -> 21608[label="",style="dashed", color="magenta", weight=3]; 798 -> 21609[label="",style="dashed", color="magenta", weight=3]; 798 -> 21610[label="",style="dashed", color="magenta", weight=3]; 798 -> 21611[label="",style="dashed", color="magenta", weight=3]; 798 -> 21612[label="",style="dashed", color="magenta", weight=3]; 798 -> 21613[label="",style="dashed", color="magenta", weight=3]; 21660[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM2 ywz1894 ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) False)",fontsize=16,color="black",shape="box"];21660 -> 21686[label="",style="solid", color="black", weight=3]; 21661[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM2 ywz1894 ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) True)",fontsize=16,color="black",shape="box"];21661 -> 21687[label="",style="solid", color="black", weight=3]; 22576[label="ywz41",fontsize=16,color="green",shape="box"];22577[label="ywz42",fontsize=16,color="green",shape="box"];22578[label="Pos (Succ ywz4000)",fontsize=16,color="green",shape="box"];22579 -> 12889[label="",style="dashed", color="red", weight=0]; 22579[label="primCmpNat Zero (Succ ywz4000) == LT",fontsize=16,color="magenta"];22579 -> 22629[label="",style="dashed", color="magenta", weight=3]; 22579 -> 22630[label="",style="dashed", color="magenta", weight=3]; 22580[label="ywz43",fontsize=16,color="green",shape="box"];22581[label="ywz41",fontsize=16,color="green",shape="box"];22582[label="ywz42",fontsize=16,color="green",shape="box"];22583[label="ywz4000",fontsize=16,color="green",shape="box"];22584[label="ywz43",fontsize=16,color="green",shape="box"];22585[label="ywz44",fontsize=16,color="green",shape="box"];22586[label="ywz51",fontsize=16,color="green",shape="box"];22587[label="ywz44",fontsize=16,color="green",shape="box"];22588[label="ywz3",fontsize=16,color="green",shape="box"];22575[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM2 ywz2034 ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) ywz2039)",fontsize=16,color="burlywood",shape="triangle"];25539[label="ywz2039/False",fontsize=10,color="white",style="solid",shape="box"];22575 -> 25539[label="",style="solid", color="burlywood", weight=9]; 25539 -> 22631[label="",style="solid", color="burlywood", weight=3]; 25540[label="ywz2039/True",fontsize=10,color="white",style="solid",shape="box"];22575 -> 25540[label="",style="solid", color="burlywood", weight=9]; 25540 -> 22632[label="",style="solid", color="burlywood", weight=3]; 801[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False)",fontsize=16,color="black",shape="box"];801 -> 913[label="",style="solid", color="black", weight=3]; 21917[label="ywz42",fontsize=16,color="green",shape="box"];21918[label="ywz44",fontsize=16,color="green",shape="box"];21919 -> 12118[label="",style="dashed", color="red", weight=0]; 21919[label="GT == LT",fontsize=16,color="magenta"];21920[label="Neg (Succ ywz4000)",fontsize=16,color="green",shape="box"];21921[label="ywz42",fontsize=16,color="green",shape="box"];21922[label="ywz41",fontsize=16,color="green",shape="box"];21923[label="ywz51",fontsize=16,color="green",shape="box"];21924[label="ywz43",fontsize=16,color="green",shape="box"];21925[label="ywz3",fontsize=16,color="green",shape="box"];21926[label="ywz4000",fontsize=16,color="green",shape="box"];21927[label="ywz43",fontsize=16,color="green",shape="box"];21928[label="ywz44",fontsize=16,color="green",shape="box"];21929[label="ywz41",fontsize=16,color="green",shape="box"];21916[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM2 ywz1949 ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) ywz1954)",fontsize=16,color="burlywood",shape="triangle"];25541[label="ywz1954/False",fontsize=10,color="white",style="solid",shape="box"];21916 -> 25541[label="",style="solid", color="burlywood", weight=9]; 25541 -> 21957[label="",style="solid", color="burlywood", weight=3]; 25542[label="ywz1954/True",fontsize=10,color="white",style="solid",shape="box"];21916 -> 25542[label="",style="solid", color="burlywood", weight=9]; 25542 -> 21958[label="",style="solid", color="burlywood", weight=3]; 803[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False)",fontsize=16,color="black",shape="box"];803 -> 915[label="",style="solid", color="black", weight=3]; 19844[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM2 ywz1702 ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) False)",fontsize=16,color="black",shape="box"];19844 -> 19860[label="",style="solid", color="black", weight=3]; 19845[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM2 ywz1702 ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) True)",fontsize=16,color="black",shape="box"];19845 -> 19861[label="",style="solid", color="black", weight=3]; 805 -> 18018[label="",style="dashed", color="red", weight=0]; 805[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44) (Neg (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (primCmpNat ywz4000 ywz5000 == LT))",fontsize=16,color="magenta"];805 -> 18019[label="",style="dashed", color="magenta", weight=3]; 805 -> 18020[label="",style="dashed", color="magenta", weight=3]; 805 -> 18021[label="",style="dashed", color="magenta", weight=3]; 805 -> 18022[label="",style="dashed", color="magenta", weight=3]; 805 -> 18023[label="",style="dashed", color="magenta", weight=3]; 805 -> 18024[label="",style="dashed", color="magenta", weight=3]; 805 -> 18025[label="",style="dashed", color="magenta", weight=3]; 805 -> 18026[label="",style="dashed", color="magenta", weight=3]; 805 -> 18027[label="",style="dashed", color="magenta", weight=3]; 805 -> 18028[label="",style="dashed", color="magenta", weight=3]; 805 -> 18029[label="",style="dashed", color="magenta", weight=3]; 805 -> 18030[label="",style="dashed", color="magenta", weight=3]; 805 -> 18031[label="",style="dashed", color="magenta", weight=3]; 805 -> 18032[label="",style="dashed", color="magenta", weight=3]; 806 -> 20444[label="",style="dashed", color="red", weight=0]; 806[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg (Succ ywz5000)) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (LT == LT))",fontsize=16,color="magenta"];806 -> 20445[label="",style="dashed", color="magenta", weight=3]; 806 -> 20446[label="",style="dashed", color="magenta", weight=3]; 806 -> 20447[label="",style="dashed", color="magenta", weight=3]; 806 -> 20448[label="",style="dashed", color="magenta", weight=3]; 806 -> 20449[label="",style="dashed", color="magenta", weight=3]; 806 -> 20450[label="",style="dashed", color="magenta", weight=3]; 806 -> 20451[label="",style="dashed", color="magenta", weight=3]; 806 -> 20452[label="",style="dashed", color="magenta", weight=3]; 806 -> 20453[label="",style="dashed", color="magenta", weight=3]; 806 -> 20454[label="",style="dashed", color="magenta", weight=3]; 806 -> 20455[label="",style="dashed", color="magenta", weight=3]; 806 -> 20456[label="",style="dashed", color="magenta", weight=3]; 806 -> 20457[label="",style="dashed", color="magenta", weight=3]; 22321[label="ywz43",fontsize=16,color="green",shape="box"];22322[label="ywz51",fontsize=16,color="green",shape="box"];22323[label="Pos (Succ ywz4000)",fontsize=16,color="green",shape="box"];22324[label="ywz3",fontsize=16,color="green",shape="box"];22325[label="ywz44",fontsize=16,color="green",shape="box"];22326 -> 12125[label="",style="dashed", color="red", weight=0]; 22326[label="LT == LT",fontsize=16,color="magenta"];22327[label="ywz43",fontsize=16,color="green",shape="box"];22328[label="ywz4000",fontsize=16,color="green",shape="box"];22329[label="ywz42",fontsize=16,color="green",shape="box"];22330[label="ywz41",fontsize=16,color="green",shape="box"];22331[label="ywz44",fontsize=16,color="green",shape="box"];22332[label="ywz41",fontsize=16,color="green",shape="box"];22333[label="ywz42",fontsize=16,color="green",shape="box"];22320[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM2 ywz2005 ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) ywz2024)",fontsize=16,color="burlywood",shape="triangle"];25543[label="ywz2024/False",fontsize=10,color="white",style="solid",shape="box"];22320 -> 25543[label="",style="solid", color="burlywood", weight=9]; 25543 -> 22348[label="",style="solid", color="burlywood", weight=3]; 25544[label="ywz2024/True",fontsize=10,color="white",style="solid",shape="box"];22320 -> 25544[label="",style="solid", color="burlywood", weight=9]; 25544 -> 22349[label="",style="solid", color="burlywood", weight=3]; 808[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False)",fontsize=16,color="black",shape="box"];808 -> 922[label="",style="solid", color="black", weight=3]; 24655[label="ywz41",fontsize=16,color="green",shape="box"];24656[label="ywz44",fontsize=16,color="green",shape="box"];24657[label="ywz51",fontsize=16,color="green",shape="box"];24658[label="ywz44",fontsize=16,color="green",shape="box"];24659[label="ywz41",fontsize=16,color="green",shape="box"];24660[label="ywz43",fontsize=16,color="green",shape="box"];24661[label="ywz42",fontsize=16,color="green",shape="box"];24662[label="ywz42",fontsize=16,color="green",shape="box"];24663[label="ywz4000",fontsize=16,color="green",shape="box"];24664[label="ywz3",fontsize=16,color="green",shape="box"];24665[label="ywz43",fontsize=16,color="green",shape="box"];24666 -> 12889[label="",style="dashed", color="red", weight=0]; 24666[label="primCmpNat (Succ ywz4000) Zero == LT",fontsize=16,color="magenta"];24666 -> 24695[label="",style="dashed", color="magenta", weight=3]; 24666 -> 24696[label="",style="dashed", color="magenta", weight=3]; 24667[label="Neg (Succ ywz4000)",fontsize=16,color="green",shape="box"];24654[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM2 ywz2383 ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) ywz2404)",fontsize=16,color="burlywood",shape="triangle"];25545[label="ywz2404/False",fontsize=10,color="white",style="solid",shape="box"];24654 -> 25545[label="",style="solid", color="burlywood", weight=9]; 25545 -> 24697[label="",style="solid", color="burlywood", weight=3]; 25546[label="ywz2404/True",fontsize=10,color="white",style="solid",shape="box"];24654 -> 25546[label="",style="solid", color="burlywood", weight=9]; 25546 -> 24698[label="",style="solid", color="burlywood", weight=3]; 810[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM2 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) 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ywz811000 == LT",fontsize=16,color="magenta"];13070 -> 13143[label="",style="dashed", color="magenta", weight=3]; 13070 -> 13144[label="",style="dashed", color="magenta", weight=3]; 13071 -> 12118[label="",style="dashed", color="red", weight=0]; 13071[label="GT == LT",fontsize=16,color="magenta"];13072 -> 12125[label="",style="dashed", color="red", weight=0]; 13072[label="LT == LT",fontsize=16,color="magenta"];13073 -> 12117[label="",style="dashed", color="red", weight=0]; 13073[label="EQ == LT",fontsize=16,color="magenta"];15509 -> 12612[label="",style="dashed", color="red", weight=0]; 15509[label="Pos (Succ Zero) + FiniteMap.mkBranchLeft_size ywz1238 ywz1235 ywz1237 + FiniteMap.mkBranchRight_size ywz1238 ywz1235 ywz1237",fontsize=16,color="magenta"];15509 -> 15510[label="",style="dashed", color="magenta", weight=3]; 15509 -> 15511[label="",style="dashed", color="magenta", weight=3]; 15508[label="FiniteMap.mkBranchUnbox ywz1238 ywz1235 ywz1237 ywz1245",fontsize=16,color="black",shape="triangle"];15508 -> 15512[label="",style="solid", color="black", weight=3]; 14538[label="ywz631",fontsize=16,color="green",shape="box"];14539[label="ywz633",fontsize=16,color="green",shape="box"];14540[label="ywz630",fontsize=16,color="green",shape="box"];14541[label="ywz632",fontsize=16,color="green",shape="box"];14542[label="ywz634",fontsize=16,color="green",shape="box"];14780 -> 10999[label="",style="dashed", color="red", weight=0]; 14780[label="ywz50 < ywz740",fontsize=16,color="magenta"];14780 -> 15006[label="",style="dashed", color="magenta", weight=3]; 14780 -> 15007[label="",style="dashed", color="magenta", weight=3]; 14993[label="ywz743",fontsize=16,color="green",shape="box"];14994[label="ywz6330",fontsize=16,color="green",shape="box"];14995[label="ywz6332",fontsize=16,color="green",shape="box"];14996[label="ywz6331",fontsize=16,color="green",shape="box"];14997[label="ywz6334",fontsize=16,color="green",shape="box"];14998[label="ywz6333",fontsize=16,color="green",shape="box"];14999[label="ywz744",fontsize=16,color="green",shape="box"];15000[label="ywz740",fontsize=16,color="green",shape="box"];15001[label="ywz741",fontsize=16,color="green",shape="box"];15002[label="ywz742",fontsize=16,color="green",shape="box"];13003 -> 5537[label="",style="dashed", color="red", weight=0]; 13003[label="primPlusNat ywz10490 ywz10480",fontsize=16,color="magenta"];13003 -> 13051[label="",style="dashed", color="magenta", weight=3]; 13003 -> 13052[label="",style="dashed", color="magenta", weight=3]; 13004[label="primMinusNat (Succ ywz104900) ywz10480",fontsize=16,color="burlywood",shape="box"];25547[label="ywz10480/Succ ywz104800",fontsize=10,color="white",style="solid",shape="box"];13004 -> 25547[label="",style="solid", color="burlywood", weight=9]; 25547 -> 13053[label="",style="solid", color="burlywood", weight=3]; 25548[label="ywz10480/Zero",fontsize=10,color="white",style="solid",shape="box"];13004 -> 25548[label="",style="solid", color="burlywood", weight=9]; 25548 -> 13054[label="",style="solid", color="burlywood", weight=3]; 13005[label="primMinusNat Zero ywz10480",fontsize=16,color="burlywood",shape="box"];25549[label="ywz10480/Succ ywz104800",fontsize=10,color="white",style="solid",shape="box"];13005 -> 25549[label="",style="solid", color="burlywood", weight=9]; 25549 -> 13055[label="",style="solid", color="burlywood", weight=3]; 25550[label="ywz10480/Zero",fontsize=10,color="white",style="solid",shape="box"];13005 -> 25550[label="",style="solid", color="burlywood", weight=9]; 25550 -> 13056[label="",style="solid", color="burlywood", weight=3]; 13006[label="ywz10490",fontsize=16,color="green",shape="box"];13007[label="ywz10480",fontsize=16,color="green",shape="box"];13008 -> 5537[label="",style="dashed", color="red", weight=0]; 13008[label="primPlusNat ywz10490 ywz10480",fontsize=16,color="magenta"];13008 -> 13057[label="",style="dashed", color="magenta", weight=3]; 13008 -> 13058[label="",style="dashed", color="magenta", weight=3]; 13579[label="ywz1007",fontsize=16,color="green",shape="box"];13580[label="ywz70",fontsize=16,color="green",shape="box"];13581[label="ywz71",fontsize=16,color="green",shape="box"];13582[label="ywz73",fontsize=16,color="green",shape="box"];13583[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos ywz11570) ywz1154 == GT)",fontsize=16,color="burlywood",shape="box"];25551[label="ywz11570/Succ ywz115700",fontsize=10,color="white",style="solid",shape="box"];13583 -> 25551[label="",style="solid", color="burlywood", weight=9]; 25551 -> 13633[label="",style="solid", color="burlywood", weight=3]; 25552[label="ywz11570/Zero",fontsize=10,color="white",style="solid",shape="box"];13583 -> 25552[label="",style="solid", color="burlywood", weight=9]; 25552 -> 13634[label="",style="solid", color="burlywood", weight=3]; 13584[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg ywz11570) ywz1154 == GT)",fontsize=16,color="burlywood",shape="box"];25553[label="ywz11570/Succ ywz115700",fontsize=10,color="white",style="solid",shape="box"];13584 -> 25553[label="",style="solid", color="burlywood", weight=9]; 25553 -> 13635[label="",style="solid", color="burlywood", weight=3]; 25554[label="ywz11570/Zero",fontsize=10,color="white",style="solid",shape="box"];13584 -> 25554[label="",style="solid", color="burlywood", weight=9]; 25554 -> 13636[label="",style="solid", color="burlywood", weight=3]; 6488[label="FiniteMap.splitLT1 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (Pos (Succ ywz432) > Pos (Succ ywz427))",fontsize=16,color="black",shape="box"];6488 -> 6527[label="",style="solid", color="black", weight=3]; 6489 -> 767[label="",style="dashed", color="red", weight=0]; 6489[label="FiniteMap.splitLT ywz430 (Pos (Succ ywz432))",fontsize=16,color="magenta"];6489 -> 6528[label="",style="dashed", color="magenta", weight=3]; 6489 -> 6529[label="",style="dashed", color="magenta", weight=3]; 534[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) (GT == GT)",fontsize=16,color="black",shape="box"];534 -> 621[label="",style="solid", color="black", weight=3]; 535[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 FiniteMap.EmptyFM (FiniteMap.splitLT ywz44 (Pos (Succ ywz5000)))",fontsize=16,color="black",shape="box"];535 -> 622[label="",style="solid", color="black", weight=3]; 536[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (FiniteMap.splitLT ywz44 (Pos (Succ 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539[label="FiniteMap.splitLT0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];539 -> 628[label="",style="solid", color="black", weight=3]; 6525[label="FiniteMap.splitLT1 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (Neg (Succ ywz441) > Neg (Succ ywz436))",fontsize=16,color="black",shape="box"];6525 -> 6601[label="",style="solid", color="black", weight=3]; 6526 -> 156[label="",style="dashed", color="red", weight=0]; 6526[label="FiniteMap.splitLT ywz439 (Neg (Succ ywz441))",fontsize=16,color="magenta"];6526 -> 6602[label="",style="dashed", color="magenta", weight=3]; 6526 -> 6603[label="",style="dashed", color="magenta", weight=3]; 547[label="FiniteMap.splitLT0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];547 -> 636[label="",style="solid", color="black", weight=3]; 548[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (GT == GT)",fontsize=16,color="black",shape="box"];548 -> 637[label="",style="solid", color="black", weight=3]; 549[label="FiniteMap.splitLT0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];549 -> 638[label="",style="solid", color="black", weight=3]; 6599 -> 165[label="",style="dashed", color="red", weight=0]; 6599[label="FiniteMap.splitGT ywz449 (Pos (Succ ywz450))",fontsize=16,color="magenta"];6599 -> 6699[label="",style="dashed", color="magenta", weight=3]; 6599 -> 6700[label="",style="dashed", color="magenta", weight=3]; 6600 -> 20851[label="",style="dashed", color="red", weight=0]; 6600[label="FiniteMap.splitGT1 (Pos (Succ ywz445)) ywz446 ywz447 ywz448 ywz449 (Pos (Succ ywz450)) (Pos (Succ ywz450) < Pos (Succ ywz445))",fontsize=16,color="magenta"];6600 -> 20852[label="",style="dashed", color="magenta", weight=3]; 6600 -> 20853[label="",style="dashed", color="magenta", weight=3]; 6600 -> 20854[label="",style="dashed", color="magenta", weight=3]; 6600 -> 20855[label="",style="dashed", color="magenta", weight=3]; 6600 -> 20856[label="",style="dashed", color="magenta", weight=3]; 6600 -> 20857[label="",style="dashed", color="magenta", weight=3]; 6600 -> 20858[label="",style="dashed", color="magenta", weight=3]; 557[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (LT == LT)",fontsize=16,color="black",shape="box"];557 -> 646[label="",style="solid", color="black", weight=3]; 558[label="FiniteMap.splitGT0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];558 -> 647[label="",style="solid", color="black", weight=3]; 559[label="FiniteMap.splitGT0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) otherwise",fontsize=16,color="black",shape="box"];559 -> 648[label="",style="solid", color="black", weight=3]; 760[label="FiniteMap.splitGT ywz43 (Neg (Succ ywz5000))",fontsize=16,color="burlywood",shape="triangle"];25557[label="ywz43/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];760 -> 25557[label="",style="solid", color="burlywood", weight=9]; 25557 -> 773[label="",style="solid", color="burlywood", weight=3]; 25558[label="ywz43/FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434",fontsize=10,color="white",style="solid",shape="box"];760 -> 25558[label="",style="solid", color="burlywood", weight=9]; 25558 -> 774[label="",style="solid", color="burlywood", weight=3]; 759[label="FiniteMap.mkVBalBranch (Pos ywz400) ywz41 ywz12 ywz44",fontsize=16,color="burlywood",shape="triangle"];25559[label="ywz12/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];759 -> 25559[label="",style="solid", color="burlywood", weight=9]; 25559 -> 775[label="",style="solid", color="burlywood", weight=3]; 25560[label="ywz12/FiniteMap.Branch ywz120 ywz121 ywz122 ywz123 ywz124",fontsize=10,color="white",style="solid",shape="box"];759 -> 25560[label="",style="solid", color="burlywood", weight=9]; 25560 -> 776[label="",style="solid", color="burlywood", weight=3]; 6697 -> 760[label="",style="dashed", color="red", weight=0]; 6697[label="FiniteMap.splitGT ywz458 (Neg (Succ ywz459))",fontsize=16,color="magenta"];6697 -> 6719[label="",style="dashed", color="magenta", weight=3]; 6697 -> 6720[label="",style="dashed", color="magenta", weight=3]; 6698 -> 20997[label="",style="dashed", color="red", weight=0]; 6698[label="FiniteMap.splitGT1 (Neg (Succ ywz454)) ywz455 ywz456 ywz457 ywz458 (Neg (Succ ywz459)) (Neg (Succ ywz459) < Neg (Succ ywz454))",fontsize=16,color="magenta"];6698 -> 20998[label="",style="dashed", color="magenta", weight=3]; 6698 -> 20999[label="",style="dashed", color="magenta", weight=3]; 6698 -> 21000[label="",style="dashed", color="magenta", weight=3]; 6698 -> 21001[label="",style="dashed", color="magenta", weight=3]; 6698 -> 21002[label="",style="dashed", color="magenta", weight=3]; 6698 -> 21003[label="",style="dashed", color="magenta", weight=3]; 6698 -> 21004[label="",style="dashed", color="magenta", weight=3]; 570[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) (LT == LT)",fontsize=16,color="black",shape="box"];570 -> 660[label="",style="solid", color="black", weight=3]; 571 -> 759[label="",style="dashed", color="red", weight=0]; 571[label="FiniteMap.mkVBalBranch (Pos (Succ ywz4000)) ywz41 (FiniteMap.splitGT ywz43 (Neg Zero)) ywz44",fontsize=16,color="magenta"];571 -> 761[label="",style="dashed", color="magenta", weight=3]; 571 -> 762[label="",style="dashed", color="magenta", weight=3]; 572[label="FiniteMap.splitGT0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];572 -> 663[label="",style="solid", color="black", weight=3]; 573[label="FiniteMap.splitGT0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) otherwise",fontsize=16,color="black",shape="box"];573 -> 664[label="",style="solid", color="black", weight=3]; 15439 -> 16963[label="",style="dashed", color="red", weight=0]; 15439[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 (primCmpNat ywz5000 ywz74000 == GT)",fontsize=16,color="magenta"];15439 -> 16964[label="",style="dashed", color="magenta", weight=3]; 15439 -> 16965[label="",style="dashed", color="magenta", weight=3]; 15439 -> 16966[label="",style="dashed", color="magenta", weight=3]; 15439 -> 16967[label="",style="dashed", color="magenta", weight=3]; 15439 -> 16968[label="",style="dashed", color="magenta", weight=3]; 15439 -> 16969[label="",style="dashed", color="magenta", weight=3]; 15439 -> 16970[label="",style="dashed", color="magenta", weight=3]; 15439 -> 16971[label="",style="dashed", color="magenta", weight=3]; 15439 -> 16972[label="",style="dashed", color="magenta", weight=3]; 15440[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 (GT == GT)",fontsize=16,color="black",shape="box"];15440 -> 15477[label="",style="solid", color="black", weight=3]; 15441 -> 15478[label="",style="dashed", color="red", weight=0]; 15441[label="FiniteMap.mkBalBranch (Neg ywz7400) ywz741 ywz743 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz744 (Pos (Succ ywz5000)) ywz9)",fontsize=16,color="magenta"];15441 -> 15479[label="",style="dashed", color="magenta", weight=3]; 15442[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 (LT == GT)",fontsize=16,color="black",shape="box"];15442 -> 15481[label="",style="solid", color="black", weight=3]; 15443[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 False",fontsize=16,color="black",shape="box"];15443 -> 15482[label="",style="solid", color="black", weight=3]; 15444[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 True",fontsize=16,color="black",shape="box"];15444 -> 15483[label="",style="solid", color="black", weight=3]; 15445[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 False",fontsize=16,color="black",shape="box"];15445 -> 15484[label="",style="solid", color="black", weight=3]; 15446[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos ywz7400) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 otherwise",fontsize=16,color="black",shape="box"];15446 -> 15485[label="",style="solid", color="black", weight=3]; 15447 -> 16422[label="",style="dashed", color="red", weight=0]; 15447[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 (primCmpNat ywz74000 ywz5000 == GT)",fontsize=16,color="magenta"];15447 -> 16423[label="",style="dashed", color="magenta", weight=3]; 15447 -> 16424[label="",style="dashed", color="magenta", weight=3]; 15447 -> 16425[label="",style="dashed", color="magenta", weight=3]; 15447 -> 16426[label="",style="dashed", color="magenta", weight=3]; 15447 -> 16427[label="",style="dashed", color="magenta", weight=3]; 15447 -> 16428[label="",style="dashed", color="magenta", weight=3]; 15447 -> 16429[label="",style="dashed", color="magenta", weight=3]; 15447 -> 16430[label="",style="dashed", color="magenta", weight=3]; 15447 -> 16431[label="",style="dashed", color="magenta", weight=3]; 15448[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 (LT == GT)",fontsize=16,color="black",shape="box"];15448 -> 15488[label="",style="solid", color="black", weight=3]; 15449[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 False",fontsize=16,color="black",shape="box"];15449 -> 15489[label="",style="solid", color="black", weight=3]; 15450[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 False",fontsize=16,color="black",shape="box"];15450 -> 15490[label="",style="solid", color="black", weight=3]; 15451[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 (GT == GT)",fontsize=16,color="black",shape="box"];15451 -> 15491[label="",style="solid", color="black", weight=3]; 15452[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 False",fontsize=16,color="black",shape="box"];15452 -> 15492[label="",style="solid", color="black", weight=3]; 15453 -> 83[label="",style="dashed", color="red", weight=0]; 15453[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];15454 -> 83[label="",style="dashed", color="red", weight=0]; 15454[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];17541[label="ywz43",fontsize=16,color="green",shape="box"];17542[label="ywz44",fontsize=16,color="green",shape="box"];17543[label="ywz42",fontsize=16,color="green",shape="box"];17544[label="ywz44",fontsize=16,color="green",shape="box"];17545[label="ywz41",fontsize=16,color="green",shape="box"];17546[label="Pos (Succ ywz4000)",fontsize=16,color="green",shape="box"];17547[label="ywz41",fontsize=16,color="green",shape="box"];17548[label="ywz3",fontsize=16,color="green",shape="box"];17549[label="ywz4000",fontsize=16,color="green",shape="box"];17550[label="ywz42",fontsize=16,color="green",shape="box"];17551[label="ywz43",fontsize=16,color="green",shape="box"];17552 -> 12889[label="",style="dashed", color="red", weight=0]; 17552[label="primCmpNat ywz5000 ywz4000 == LT",fontsize=16,color="magenta"];17552 -> 17668[label="",style="dashed", color="magenta", weight=3]; 17552 -> 17669[label="",style="dashed", color="magenta", weight=3]; 17553[label="ywz5000",fontsize=16,color="green",shape="box"];17554[label="ywz51",fontsize=16,color="green",shape="box"];17540[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM2 ywz1444 ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) ywz1450)",fontsize=16,color="burlywood",shape="triangle"];25561[label="ywz1450/False",fontsize=10,color="white",style="solid",shape="box"];17540 -> 25561[label="",style="solid", color="burlywood", weight=9]; 25561 -> 17670[label="",style="solid", color="burlywood", weight=3]; 25562[label="ywz1450/True",fontsize=10,color="white",style="solid",shape="box"];17540 -> 25562[label="",style="solid", color="burlywood", weight=9]; 25562 -> 17671[label="",style="solid", color="burlywood", weight=3]; 21601[label="ywz42",fontsize=16,color="green",shape="box"];21602[label="ywz43",fontsize=16,color="green",shape="box"];21603[label="Pos Zero",fontsize=16,color="green",shape="box"];21604 -> 12118[label="",style="dashed", color="red", weight=0]; 21604[label="GT == LT",fontsize=16,color="magenta"];21605[label="ywz5000",fontsize=16,color="green",shape="box"];21606[label="ywz3",fontsize=16,color="green",shape="box"];21607[label="ywz41",fontsize=16,color="green",shape="box"];21608[label="ywz42",fontsize=16,color="green",shape="box"];21609[label="ywz43",fontsize=16,color="green",shape="box"];21610[label="ywz44",fontsize=16,color="green",shape="box"];21611[label="ywz44",fontsize=16,color="green",shape="box"];21612[label="ywz51",fontsize=16,color="green",shape="box"];21613[label="ywz41",fontsize=16,color="green",shape="box"];21600[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM2 ywz1880 ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) ywz1899)",fontsize=16,color="burlywood",shape="triangle"];25563[label="ywz1899/False",fontsize=10,color="white",style="solid",shape="box"];21600 -> 25563[label="",style="solid", color="burlywood", weight=9]; 25563 -> 21628[label="",style="solid", color="burlywood", weight=3]; 25564[label="ywz1899/True",fontsize=10,color="white",style="solid",shape="box"];21600 -> 25564[label="",style="solid", color="burlywood", weight=9]; 25564 -> 21629[label="",style="solid", color="burlywood", weight=3]; 21686[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 ywz1894 ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (Pos (Succ ywz1891) > ywz1894))",fontsize=16,color="black",shape="box"];21686 -> 21712[label="",style="solid", color="black", weight=3]; 21687[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM ywz1897 (Pos (Succ ywz1891)))",fontsize=16,color="burlywood",shape="triangle"];25565[label="ywz1897/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];21687 -> 25565[label="",style="solid", color="burlywood", weight=9]; 25565 -> 21713[label="",style="solid", color="burlywood", weight=3]; 25566[label="ywz1897/FiniteMap.Branch ywz18970 ywz18971 ywz18972 ywz18973 ywz18974",fontsize=10,color="white",style="solid",shape="box"];21687 -> 25566[label="",style="solid", color="burlywood", weight=9]; 25566 -> 21714[label="",style="solid", color="burlywood", weight=3]; 22629[label="Zero",fontsize=16,color="green",shape="box"];22630[label="Succ ywz4000",fontsize=16,color="green",shape="box"];22631[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM2 ywz2034 ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) False)",fontsize=16,color="black",shape="box"];22631 -> 22696[label="",style="solid", color="black", weight=3]; 22632[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM2 ywz2034 ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) True)",fontsize=16,color="black",shape="box"];22632 -> 22697[label="",style="solid", color="black", weight=3]; 913[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (Pos Zero > Pos Zero))",fontsize=16,color="black",shape="box"];913 -> 1029[label="",style="solid", color="black", weight=3]; 21957[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM2 ywz1949 ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) False)",fontsize=16,color="black",shape="box"];21957 -> 21996[label="",style="solid", color="black", weight=3]; 21958[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM2 ywz1949 ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) True)",fontsize=16,color="black",shape="box"];21958 -> 21997[label="",style="solid", color="black", weight=3]; 915[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (Pos Zero > Neg Zero))",fontsize=16,color="black",shape="box"];915 -> 1031[label="",style="solid", color="black", weight=3]; 19860[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 ywz1702 ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (Neg (Succ ywz1699) > ywz1702))",fontsize=16,color="black",shape="box"];19860 -> 19880[label="",style="solid", color="black", weight=3]; 19861[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM ywz1705 (Neg (Succ ywz1699)))",fontsize=16,color="burlywood",shape="triangle"];25567[label="ywz1705/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];19861 -> 25567[label="",style="solid", color="burlywood", weight=9]; 25567 -> 19881[label="",style="solid", color="burlywood", weight=3]; 25568[label="ywz1705/FiniteMap.Branch ywz17050 ywz17051 ywz17052 ywz17053 ywz17054",fontsize=10,color="white",style="solid",shape="box"];19861 -> 25568[label="",style="solid", color="burlywood", weight=9]; 25568 -> 19882[label="",style="solid", color="burlywood", weight=3]; 18019[label="ywz42",fontsize=16,color="green",shape="box"];18020[label="ywz4000",fontsize=16,color="green",shape="box"];18021[label="ywz43",fontsize=16,color="green",shape="box"];18022[label="ywz51",fontsize=16,color="green",shape="box"];18023[label="Neg (Succ ywz4000)",fontsize=16,color="green",shape="box"];18024 -> 12889[label="",style="dashed", color="red", weight=0]; 18024[label="primCmpNat ywz4000 ywz5000 == LT",fontsize=16,color="magenta"];18024 -> 18048[label="",style="dashed", color="magenta", weight=3]; 18024 -> 18049[label="",style="dashed", color="magenta", weight=3]; 18025[label="ywz5000",fontsize=16,color="green",shape="box"];18026[label="ywz42",fontsize=16,color="green",shape="box"];18027[label="ywz44",fontsize=16,color="green",shape="box"];18028[label="ywz3",fontsize=16,color="green",shape="box"];18029[label="ywz41",fontsize=16,color="green",shape="box"];18030[label="ywz43",fontsize=16,color="green",shape="box"];18031[label="ywz44",fontsize=16,color="green",shape="box"];18032[label="ywz41",fontsize=16,color="green",shape="box"];18018[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM2 ywz1480 ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) ywz1486)",fontsize=16,color="burlywood",shape="triangle"];25569[label="ywz1486/False",fontsize=10,color="white",style="solid",shape="box"];18018 -> 25569[label="",style="solid", color="burlywood", weight=9]; 25569 -> 18050[label="",style="solid", color="burlywood", weight=3]; 25570[label="ywz1486/True",fontsize=10,color="white",style="solid",shape="box"];18018 -> 25570[label="",style="solid", color="burlywood", weight=9]; 25570 -> 18051[label="",style="solid", color="burlywood", weight=3]; 20445[label="ywz3",fontsize=16,color="green",shape="box"];20446[label="ywz41",fontsize=16,color="green",shape="box"];20447[label="ywz44",fontsize=16,color="green",shape="box"];20448 -> 12125[label="",style="dashed", color="red", weight=0]; 20448[label="LT == LT",fontsize=16,color="magenta"];20449[label="Neg Zero",fontsize=16,color="green",shape="box"];20450[label="ywz51",fontsize=16,color="green",shape="box"];20451[label="ywz41",fontsize=16,color="green",shape="box"];20452[label="ywz43",fontsize=16,color="green",shape="box"];20453[label="ywz42",fontsize=16,color="green",shape="box"];20454[label="ywz42",fontsize=16,color="green",shape="box"];20455[label="ywz44",fontsize=16,color="green",shape="box"];20456[label="ywz5000",fontsize=16,color="green",shape="box"];20457[label="ywz43",fontsize=16,color="green",shape="box"];20444[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM2 ywz1789 ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) ywz1794)",fontsize=16,color="burlywood",shape="triangle"];25571[label="ywz1794/False",fontsize=10,color="white",style="solid",shape="box"];20444 -> 25571[label="",style="solid", color="burlywood", weight=9]; 25571 -> 20485[label="",style="solid", color="burlywood", weight=3]; 25572[label="ywz1794/True",fontsize=10,color="white",style="solid",shape="box"];20444 -> 25572[label="",style="solid", color="burlywood", weight=9]; 25572 -> 20486[label="",style="solid", color="burlywood", weight=3]; 22348[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM2 ywz2005 ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) False)",fontsize=16,color="black",shape="box"];22348 -> 22415[label="",style="solid", color="black", weight=3]; 22349[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM2 ywz2005 ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) True)",fontsize=16,color="black",shape="box"];22349 -> 22416[label="",style="solid", color="black", weight=3]; 922[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (Neg Zero > Pos Zero))",fontsize=16,color="black",shape="box"];922 -> 1041[label="",style="solid", color="black", weight=3]; 24695[label="Succ ywz4000",fontsize=16,color="green",shape="box"];24696[label="Zero",fontsize=16,color="green",shape="box"];24697[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM2 ywz2383 ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) False)",fontsize=16,color="black",shape="box"];24697 -> 24845[label="",style="solid", color="black", weight=3]; 24698[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM2 ywz2383 ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) True)",fontsize=16,color="black",shape="box"];24698 -> 24846[label="",style="solid", color="black", weight=3]; 924[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (Neg Zero > Neg Zero))",fontsize=16,color="black",shape="box"];924 -> 1043[label="",style="solid", color="black", weight=3]; 1659[label="primPlusNat (primPlusNat (primMulNat (Succ (Succ Zero)) (Succ ywz7200)) (Succ ywz7200)) (Succ ywz7200)",fontsize=16,color="black",shape="box"];1659 -> 1668[label="",style="solid", color="black", weight=3]; 6684[label="Succ (Succ (primPlusNat ywz250000 ywz372000))",fontsize=16,color="green",shape="box"];6684 -> 7381[label="",style="dashed", color="green", weight=3]; 6685[label="Succ ywz250000",fontsize=16,color="green",shape="box"];6686[label="Succ ywz372000",fontsize=16,color="green",shape="box"];6687[label="Zero",fontsize=16,color="green",shape="box"];13143[label="ywz821000",fontsize=16,color="green",shape="box"];13144[label="ywz811000",fontsize=16,color="green",shape="box"];15510 -> 12612[label="",style="dashed", color="red", weight=0]; 15510[label="Pos (Succ Zero) + FiniteMap.mkBranchLeft_size ywz1238 ywz1235 ywz1237",fontsize=16,color="magenta"];15510 -> 15534[label="",style="dashed", color="magenta", weight=3]; 15510 -> 15535[label="",style="dashed", color="magenta", weight=3]; 15511[label="FiniteMap.mkBranchRight_size ywz1238 ywz1235 ywz1237",fontsize=16,color="black",shape="box"];15511 -> 15536[label="",style="solid", color="black", weight=3]; 15512[label="ywz1245",fontsize=16,color="green",shape="box"];15006[label="ywz50",fontsize=16,color="green",shape="box"];15007[label="ywz740",fontsize=16,color="green",shape="box"];13051[label="ywz10490",fontsize=16,color="green",shape="box"];13052[label="ywz10480",fontsize=16,color="green",shape="box"];13053[label="primMinusNat (Succ ywz104900) (Succ ywz104800)",fontsize=16,color="black",shape="box"];13053 -> 13124[label="",style="solid", color="black", weight=3]; 13054[label="primMinusNat (Succ ywz104900) Zero",fontsize=16,color="black",shape="box"];13054 -> 13125[label="",style="solid", color="black", weight=3]; 13055[label="primMinusNat Zero (Succ ywz104800)",fontsize=16,color="black",shape="box"];13055 -> 13126[label="",style="solid", color="black", weight=3]; 13056[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];13056 -> 13127[label="",style="solid", color="black", weight=3]; 13057[label="ywz10490",fontsize=16,color="green",shape="box"];13058[label="ywz10480",fontsize=16,color="green",shape="box"];13633[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos (Succ ywz115700)) ywz1154 == GT)",fontsize=16,color="burlywood",shape="box"];25573[label="ywz1154/Pos ywz11540",fontsize=10,color="white",style="solid",shape="box"];13633 -> 25573[label="",style="solid", color="burlywood", weight=9]; 25573 -> 14098[label="",style="solid", color="burlywood", weight=3]; 25574[label="ywz1154/Neg ywz11540",fontsize=10,color="white",style="solid",shape="box"];13633 -> 25574[label="",style="solid", color="burlywood", weight=9]; 25574 -> 14099[label="",style="solid", color="burlywood", weight=3]; 13634[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) ywz1154 == GT)",fontsize=16,color="burlywood",shape="box"];25575[label="ywz1154/Pos ywz11540",fontsize=10,color="white",style="solid",shape="box"];13634 -> 25575[label="",style="solid", color="burlywood", weight=9]; 25575 -> 14100[label="",style="solid", color="burlywood", weight=3]; 25576[label="ywz1154/Neg ywz11540",fontsize=10,color="white",style="solid",shape="box"];13634 -> 25576[label="",style="solid", color="burlywood", weight=9]; 25576 -> 14101[label="",style="solid", color="burlywood", weight=3]; 13635[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg (Succ ywz115700)) ywz1154 == GT)",fontsize=16,color="burlywood",shape="box"];25577[label="ywz1154/Pos ywz11540",fontsize=10,color="white",style="solid",shape="box"];13635 -> 25577[label="",style="solid", color="burlywood", weight=9]; 25577 -> 14102[label="",style="solid", color="burlywood", weight=3]; 25578[label="ywz1154/Neg ywz11540",fontsize=10,color="white",style="solid",shape="box"];13635 -> 25578[label="",style="solid", color="burlywood", weight=9]; 25578 -> 14103[label="",style="solid", color="burlywood", weight=3]; 13636[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) ywz1154 == GT)",fontsize=16,color="burlywood",shape="box"];25579[label="ywz1154/Pos ywz11540",fontsize=10,color="white",style="solid",shape="box"];13636 -> 25579[label="",style="solid", color="burlywood", weight=9]; 25579 -> 14104[label="",style="solid", color="burlywood", weight=3]; 25580[label="ywz1154/Neg ywz11540",fontsize=10,color="white",style="solid",shape="box"];13636 -> 25580[label="",style="solid", color="burlywood", weight=9]; 25580 -> 14105[label="",style="solid", color="burlywood", weight=3]; 6527[label="FiniteMap.splitLT1 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (compare (Pos (Succ ywz432)) (Pos (Succ ywz427)) == GT)",fontsize=16,color="black",shape="box"];6527 -> 6604[label="",style="solid", color="black", weight=3]; 6528[label="ywz430",fontsize=16,color="green",shape="box"];6529[label="ywz432",fontsize=16,color="green",shape="box"];767[label="FiniteMap.splitLT ywz44 (Pos (Succ ywz5000))",fontsize=16,color="burlywood",shape="triangle"];25581[label="ywz44/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];767 -> 25581[label="",style="solid", color="burlywood", weight=9]; 25581 -> 972[label="",style="solid", color="burlywood", weight=3]; 25582[label="ywz44/FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=10,color="white",style="solid",shape="box"];767 -> 25582[label="",style="solid", color="burlywood", weight=9]; 25582 -> 973[label="",style="solid", color="burlywood", weight=3]; 621[label="FiniteMap.splitLT1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos (Succ ywz5000)) True",fontsize=16,color="black",shape="box"];621 -> 725[label="",style="solid", color="black", weight=3]; 622[label="FiniteMap.mkVBalBranch5 (Neg ywz400) ywz41 FiniteMap.EmptyFM (FiniteMap.splitLT ywz44 (Pos (Succ ywz5000)))",fontsize=16,color="black",shape="box"];622 -> 726[label="",style="solid", color="black", weight=3]; 623[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (FiniteMap.splitLT FiniteMap.EmptyFM (Pos (Succ ywz5000)))",fontsize=16,color="black",shape="box"];623 -> 727[label="",style="solid", color="black", weight=3]; 624[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (FiniteMap.splitLT (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos (Succ ywz5000)))",fontsize=16,color="black",shape="box"];624 -> 728[label="",style="solid", color="black", weight=3]; 625[label="FiniteMap.splitLT0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True",fontsize=16,color="black",shape="box"];625 -> 729[label="",style="solid", color="black", weight=3]; 627 -> 235[label="",style="dashed", color="red", weight=0]; 627[label="FiniteMap.splitLT ywz44 (Pos Zero)",fontsize=16,color="magenta"];627 -> 730[label="",style="dashed", color="magenta", weight=3]; 626[label="FiniteMap.mkVBalBranch (Neg (Succ ywz4000)) ywz41 ywz43 ywz10",fontsize=16,color="burlywood",shape="triangle"];25583[label="ywz43/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];626 -> 25583[label="",style="solid", color="burlywood", weight=9]; 25583 -> 731[label="",style="solid", color="burlywood", weight=3]; 25584[label="ywz43/FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434",fontsize=10,color="white",style="solid",shape="box"];626 -> 25584[label="",style="solid", color="burlywood", weight=9]; 25584 -> 732[label="",style="solid", color="burlywood", weight=3]; 628[label="FiniteMap.splitLT0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True",fontsize=16,color="black",shape="box"];628 -> 733[label="",style="solid", color="black", weight=3]; 6601[label="FiniteMap.splitLT1 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (compare (Neg (Succ ywz441)) (Neg (Succ ywz436)) == GT)",fontsize=16,color="black",shape="box"];6601 -> 6702[label="",style="solid", color="black", weight=3]; 6602[label="ywz441",fontsize=16,color="green",shape="box"];6603[label="ywz439",fontsize=16,color="green",shape="box"];636[label="FiniteMap.splitLT0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True",fontsize=16,color="black",shape="box"];636 -> 743[label="",style="solid", color="black", weight=3]; 637[label="FiniteMap.splitLT1 (Neg (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True",fontsize=16,color="black",shape="box"];637 -> 744[label="",style="solid", color="black", weight=3]; 638[label="FiniteMap.splitLT0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True",fontsize=16,color="black",shape="box"];638 -> 745[label="",style="solid", color="black", weight=3]; 6699[label="ywz449",fontsize=16,color="green",shape="box"];6700[label="ywz450",fontsize=16,color="green",shape="box"];20852 -> 10999[label="",style="dashed", color="red", weight=0]; 20852[label="Pos (Succ ywz450) < Pos (Succ ywz445)",fontsize=16,color="magenta"];20852 -> 20881[label="",style="dashed", color="magenta", weight=3]; 20852 -> 20882[label="",style="dashed", color="magenta", weight=3]; 20853[label="ywz449",fontsize=16,color="green",shape="box"];20854[label="ywz446",fontsize=16,color="green",shape="box"];20855[label="ywz447",fontsize=16,color="green",shape="box"];20856[label="ywz448",fontsize=16,color="green",shape="box"];20857[label="ywz450",fontsize=16,color="green",shape="box"];20858[label="ywz445",fontsize=16,color="green",shape="box"];20851[label="FiniteMap.splitGT1 (Pos (Succ ywz1827)) ywz1828 ywz1829 ywz1830 ywz1831 (Pos (Succ ywz1832)) ywz1835",fontsize=16,color="burlywood",shape="triangle"];25585[label="ywz1835/False",fontsize=10,color="white",style="solid",shape="box"];20851 -> 25585[label="",style="solid", color="burlywood", weight=9]; 25585 -> 20883[label="",style="solid", color="burlywood", weight=3]; 25586[label="ywz1835/True",fontsize=10,color="white",style="solid",shape="box"];20851 -> 25586[label="",style="solid", color="burlywood", weight=9]; 25586 -> 20884[label="",style="solid", color="burlywood", weight=3]; 646[label="FiniteMap.splitGT1 (Pos (Succ ywz4000)) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True",fontsize=16,color="black",shape="box"];646 -> 755[label="",style="solid", color="black", weight=3]; 647[label="FiniteMap.splitGT0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True",fontsize=16,color="black",shape="box"];647 -> 756[label="",style="solid", color="black", weight=3]; 648[label="FiniteMap.splitGT0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True",fontsize=16,color="black",shape="box"];648 -> 757[label="",style="solid", color="black", weight=3]; 773[label="FiniteMap.splitGT FiniteMap.EmptyFM (Neg (Succ ywz5000))",fontsize=16,color="black",shape="box"];773 -> 859[label="",style="solid", color="black", weight=3]; 774[label="FiniteMap.splitGT (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Neg (Succ ywz5000))",fontsize=16,color="black",shape="box"];774 -> 860[label="",style="solid", color="black", weight=3]; 775[label="FiniteMap.mkVBalBranch (Pos ywz400) ywz41 FiniteMap.EmptyFM ywz44",fontsize=16,color="black",shape="box"];775 -> 861[label="",style="solid", color="black", weight=3]; 776[label="FiniteMap.mkVBalBranch (Pos ywz400) ywz41 (FiniteMap.Branch ywz120 ywz121 ywz122 ywz123 ywz124) ywz44",fontsize=16,color="burlywood",shape="box"];25587[label="ywz44/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];776 -> 25587[label="",style="solid", color="burlywood", weight=9]; 25587 -> 862[label="",style="solid", color="burlywood", weight=3]; 25588[label="ywz44/FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=10,color="white",style="solid",shape="box"];776 -> 25588[label="",style="solid", color="burlywood", weight=9]; 25588 -> 863[label="",style="solid", color="burlywood", weight=3]; 6719[label="ywz459",fontsize=16,color="green",shape="box"];6720[label="ywz458",fontsize=16,color="green",shape="box"];20998[label="ywz458",fontsize=16,color="green",shape="box"];20999 -> 10999[label="",style="dashed", color="red", weight=0]; 20999[label="Neg (Succ ywz459) < Neg (Succ ywz454)",fontsize=16,color="magenta"];20999 -> 21027[label="",style="dashed", color="magenta", weight=3]; 20999 -> 21028[label="",style="dashed", color="magenta", weight=3]; 21000[label="ywz455",fontsize=16,color="green",shape="box"];21001[label="ywz456",fontsize=16,color="green",shape="box"];21002[label="ywz457",fontsize=16,color="green",shape="box"];21003[label="ywz459",fontsize=16,color="green",shape="box"];21004[label="ywz454",fontsize=16,color="green",shape="box"];20997[label="FiniteMap.splitGT1 (Neg (Succ ywz1837)) ywz1838 ywz1839 ywz1840 ywz1841 (Neg (Succ ywz1842)) ywz1845",fontsize=16,color="burlywood",shape="triangle"];25589[label="ywz1845/False",fontsize=10,color="white",style="solid",shape="box"];20997 -> 25589[label="",style="solid", color="burlywood", weight=9]; 25589 -> 21029[label="",style="solid", color="burlywood", weight=3]; 25590[label="ywz1845/True",fontsize=10,color="white",style="solid",shape="box"];20997 -> 25590[label="",style="solid", color="burlywood", weight=9]; 25590 -> 21030[label="",style="solid", color="burlywood", weight=3]; 660[label="FiniteMap.splitGT1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg (Succ ywz5000)) True",fontsize=16,color="black",shape="box"];660 -> 793[label="",style="solid", color="black", weight=3]; 761[label="Succ ywz4000",fontsize=16,color="green",shape="box"];762 -> 271[label="",style="dashed", color="red", weight=0]; 762[label="FiniteMap.splitGT ywz43 (Neg Zero)",fontsize=16,color="magenta"];762 -> 794[label="",style="dashed", color="magenta", weight=3]; 663[label="FiniteMap.splitGT0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True",fontsize=16,color="black",shape="box"];663 -> 795[label="",style="solid", color="black", weight=3]; 664[label="FiniteMap.splitGT0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True",fontsize=16,color="black",shape="box"];664 -> 796[label="",style="solid", color="black", weight=3]; 16964[label="ywz741",fontsize=16,color="green",shape="box"];16965[label="ywz74000",fontsize=16,color="green",shape="box"];16966[label="ywz743",fontsize=16,color="green",shape="box"];16967[label="ywz9",fontsize=16,color="green",shape="box"];16968[label="ywz5000",fontsize=16,color="green",shape="box"];16969[label="ywz5000",fontsize=16,color="green",shape="box"];16970[label="ywz742",fontsize=16,color="green",shape="box"];16971[label="ywz744",fontsize=16,color="green",shape="box"];16972[label="ywz74000",fontsize=16,color="green",shape="box"];16963[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (primCmpNat ywz1419 ywz1420 == GT)",fontsize=16,color="burlywood",shape="triangle"];25591[label="ywz1419/Succ ywz14190",fontsize=10,color="white",style="solid",shape="box"];16963 -> 25591[label="",style="solid", color="burlywood", weight=9]; 25591 -> 17054[label="",style="solid", color="burlywood", weight=3]; 25592[label="ywz1419/Zero",fontsize=10,color="white",style="solid",shape="box"];16963 -> 25592[label="",style="solid", color="burlywood", weight=9]; 25592 -> 17055[label="",style="solid", color="burlywood", weight=3]; 15477[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Pos (Succ ywz5000)) ywz9 True",fontsize=16,color="black",shape="box"];15477 -> 15497[label="",style="solid", color="black", weight=3]; 15479 -> 15167[label="",style="dashed", color="red", weight=0]; 15479[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz744 (Pos (Succ ywz5000)) ywz9",fontsize=16,color="magenta"];15479 -> 15498[label="",style="dashed", color="magenta", weight=3]; 15479 -> 15499[label="",style="dashed", color="magenta", weight=3]; 15478[label="FiniteMap.mkBalBranch (Neg ywz7400) ywz741 ywz743 ywz1243",fontsize=16,color="black",shape="triangle"];15478 -> 15500[label="",style="solid", color="black", weight=3]; 15481[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 False",fontsize=16,color="black",shape="box"];15481 -> 15513[label="",style="solid", color="black", weight=3]; 15482[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 otherwise",fontsize=16,color="black",shape="box"];15482 -> 15514[label="",style="solid", color="black", weight=3]; 15483 -> 15478[label="",style="dashed", color="red", weight=0]; 15483[label="FiniteMap.mkBalBranch (Neg (Succ ywz74000)) ywz741 ywz743 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz744 (Pos Zero) ywz9)",fontsize=16,color="magenta"];15483 -> 15515[label="",style="dashed", color="magenta", weight=3]; 15483 -> 15516[label="",style="dashed", color="magenta", weight=3]; 15484[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 otherwise",fontsize=16,color="black",shape="box"];15484 -> 15517[label="",style="solid", color="black", weight=3]; 15485[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos ywz7400) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 True",fontsize=16,color="black",shape="box"];15485 -> 15518[label="",style="solid", color="black", weight=3]; 16423[label="ywz743",fontsize=16,color="green",shape="box"];16424[label="ywz74000",fontsize=16,color="green",shape="box"];16425[label="ywz5000",fontsize=16,color="green",shape="box"];16426[label="ywz744",fontsize=16,color="green",shape="box"];16427[label="ywz741",fontsize=16,color="green",shape="box"];16428[label="ywz74000",fontsize=16,color="green",shape="box"];16429[label="ywz9",fontsize=16,color="green",shape="box"];16430[label="ywz742",fontsize=16,color="green",shape="box"];16431[label="ywz5000",fontsize=16,color="green",shape="box"];16422[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (primCmpNat ywz1368 ywz1369 == GT)",fontsize=16,color="burlywood",shape="triangle"];25593[label="ywz1368/Succ ywz13680",fontsize=10,color="white",style="solid",shape="box"];16422 -> 25593[label="",style="solid", color="burlywood", weight=9]; 25593 -> 16504[label="",style="solid", color="burlywood", weight=3]; 25594[label="ywz1368/Zero",fontsize=10,color="white",style="solid",shape="box"];16422 -> 25594[label="",style="solid", color="burlywood", weight=9]; 25594 -> 16505[label="",style="solid", color="burlywood", weight=3]; 15488[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 False",fontsize=16,color="black",shape="box"];15488 -> 15523[label="",style="solid", color="black", weight=3]; 15489[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 otherwise",fontsize=16,color="black",shape="box"];15489 -> 15524[label="",style="solid", color="black", weight=3]; 15490[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 otherwise",fontsize=16,color="black",shape="box"];15490 -> 15525[label="",style="solid", color="black", weight=3]; 15491[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 True",fontsize=16,color="black",shape="box"];15491 -> 15526[label="",style="solid", color="black", weight=3]; 15492[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 otherwise",fontsize=16,color="black",shape="box"];15492 -> 15527[label="",style="solid", color="black", weight=3]; 17668[label="ywz5000",fontsize=16,color="green",shape="box"];17669[label="ywz4000",fontsize=16,color="green",shape="box"];17670[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM2 ywz1444 ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) False)",fontsize=16,color="black",shape="box"];17670 -> 17687[label="",style="solid", color="black", weight=3]; 17671[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM2 ywz1444 ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) True)",fontsize=16,color="black",shape="box"];17671 -> 17688[label="",style="solid", color="black", weight=3]; 21628[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM2 ywz1880 ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) False)",fontsize=16,color="black",shape="box"];21628 -> 21662[label="",style="solid", color="black", weight=3]; 21629[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM2 ywz1880 ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) True)",fontsize=16,color="black",shape="box"];21629 -> 21663[label="",style="solid", color="black", weight=3]; 21712[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 ywz1894 ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (compare (Pos (Succ ywz1891)) ywz1894 == GT))",fontsize=16,color="black",shape="box"];21712 -> 21754[label="",style="solid", color="black", weight=3]; 21713[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos (Succ ywz1891)))",fontsize=16,color="black",shape="box"];21713 -> 21755[label="",style="solid", color="black", weight=3]; 21714[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM (FiniteMap.Branch ywz18970 ywz18971 ywz18972 ywz18973 ywz18974) (Pos (Succ ywz1891)))",fontsize=16,color="black",shape="box"];21714 -> 21756[label="",style="solid", color="black", weight=3]; 22696[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 ywz2034 ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (Pos Zero > ywz2034))",fontsize=16,color="black",shape="box"];22696 -> 22742[label="",style="solid", color="black", weight=3]; 22697[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM ywz2037 (Pos Zero))",fontsize=16,color="burlywood",shape="triangle"];25595[label="ywz2037/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];22697 -> 25595[label="",style="solid", color="burlywood", weight=9]; 25595 -> 22743[label="",style="solid", color="burlywood", weight=3]; 25596[label="ywz2037/FiniteMap.Branch ywz20370 ywz20371 ywz20372 ywz20373 ywz20374",fontsize=10,color="white",style="solid",shape="box"];22697 -> 25596[label="",style="solid", color="burlywood", weight=9]; 25596 -> 22744[label="",style="solid", color="burlywood", weight=3]; 1029[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (compare (Pos Zero) (Pos Zero) == GT))",fontsize=16,color="black",shape="box"];1029 -> 1172[label="",style="solid", color="black", weight=3]; 21996[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 ywz1949 ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (Pos Zero > ywz1949))",fontsize=16,color="black",shape="box"];21996 -> 22041[label="",style="solid", color="black", weight=3]; 21997[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM ywz1952 (Pos Zero))",fontsize=16,color="burlywood",shape="triangle"];25597[label="ywz1952/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];21997 -> 25597[label="",style="solid", color="burlywood", weight=9]; 25597 -> 22042[label="",style="solid", color="burlywood", weight=3]; 25598[label="ywz1952/FiniteMap.Branch ywz19520 ywz19521 ywz19522 ywz19523 ywz19524",fontsize=10,color="white",style="solid",shape="box"];21997 -> 25598[label="",style="solid", color="burlywood", weight=9]; 25598 -> 22043[label="",style="solid", color="burlywood", weight=3]; 1031[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (compare (Pos Zero) (Neg Zero) == GT))",fontsize=16,color="black",shape="box"];1031 -> 1174[label="",style="solid", color="black", weight=3]; 19880[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 ywz1702 ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (compare (Neg (Succ ywz1699)) ywz1702 == GT))",fontsize=16,color="black",shape="box"];19880 -> 19934[label="",style="solid", color="black", weight=3]; 19881[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg (Succ ywz1699)))",fontsize=16,color="black",shape="box"];19881 -> 19935[label="",style="solid", color="black", weight=3]; 19882[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM (FiniteMap.Branch ywz17050 ywz17051 ywz17052 ywz17053 ywz17054) (Neg (Succ ywz1699)))",fontsize=16,color="black",shape="box"];19882 -> 19936[label="",style="solid", color="black", weight=3]; 18048[label="ywz4000",fontsize=16,color="green",shape="box"];18049[label="ywz5000",fontsize=16,color="green",shape="box"];18050[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM2 ywz1480 ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) False)",fontsize=16,color="black",shape="box"];18050 -> 18058[label="",style="solid", color="black", weight=3]; 18051[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM2 ywz1480 ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) True)",fontsize=16,color="black",shape="box"];18051 -> 18059[label="",style="solid", color="black", weight=3]; 20485[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM2 ywz1789 ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) False)",fontsize=16,color="black",shape="box"];20485 -> 20517[label="",style="solid", color="black", weight=3]; 20486[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM2 ywz1789 ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) True)",fontsize=16,color="black",shape="box"];20486 -> 20518[label="",style="solid", color="black", weight=3]; 22415[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 ywz2005 ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (Neg Zero > ywz2005))",fontsize=16,color="black",shape="box"];22415 -> 22572[label="",style="solid", color="black", weight=3]; 22416[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM ywz2008 (Neg Zero))",fontsize=16,color="burlywood",shape="triangle"];25599[label="ywz2008/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];22416 -> 25599[label="",style="solid", color="burlywood", weight=9]; 25599 -> 22573[label="",style="solid", color="burlywood", weight=3]; 25600[label="ywz2008/FiniteMap.Branch ywz20080 ywz20081 ywz20082 ywz20083 ywz20084",fontsize=10,color="white",style="solid",shape="box"];22416 -> 25600[label="",style="solid", color="burlywood", weight=9]; 25600 -> 22574[label="",style="solid", color="burlywood", weight=3]; 1041[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (compare (Neg Zero) (Pos Zero) == GT))",fontsize=16,color="black",shape="box"];1041 -> 1185[label="",style="solid", color="black", weight=3]; 24845[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 ywz2383 ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (Neg Zero > ywz2383))",fontsize=16,color="black",shape="box"];24845 -> 25005[label="",style="solid", color="black", weight=3]; 24846[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM ywz2386 (Neg Zero))",fontsize=16,color="burlywood",shape="triangle"];25601[label="ywz2386/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];24846 -> 25601[label="",style="solid", color="burlywood", weight=9]; 25601 -> 25006[label="",style="solid", color="burlywood", weight=3]; 25602[label="ywz2386/FiniteMap.Branch ywz23860 ywz23861 ywz23862 ywz23863 ywz23864",fontsize=10,color="white",style="solid",shape="box"];24846 -> 25602[label="",style="solid", color="burlywood", weight=9]; 25602 -> 25007[label="",style="solid", color="burlywood", weight=3]; 1043[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (compare (Neg Zero) (Neg Zero) == GT))",fontsize=16,color="black",shape="box"];1043 -> 1187[label="",style="solid", color="black", weight=3]; 1668[label="primPlusNat (primPlusNat (primPlusNat (primMulNat (Succ Zero) (Succ ywz7200)) (Succ ywz7200)) (Succ ywz7200)) (Succ ywz7200)",fontsize=16,color="black",shape="box"];1668 -> 1813[label="",style="solid", color="black", weight=3]; 7381 -> 5537[label="",style="dashed", color="red", weight=0]; 7381[label="primPlusNat ywz250000 ywz372000",fontsize=16,color="magenta"];7381 -> 7820[label="",style="dashed", color="magenta", weight=3]; 7381 -> 7821[label="",style="dashed", color="magenta", weight=3]; 15534[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];15535[label="FiniteMap.mkBranchLeft_size ywz1238 ywz1235 ywz1237",fontsize=16,color="black",shape="box"];15535 -> 15570[label="",style="solid", color="black", weight=3]; 15536[label="FiniteMap.sizeFM ywz1238",fontsize=16,color="burlywood",shape="triangle"];25603[label="ywz1238/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];15536 -> 25603[label="",style="solid", color="burlywood", weight=9]; 25603 -> 15571[label="",style="solid", color="burlywood", weight=3]; 25604[label="ywz1238/FiniteMap.Branch ywz12380 ywz12381 ywz12382 ywz12383 ywz12384",fontsize=10,color="white",style="solid",shape="box"];15536 -> 25604[label="",style="solid", color="burlywood", weight=9]; 25604 -> 15572[label="",style="solid", color="burlywood", weight=3]; 13124 -> 12934[label="",style="dashed", color="red", weight=0]; 13124[label="primMinusNat ywz104900 ywz104800",fontsize=16,color="magenta"];13124 -> 13379[label="",style="dashed", color="magenta", weight=3]; 13124 -> 13380[label="",style="dashed", color="magenta", weight=3]; 13125[label="Pos (Succ ywz104900)",fontsize=16,color="green",shape="box"];13126[label="Neg (Succ ywz104800)",fontsize=16,color="green",shape="box"];13127[label="Pos Zero",fontsize=16,color="green",shape="box"];14098[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos (Succ ywz115700)) (Pos ywz11540) == GT)",fontsize=16,color="black",shape="box"];14098 -> 14175[label="",style="solid", color="black", weight=3]; 14099[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos (Succ ywz115700)) (Neg ywz11540) == GT)",fontsize=16,color="black",shape="box"];14099 -> 14176[label="",style="solid", color="black", weight=3]; 14100[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Pos ywz11540) == GT)",fontsize=16,color="burlywood",shape="box"];25605[label="ywz11540/Succ ywz115400",fontsize=10,color="white",style="solid",shape="box"];14100 -> 25605[label="",style="solid", color="burlywood", weight=9]; 25605 -> 14177[label="",style="solid", color="burlywood", weight=3]; 25606[label="ywz11540/Zero",fontsize=10,color="white",style="solid",shape="box"];14100 -> 25606[label="",style="solid", color="burlywood", weight=9]; 25606 -> 14178[label="",style="solid", color="burlywood", weight=3]; 14101[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Neg ywz11540) == GT)",fontsize=16,color="burlywood",shape="box"];25607[label="ywz11540/Succ ywz115400",fontsize=10,color="white",style="solid",shape="box"];14101 -> 25607[label="",style="solid", color="burlywood", weight=9]; 25607 -> 14179[label="",style="solid", color="burlywood", weight=3]; 25608[label="ywz11540/Zero",fontsize=10,color="white",style="solid",shape="box"];14101 -> 25608[label="",style="solid", color="burlywood", weight=9]; 25608 -> 14180[label="",style="solid", color="burlywood", weight=3]; 14102[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg (Succ ywz115700)) (Pos ywz11540) == GT)",fontsize=16,color="black",shape="box"];14102 -> 14181[label="",style="solid", color="black", weight=3]; 14103[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg (Succ ywz115700)) (Neg ywz11540) == GT)",fontsize=16,color="black",shape="box"];14103 -> 14182[label="",style="solid", color="black", weight=3]; 14104[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Pos ywz11540) == GT)",fontsize=16,color="burlywood",shape="box"];25609[label="ywz11540/Succ ywz115400",fontsize=10,color="white",style="solid",shape="box"];14104 -> 25609[label="",style="solid", color="burlywood", weight=9]; 25609 -> 14183[label="",style="solid", color="burlywood", weight=3]; 25610[label="ywz11540/Zero",fontsize=10,color="white",style="solid",shape="box"];14104 -> 25610[label="",style="solid", color="burlywood", weight=9]; 25610 -> 14184[label="",style="solid", color="burlywood", weight=3]; 14105[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Neg ywz11540) == GT)",fontsize=16,color="burlywood",shape="box"];25611[label="ywz11540/Succ ywz115400",fontsize=10,color="white",style="solid",shape="box"];14105 -> 25611[label="",style="solid", color="burlywood", weight=9]; 25611 -> 14185[label="",style="solid", color="burlywood", weight=3]; 25612[label="ywz11540/Zero",fontsize=10,color="white",style="solid",shape="box"];14105 -> 25612[label="",style="solid", color="burlywood", weight=9]; 25612 -> 14186[label="",style="solid", color="burlywood", weight=3]; 6604[label="FiniteMap.splitLT1 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpInt (Pos (Succ ywz432)) (Pos (Succ ywz427)) == GT)",fontsize=16,color="black",shape="box"];6604 -> 6703[label="",style="solid", color="black", weight=3]; 972[label="FiniteMap.splitLT FiniteMap.EmptyFM (Pos (Succ ywz5000))",fontsize=16,color="black",shape="box"];972 -> 1115[label="",style="solid", color="black", weight=3]; 973[label="FiniteMap.splitLT (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos (Succ ywz5000))",fontsize=16,color="black",shape="box"];973 -> 1116[label="",style="solid", color="black", weight=3]; 725 -> 759[label="",style="dashed", color="red", weight=0]; 725[label="FiniteMap.mkVBalBranch (Pos Zero) ywz41 ywz43 (FiniteMap.splitLT ywz44 (Pos (Succ ywz5000)))",fontsize=16,color="magenta"];725 -> 767[label="",style="dashed", color="magenta", weight=3]; 725 -> 768[label="",style="dashed", color="magenta", weight=3]; 725 -> 769[label="",style="dashed", color="magenta", weight=3]; 726[label="FiniteMap.addToFM (FiniteMap.splitLT ywz44 (Pos (Succ ywz5000))) (Neg ywz400) ywz41",fontsize=16,color="black",shape="box"];726 -> 853[label="",style="solid", color="black", weight=3]; 727 -> 855[label="",style="dashed", color="red", weight=0]; 727[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos (Succ ywz5000)))",fontsize=16,color="magenta"];727 -> 856[label="",style="dashed", color="magenta", weight=3]; 728 -> 855[label="",style="dashed", color="red", weight=0]; 728[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (FiniteMap.splitLT3 (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos (Succ ywz5000)))",fontsize=16,color="magenta"];728 -> 857[label="",style="dashed", color="magenta", weight=3]; 729[label="ywz43",fontsize=16,color="green",shape="box"];730[label="ywz44",fontsize=16,color="green",shape="box"];731[label="FiniteMap.mkVBalBranch (Neg (Succ ywz4000)) ywz41 FiniteMap.EmptyFM ywz10",fontsize=16,color="black",shape="box"];731 -> 864[label="",style="solid", color="black", weight=3]; 732[label="FiniteMap.mkVBalBranch (Neg (Succ ywz4000)) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) ywz10",fontsize=16,color="burlywood",shape="box"];25613[label="ywz10/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];732 -> 25613[label="",style="solid", color="burlywood", weight=9]; 25613 -> 865[label="",style="solid", color="burlywood", weight=3]; 25614[label="ywz10/FiniteMap.Branch ywz100 ywz101 ywz102 ywz103 ywz104",fontsize=10,color="white",style="solid",shape="box"];732 -> 25614[label="",style="solid", color="burlywood", weight=9]; 25614 -> 866[label="",style="solid", color="burlywood", weight=3]; 733[label="ywz43",fontsize=16,color="green",shape="box"];6702[label="FiniteMap.splitLT1 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpInt (Neg (Succ ywz441)) (Neg (Succ ywz436)) == GT)",fontsize=16,color="black",shape="box"];6702 -> 6723[label="",style="solid", color="black", weight=3]; 743[label="ywz43",fontsize=16,color="green",shape="box"];744 -> 626[label="",style="dashed", color="red", weight=0]; 744[label="FiniteMap.mkVBalBranch (Neg (Succ ywz4000)) ywz41 ywz43 (FiniteMap.splitLT ywz44 (Neg Zero))",fontsize=16,color="magenta"];744 -> 876[label="",style="dashed", color="magenta", weight=3]; 745[label="ywz43",fontsize=16,color="green",shape="box"];20881[label="Pos (Succ ywz450)",fontsize=16,color="green",shape="box"];20882[label="Pos (Succ ywz445)",fontsize=16,color="green",shape="box"];20883[label="FiniteMap.splitGT1 (Pos (Succ ywz1827)) ywz1828 ywz1829 ywz1830 ywz1831 (Pos (Succ ywz1832)) False",fontsize=16,color="black",shape="box"];20883 -> 20995[label="",style="solid", color="black", weight=3]; 20884[label="FiniteMap.splitGT1 (Pos (Succ ywz1827)) ywz1828 ywz1829 ywz1830 ywz1831 (Pos (Succ ywz1832)) True",fontsize=16,color="black",shape="box"];20884 -> 20996[label="",style="solid", color="black", weight=3]; 755 -> 759[label="",style="dashed", color="red", weight=0]; 755[label="FiniteMap.mkVBalBranch (Pos (Succ ywz4000)) ywz41 (FiniteMap.splitGT ywz43 (Pos Zero)) ywz44",fontsize=16,color="magenta"];755 -> 770[label="",style="dashed", color="magenta", weight=3]; 755 -> 771[label="",style="dashed", color="magenta", weight=3]; 756[label="ywz44",fontsize=16,color="green",shape="box"];757[label="ywz44",fontsize=16,color="green",shape="box"];859[label="FiniteMap.splitGT4 FiniteMap.EmptyFM (Neg (Succ ywz5000))",fontsize=16,color="black",shape="box"];859 -> 898[label="",style="solid", color="black", weight=3]; 860 -> 28[label="",style="dashed", color="red", weight=0]; 860[label="FiniteMap.splitGT3 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Neg (Succ ywz5000))",fontsize=16,color="magenta"];860 -> 899[label="",style="dashed", color="magenta", weight=3]; 860 -> 900[label="",style="dashed", color="magenta", weight=3]; 860 -> 901[label="",style="dashed", color="magenta", weight=3]; 860 -> 902[label="",style="dashed", color="magenta", weight=3]; 860 -> 903[label="",style="dashed", color="magenta", weight=3]; 860 -> 904[label="",style="dashed", color="magenta", weight=3]; 861[label="FiniteMap.mkVBalBranch5 (Pos ywz400) ywz41 FiniteMap.EmptyFM ywz44",fontsize=16,color="black",shape="box"];861 -> 905[label="",style="solid", color="black", weight=3]; 862[label="FiniteMap.mkVBalBranch (Pos ywz400) ywz41 (FiniteMap.Branch ywz120 ywz121 ywz122 ywz123 ywz124) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];862 -> 906[label="",style="solid", color="black", weight=3]; 863[label="FiniteMap.mkVBalBranch (Pos ywz400) ywz41 (FiniteMap.Branch ywz120 ywz121 ywz122 ywz123 ywz124) (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444)",fontsize=16,color="black",shape="box"];863 -> 907[label="",style="solid", color="black", weight=3]; 21027[label="Neg (Succ ywz459)",fontsize=16,color="green",shape="box"];21028[label="Neg (Succ ywz454)",fontsize=16,color="green",shape="box"];21029[label="FiniteMap.splitGT1 (Neg (Succ ywz1837)) ywz1838 ywz1839 ywz1840 ywz1841 (Neg (Succ ywz1842)) False",fontsize=16,color="black",shape="box"];21029 -> 21077[label="",style="solid", color="black", weight=3]; 21030[label="FiniteMap.splitGT1 (Neg (Succ ywz1837)) ywz1838 ywz1839 ywz1840 ywz1841 (Neg (Succ ywz1842)) True",fontsize=16,color="black",shape="box"];21030 -> 21078[label="",style="solid", color="black", weight=3]; 793 -> 896[label="",style="dashed", color="red", weight=0]; 793[label="FiniteMap.mkVBalBranch (Neg Zero) ywz41 (FiniteMap.splitGT ywz43 (Neg (Succ ywz5000))) ywz44",fontsize=16,color="magenta"];793 -> 897[label="",style="dashed", color="magenta", weight=3]; 794[label="ywz43",fontsize=16,color="green",shape="box"];795[label="ywz44",fontsize=16,color="green",shape="box"];796[label="ywz44",fontsize=16,color="green",shape="box"];17054[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (primCmpNat (Succ ywz14190) ywz1420 == GT)",fontsize=16,color="burlywood",shape="box"];25615[label="ywz1420/Succ ywz14200",fontsize=10,color="white",style="solid",shape="box"];17054 -> 25615[label="",style="solid", color="burlywood", weight=9]; 25615 -> 17067[label="",style="solid", color="burlywood", weight=3]; 25616[label="ywz1420/Zero",fontsize=10,color="white",style="solid",shape="box"];17054 -> 25616[label="",style="solid", color="burlywood", weight=9]; 25616 -> 17068[label="",style="solid", color="burlywood", weight=3]; 17055[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (primCmpNat Zero ywz1420 == 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ywz1243",fontsize=16,color="black",shape="box"];15500 -> 15537[label="",style="solid", color="black", weight=3]; 15513[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 otherwise",fontsize=16,color="black",shape="box"];15513 -> 15538[label="",style="solid", color="black", weight=3]; 15514[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 True",fontsize=16,color="black",shape="box"];15514 -> 15539[label="",style="solid", color="black", weight=3]; 15515[label="Succ ywz74000",fontsize=16,color="green",shape="box"];15516 -> 15167[label="",style="dashed", color="red", weight=0]; 15516[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz744 (Pos Zero) ywz9",fontsize=16,color="magenta"];15516 -> 15540[label="",style="dashed", color="magenta", weight=3]; 15516 -> 15541[label="",style="dashed", color="magenta", weight=3]; 15517[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 True",fontsize=16,color="black",shape="box"];15517 -> 15542[label="",style="solid", color="black", weight=3]; 15518[label="FiniteMap.Branch (Neg (Succ ywz5000)) (FiniteMap.addToFM0 ywz741 ywz9) ywz742 ywz743 ywz744",fontsize=16,color="green",shape="box"];15518 -> 15543[label="",style="dashed", color="green", weight=3]; 16504[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (primCmpNat (Succ ywz13680) ywz1369 == GT)",fontsize=16,color="burlywood",shape="box"];25619[label="ywz1369/Succ ywz13690",fontsize=10,color="white",style="solid",shape="box"];16504 -> 25619[label="",style="solid", color="burlywood", weight=9]; 25619 -> 16540[label="",style="solid", color="burlywood", weight=3]; 25620[label="ywz1369/Zero",fontsize=10,color="white",style="solid",shape="box"];16504 -> 25620[label="",style="solid", color="burlywood", weight=9]; 25620 -> 16541[label="",style="solid", color="burlywood", weight=3]; 16505[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (primCmpNat Zero ywz1369 == GT)",fontsize=16,color="burlywood",shape="box"];25621[label="ywz1369/Succ ywz13690",fontsize=10,color="white",style="solid",shape="box"];16505 -> 25621[label="",style="solid", color="burlywood", weight=9]; 25621 -> 16542[label="",style="solid", color="burlywood", weight=3]; 25622[label="ywz1369/Zero",fontsize=10,color="white",style="solid",shape="box"];16505 -> 25622[label="",style="solid", color="burlywood", weight=9]; 25622 -> 16543[label="",style="solid", color="burlywood", weight=3]; 15523[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 otherwise",fontsize=16,color="black",shape="box"];15523 -> 15548[label="",style="solid", color="black", weight=3]; 15524[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 True",fontsize=16,color="black",shape="box"];15524 -> 15549[label="",style="solid", color="black", weight=3]; 15525[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 True",fontsize=16,color="black",shape="box"];15525 -> 15550[label="",style="solid", color="black", weight=3]; 15526 -> 15478[label="",style="dashed", color="red", weight=0]; 15526[label="FiniteMap.mkBalBranch (Neg (Succ ywz74000)) ywz741 ywz743 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz744 (Neg Zero) ywz9)",fontsize=16,color="magenta"];15526 -> 15551[label="",style="dashed", color="magenta", weight=3]; 15526 -> 15552[label="",style="dashed", color="magenta", weight=3]; 15527[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg Zero) ywz9 True",fontsize=16,color="black",shape="box"];15527 -> 15553[label="",style="solid", color="black", weight=3]; 17687[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 ywz1444 ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (Pos (Succ ywz1441) > ywz1444))",fontsize=16,color="black",shape="box"];17687 -> 17703[label="",style="solid", color="black", weight=3]; 17688[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM ywz1447 (Pos (Succ ywz1441)))",fontsize=16,color="burlywood",shape="triangle"];25623[label="ywz1447/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];17688 -> 25623[label="",style="solid", color="burlywood", weight=9]; 25623 -> 17704[label="",style="solid", color="burlywood", weight=3]; 25624[label="ywz1447/FiniteMap.Branch ywz14470 ywz14471 ywz14472 ywz14473 ywz14474",fontsize=10,color="white",style="solid",shape="box"];17688 -> 25624[label="",style="solid", color="burlywood", weight=9]; 25624 -> 17705[label="",style="solid", color="burlywood", weight=3]; 21662[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 ywz1880 ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (Pos (Succ ywz1877) > ywz1880))",fontsize=16,color="black",shape="box"];21662 -> 21688[label="",style="solid", color="black", weight=3]; 21663[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM ywz1883 (Pos (Succ ywz1877)))",fontsize=16,color="burlywood",shape="triangle"];25625[label="ywz1883/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];21663 -> 25625[label="",style="solid", color="burlywood", weight=9]; 25625 -> 21689[label="",style="solid", color="burlywood", weight=3]; 25626[label="ywz1883/FiniteMap.Branch ywz18830 ywz18831 ywz18832 ywz18833 ywz18834",fontsize=10,color="white",style="solid",shape="box"];21663 -> 25626[label="",style="solid", color="burlywood", weight=9]; 25626 -> 21690[label="",style="solid", color="burlywood", weight=3]; 21754[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 ywz1894 ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (primCmpInt (Pos (Succ ywz1891)) ywz1894 == GT))",fontsize=16,color="burlywood",shape="box"];25627[label="ywz1894/Pos ywz18940",fontsize=10,color="white",style="solid",shape="box"];21754 -> 25627[label="",style="solid", color="burlywood", weight=9]; 25627 -> 21903[label="",style="solid", color="burlywood", weight=3]; 25628[label="ywz1894/Neg ywz18940",fontsize=10,color="white",style="solid",shape="box"];21754 -> 25628[label="",style="solid", color="burlywood", weight=9]; 25628 -> 21904[label="",style="solid", color="burlywood", weight=3]; 21755[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos (Succ ywz1891)))",fontsize=16,color="black",shape="box"];21755 -> 21905[label="",style="solid", color="black", weight=3]; 21756[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz18970 ywz18971 ywz18972 ywz18973 ywz18974) (Pos (Succ ywz1891)))",fontsize=16,color="black",shape="box"];21756 -> 21906[label="",style="solid", color="black", weight=3]; 22742[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 ywz2034 ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (compare (Pos Zero) ywz2034 == GT))",fontsize=16,color="black",shape="box"];22742 -> 22790[label="",style="solid", color="black", weight=3]; 22743[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos Zero))",fontsize=16,color="black",shape="box"];22743 -> 22791[label="",style="solid", color="black", weight=3]; 22744[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM (FiniteMap.Branch ywz20370 ywz20371 ywz20372 ywz20373 ywz20374) (Pos Zero))",fontsize=16,color="black",shape="box"];22744 -> 22792[label="",style="solid", color="black", weight=3]; 1172[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT))",fontsize=16,color="black",shape="box"];1172 -> 1343[label="",style="solid", color="black", weight=3]; 22041[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 ywz1949 ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (compare (Pos Zero) ywz1949 == GT))",fontsize=16,color="black",shape="box"];22041 -> 22072[label="",style="solid", color="black", weight=3]; 22042[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos Zero))",fontsize=16,color="black",shape="box"];22042 -> 22073[label="",style="solid", color="black", weight=3]; 22043[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM (FiniteMap.Branch ywz19520 ywz19521 ywz19522 ywz19523 ywz19524) (Pos Zero))",fontsize=16,color="black",shape="box"];22043 -> 22074[label="",style="solid", color="black", weight=3]; 1174[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT))",fontsize=16,color="black",shape="box"];1174 -> 1345[label="",style="solid", color="black", weight=3]; 19934[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 ywz1702 ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (primCmpInt (Neg (Succ ywz1699)) ywz1702 == GT))",fontsize=16,color="burlywood",shape="box"];25629[label="ywz1702/Pos ywz17020",fontsize=10,color="white",style="solid",shape="box"];19934 -> 25629[label="",style="solid", color="burlywood", weight=9]; 25629 -> 19945[label="",style="solid", color="burlywood", weight=3]; 25630[label="ywz1702/Neg ywz17020",fontsize=10,color="white",style="solid",shape="box"];19934 -> 25630[label="",style="solid", color="burlywood", weight=9]; 25630 -> 19946[label="",style="solid", color="burlywood", weight=3]; 19935[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg (Succ ywz1699)))",fontsize=16,color="black",shape="box"];19935 -> 19947[label="",style="solid", color="black", weight=3]; 19936[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz17050 ywz17051 ywz17052 ywz17053 ywz17054) (Neg (Succ ywz1699)))",fontsize=16,color="black",shape="box"];19936 -> 19948[label="",style="solid", color="black", weight=3]; 18058[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 ywz1480 ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (Neg (Succ ywz1477) > ywz1480))",fontsize=16,color="black",shape="box"];18058 -> 18083[label="",style="solid", color="black", weight=3]; 18059[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM ywz1483 (Neg (Succ ywz1477)))",fontsize=16,color="burlywood",shape="triangle"];25631[label="ywz1483/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];18059 -> 25631[label="",style="solid", color="burlywood", weight=9]; 25631 -> 18084[label="",style="solid", color="burlywood", weight=3]; 25632[label="ywz1483/FiniteMap.Branch ywz14830 ywz14831 ywz14832 ywz14833 ywz14834",fontsize=10,color="white",style="solid",shape="box"];18059 -> 25632[label="",style="solid", color="burlywood", weight=9]; 25632 -> 18085[label="",style="solid", color="burlywood", weight=3]; 20517[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 ywz1789 ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (Neg (Succ ywz1786) > ywz1789))",fontsize=16,color="black",shape="box"];20517 -> 20644[label="",style="solid", color="black", weight=3]; 20518[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM ywz1792 (Neg (Succ 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1187[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT))",fontsize=16,color="black",shape="box"];1187 -> 1359[label="",style="solid", color="black", weight=3]; 1813[label="primPlusNat (primPlusNat (primPlusNat (primPlusNat (primMulNat Zero (Succ ywz7200)) (Succ ywz7200)) (Succ ywz7200)) (Succ ywz7200)) (Succ ywz7200)",fontsize=16,color="black",shape="box"];1813 -> 1954[label="",style="solid", color="black", weight=3]; 7820[label="ywz250000",fontsize=16,color="green",shape="box"];7821[label="ywz372000",fontsize=16,color="green",shape="box"];15570 -> 15536[label="",style="dashed", color="red", weight=0]; 15570[label="FiniteMap.sizeFM ywz1237",fontsize=16,color="magenta"];15570 -> 15608[label="",style="dashed", color="magenta", weight=3]; 15571[label="FiniteMap.sizeFM 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color="burlywood", weight=9]; 25636 -> 14240[label="",style="solid", color="burlywood", weight=3]; 14176[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (GT == GT)",fontsize=16,color="black",shape="triangle"];14176 -> 14241[label="",style="solid", color="black", weight=3]; 14177[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Pos (Succ ywz115400)) == GT)",fontsize=16,color="black",shape="box"];14177 -> 14242[label="",style="solid", color="black", weight=3]; 14178[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];14178 -> 14243[label="",style="solid", color="black", weight=3]; 14179[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Neg (Succ ywz115400)) == GT)",fontsize=16,color="black",shape="box"];14179 -> 14244[label="",style="solid", color="black", weight=3]; 14180[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];14180 -> 14245[label="",style="solid", color="black", weight=3]; 14181[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (LT == GT)",fontsize=16,color="black",shape="triangle"];14181 -> 14246[label="",style="solid", color="black", weight=3]; 14182[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat ywz11540 (Succ ywz115700) == GT)",fontsize=16,color="burlywood",shape="triangle"];25637[label="ywz11540/Succ ywz115400",fontsize=10,color="white",style="solid",shape="box"];14182 -> 25637[label="",style="solid", color="burlywood", weight=9]; 25637 -> 14247[label="",style="solid", color="burlywood", weight=3]; 25638[label="ywz11540/Zero",fontsize=10,color="white",style="solid",shape="box"];14182 -> 25638[label="",style="solid", color="burlywood", weight=9]; 25638 -> 14248[label="",style="solid", color="burlywood", weight=3]; 14183[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Pos (Succ ywz115400)) == GT)",fontsize=16,color="black",shape="box"];14183 -> 14249[label="",style="solid", color="black", weight=3]; 14184[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];14184 -> 14250[label="",style="solid", color="black", weight=3]; 14185[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Neg (Succ ywz115400)) == GT)",fontsize=16,color="black",shape="box"];14185 -> 14251[label="",style="solid", color="black", weight=3]; 14186[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];14186 -> 14252[label="",style="solid", color="black", weight=3]; 6703 -> 20555[label="",style="dashed", color="red", weight=0]; 6703[label="FiniteMap.splitLT1 (Pos (Succ ywz427)) ywz428 ywz429 ywz430 ywz431 (Pos (Succ ywz432)) (primCmpNat (Succ ywz432) (Succ ywz427) == GT)",fontsize=16,color="magenta"];6703 -> 20556[label="",style="dashed", color="magenta", weight=3]; 6703 -> 20557[label="",style="dashed", color="magenta", weight=3]; 6703 -> 20558[label="",style="dashed", color="magenta", weight=3]; 6703 -> 20559[label="",style="dashed", color="magenta", weight=3]; 6703 -> 20560[label="",style="dashed", color="magenta", weight=3]; 6703 -> 20561[label="",style="dashed", color="magenta", weight=3]; 6703 -> 20562[label="",style="dashed", color="magenta", weight=3]; 6703 -> 20563[label="",style="dashed", color="magenta", weight=3]; 1115 -> 856[label="",style="dashed", color="red", weight=0]; 1115[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos (Succ ywz5000))",fontsize=16,color="magenta"];1116 -> 27[label="",style="dashed", color="red", weight=0]; 1116[label="FiniteMap.splitLT3 (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos (Succ ywz5000))",fontsize=16,color="magenta"];1116 -> 1282[label="",style="dashed", color="magenta", weight=3]; 1116 -> 1283[label="",style="dashed", color="magenta", weight=3]; 1116 -> 1284[label="",style="dashed", color="magenta", weight=3]; 1116 -> 1285[label="",style="dashed", color="magenta", weight=3]; 1116 -> 1286[label="",style="dashed", color="magenta", weight=3]; 1116 -> 1287[label="",style="dashed", color="magenta", weight=3]; 768[label="Zero",fontsize=16,color="green",shape="box"];769[label="ywz43",fontsize=16,color="green",shape="box"];853 -> 974[label="",style="dashed", color="red", weight=0]; 853[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.splitLT ywz44 (Pos (Succ ywz5000))) (Neg ywz400) ywz41",fontsize=16,color="magenta"];853 -> 975[label="",style="dashed", color="magenta", weight=3]; 856[label="FiniteMap.splitLT4 FiniteMap.EmptyFM (Pos (Succ ywz5000))",fontsize=16,color="black",shape="triangle"];856 -> 976[label="",style="solid", color="black", weight=3]; 855[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) ywz13",fontsize=16,color="burlywood",shape="triangle"];25639[label="ywz13/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];855 -> 25639[label="",style="solid", color="burlywood", weight=9]; 25639 -> 977[label="",style="solid", color="burlywood", weight=3]; 25640[label="ywz13/FiniteMap.Branch ywz130 ywz131 ywz132 ywz133 ywz134",fontsize=10,color="white",style="solid",shape="box"];855 -> 25640[label="",style="solid", color="burlywood", weight=9]; 25640 -> 978[label="",style="solid", color="burlywood", weight=3]; 857 -> 27[label="",style="dashed", color="red", weight=0]; 857[label="FiniteMap.splitLT3 (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos (Succ ywz5000))",fontsize=16,color="magenta"];857 -> 979[label="",style="dashed", color="magenta", weight=3]; 857 -> 980[label="",style="dashed", color="magenta", weight=3]; 857 -> 981[label="",style="dashed", color="magenta", weight=3]; 857 -> 982[label="",style="dashed", color="magenta", weight=3]; 857 -> 983[label="",style="dashed", color="magenta", weight=3]; 857 -> 984[label="",style="dashed", color="magenta", weight=3]; 864[label="FiniteMap.mkVBalBranch5 (Neg (Succ ywz4000)) ywz41 FiniteMap.EmptyFM ywz10",fontsize=16,color="black",shape="box"];864 -> 985[label="",style="solid", color="black", weight=3]; 865[label="FiniteMap.mkVBalBranch (Neg (Succ ywz4000)) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];865 -> 986[label="",style="solid", color="black", weight=3]; 866[label="FiniteMap.mkVBalBranch (Neg (Succ ywz4000)) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (FiniteMap.Branch ywz100 ywz101 ywz102 ywz103 ywz104)",fontsize=16,color="black",shape="box"];866 -> 987[label="",style="solid", color="black", weight=3]; 6723 -> 20657[label="",style="dashed", color="red", weight=0]; 6723[label="FiniteMap.splitLT1 (Neg (Succ ywz436)) ywz437 ywz438 ywz439 ywz440 (Neg (Succ ywz441)) (primCmpNat (Succ ywz436) (Succ ywz441) == GT)",fontsize=16,color="magenta"];6723 -> 20658[label="",style="dashed", color="magenta", weight=3]; 6723 -> 20659[label="",style="dashed", color="magenta", weight=3]; 6723 -> 20660[label="",style="dashed", color="magenta", weight=3]; 6723 -> 20661[label="",style="dashed", color="magenta", weight=3]; 6723 -> 20662[label="",style="dashed", color="magenta", weight=3]; 6723 -> 20663[label="",style="dashed", color="magenta", weight=3]; 6723 -> 20664[label="",style="dashed", color="magenta", weight=3]; 6723 -> 20665[label="",style="dashed", color="magenta", weight=3]; 876 -> 197[label="",style="dashed", color="red", weight=0]; 876[label="FiniteMap.splitLT ywz44 (Neg Zero)",fontsize=16,color="magenta"];876 -> 997[label="",style="dashed", color="magenta", weight=3]; 20995[label="FiniteMap.splitGT0 (Pos (Succ ywz1827)) ywz1828 ywz1829 ywz1830 ywz1831 (Pos (Succ ywz1832)) otherwise",fontsize=16,color="black",shape="box"];20995 -> 21031[label="",style="solid", color="black", weight=3]; 20996 -> 759[label="",style="dashed", color="red", weight=0]; 20996[label="FiniteMap.mkVBalBranch (Pos (Succ ywz1827)) ywz1828 (FiniteMap.splitGT ywz1830 (Pos (Succ ywz1832))) ywz1831",fontsize=16,color="magenta"];20996 -> 21032[label="",style="dashed", color="magenta", weight=3]; 20996 -> 21033[label="",style="dashed", color="magenta", weight=3]; 20996 -> 21034[label="",style="dashed", color="magenta", weight=3]; 20996 -> 21035[label="",style="dashed", color="magenta", weight=3]; 770[label="Succ ywz4000",fontsize=16,color="green",shape="box"];771 -> 208[label="",style="dashed", color="red", weight=0]; 771[label="FiniteMap.splitGT ywz43 (Pos Zero)",fontsize=16,color="magenta"];771 -> 1007[label="",style="dashed", color="magenta", weight=3]; 898 -> 83[label="",style="dashed", color="red", weight=0]; 898[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];899[label="ywz434",fontsize=16,color="green",shape="box"];900[label="ywz432",fontsize=16,color="green",shape="box"];901[label="ywz431",fontsize=16,color="green",shape="box"];902[label="ywz433",fontsize=16,color="green",shape="box"];903[label="ywz430",fontsize=16,color="green",shape="box"];904[label="Neg (Succ ywz5000)",fontsize=16,color="green",shape="box"];905[label="FiniteMap.addToFM ywz44 (Pos ywz400) ywz41",fontsize=16,color="black",shape="triangle"];905 -> 1008[label="",style="solid", color="black", weight=3]; 906[label="FiniteMap.mkVBalBranch4 (Pos ywz400) ywz41 (FiniteMap.Branch ywz120 ywz121 ywz122 ywz123 ywz124) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];906 -> 1009[label="",style="solid", color="black", weight=3]; 907[label="FiniteMap.mkVBalBranch3 (Pos ywz400) ywz41 (FiniteMap.Branch ywz120 ywz121 ywz122 ywz123 ywz124) (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444)",fontsize=16,color="black",shape="box"];907 -> 1010[label="",style="solid", color="black", weight=3]; 21077[label="FiniteMap.splitGT0 (Neg (Succ ywz1837)) ywz1838 ywz1839 ywz1840 ywz1841 (Neg (Succ ywz1842)) otherwise",fontsize=16,color="black",shape="box"];21077 -> 21115[label="",style="solid", color="black", weight=3]; 21078 -> 626[label="",style="dashed", color="red", weight=0]; 21078[label="FiniteMap.mkVBalBranch (Neg (Succ ywz1837)) ywz1838 (FiniteMap.splitGT ywz1840 (Neg (Succ ywz1842))) ywz1841",fontsize=16,color="magenta"];21078 -> 21116[label="",style="dashed", color="magenta", weight=3]; 21078 -> 21117[label="",style="dashed", color="magenta", weight=3]; 21078 -> 21118[label="",style="dashed", color="magenta", weight=3]; 21078 -> 21119[label="",style="dashed", color="magenta", weight=3]; 897 -> 760[label="",style="dashed", color="red", weight=0]; 897[label="FiniteMap.splitGT ywz43 (Neg (Succ ywz5000))",fontsize=16,color="magenta"];896[label="FiniteMap.mkVBalBranch (Neg Zero) ywz41 ywz14 ywz44",fontsize=16,color="burlywood",shape="triangle"];25641[label="ywz14/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];896 -> 25641[label="",style="solid", color="burlywood", weight=9]; 25641 -> 1020[label="",style="solid", color="burlywood", weight=3]; 25642[label="ywz14/FiniteMap.Branch ywz140 ywz141 ywz142 ywz143 ywz144",fontsize=10,color="white",style="solid",shape="box"];896 -> 25642[label="",style="solid", color="burlywood", weight=9]; 25642 -> 1021[label="",style="solid", color="burlywood", weight=3]; 17067[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (primCmpNat (Succ ywz14190) (Succ ywz14200) == GT)",fontsize=16,color="black",shape="box"];17067 -> 17147[label="",style="solid", color="black", weight=3]; 17068[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (primCmpNat (Succ ywz14190) Zero == GT)",fontsize=16,color="black",shape="box"];17068 -> 17148[label="",style="solid", color="black", weight=3]; 17069[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (primCmpNat Zero (Succ ywz14200) == GT)",fontsize=16,color="black",shape="box"];17069 -> 17149[label="",style="solid", color="black", weight=3]; 17070[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];17070 -> 17150[label="",style="solid", color="black", weight=3]; 15533 -> 15167[label="",style="dashed", color="red", weight=0]; 15533[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz744 (Pos (Succ ywz5000)) ywz9",fontsize=16,color="magenta"];15533 -> 15559[label="",style="dashed", color="magenta", weight=3]; 15533 -> 15560[label="",style="dashed", color="magenta", weight=3]; 15532[label="FiniteMap.mkBalBranch (Pos Zero) ywz741 ywz743 ywz1247",fontsize=16,color="black",shape="triangle"];15532 -> 15561[label="",style="solid", color="black", weight=3]; 15537 -> 13158[label="",style="dashed", color="red", weight=0]; 15537[label="FiniteMap.mkBalBranch6MkBalBranch5 ywz1243 ywz743 (Neg ywz7400) ywz741 (Neg ywz7400) ywz741 ywz743 ywz1243 (FiniteMap.mkBalBranch6Size_l ywz1243 ywz743 (Neg ywz7400) ywz741 + FiniteMap.mkBalBranch6Size_r ywz1243 ywz743 (Neg ywz7400) ywz741 < Pos (Succ (Succ Zero)))",fontsize=16,color="magenta"];15537 -> 15573[label="",style="dashed", color="magenta", weight=3]; 15537 -> 15574[label="",style="dashed", color="magenta", weight=3]; 15537 -> 15575[label="",style="dashed", color="magenta", weight=3]; 15537 -> 15576[label="",style="dashed", color="magenta", weight=3]; 15537 -> 15577[label="",style="dashed", color="magenta", weight=3]; 15537 -> 15578[label="",style="dashed", color="magenta", weight=3]; 15538[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos (Succ ywz74000)) ywz741 ywz742 ywz743 ywz744 (Pos Zero) ywz9 True",fontsize=16,color="black",shape="box"];15538 -> 15579[label="",style="solid", color="black", weight=3]; 15539[label="FiniteMap.Branch (Pos Zero) (FiniteMap.addToFM0 ywz741 ywz9) ywz742 ywz743 ywz744",fontsize=16,color="green",shape="box"];15539 -> 15580[label="",style="dashed", color="green", weight=3]; 15540[label="ywz744",fontsize=16,color="green",shape="box"];15541[label="Pos Zero",fontsize=16,color="green",shape="box"];15542[label="FiniteMap.Branch (Pos Zero) (FiniteMap.addToFM0 ywz741 ywz9) ywz742 ywz743 ywz744",fontsize=16,color="green",shape="box"];15542 -> 15581[label="",style="dashed", color="green", weight=3]; 15543[label="FiniteMap.addToFM0 ywz741 ywz9",fontsize=16,color="black",shape="triangle"];15543 -> 15582[label="",style="solid", color="black", weight=3]; 16540[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (primCmpNat (Succ ywz13680) (Succ ywz13690) == GT)",fontsize=16,color="black",shape="box"];16540 -> 16553[label="",style="solid", color="black", weight=3]; 16541[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (primCmpNat (Succ ywz13680) Zero == GT)",fontsize=16,color="black",shape="box"];16541 -> 16554[label="",style="solid", color="black", weight=3]; 16542[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (primCmpNat Zero (Succ ywz13690) == GT)",fontsize=16,color="black",shape="box"];16542 -> 16555[label="",style="solid", color="black", weight=3]; 16543[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];16543 -> 16556[label="",style="solid", color="black", weight=3]; 15548[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg Zero) ywz741 ywz742 ywz743 ywz744 (Neg (Succ ywz5000)) ywz9 True",fontsize=16,color="black",shape="box"];15548 -> 15588[label="",style="solid", color="black", weight=3]; 15549[label="FiniteMap.Branch (Neg Zero) (FiniteMap.addToFM0 ywz741 ywz9) ywz742 ywz743 ywz744",fontsize=16,color="green",shape="box"];15549 -> 15589[label="",style="dashed", color="green", weight=3]; 15550[label="FiniteMap.Branch (Neg Zero) (FiniteMap.addToFM0 ywz741 ywz9) ywz742 ywz743 ywz744",fontsize=16,color="green",shape="box"];15550 -> 15590[label="",style="dashed", color="green", weight=3]; 15551[label="Succ ywz74000",fontsize=16,color="green",shape="box"];15552 -> 15167[label="",style="dashed", color="red", weight=0]; 15552[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz744 (Neg Zero) ywz9",fontsize=16,color="magenta"];15552 -> 15591[label="",style="dashed", color="magenta", weight=3]; 15552 -> 15592[label="",style="dashed", color="magenta", weight=3]; 15553[label="FiniteMap.Branch (Neg Zero) (FiniteMap.addToFM0 ywz741 ywz9) ywz742 ywz743 ywz744",fontsize=16,color="green",shape="box"];15553 -> 15593[label="",style="dashed", color="green", weight=3]; 17703[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 ywz1444 ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (compare (Pos (Succ ywz1441)) ywz1444 == GT))",fontsize=16,color="black",shape="box"];17703 -> 17740[label="",style="solid", color="black", weight=3]; 17704[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos (Succ ywz1441)))",fontsize=16,color="black",shape="box"];17704 -> 17741[label="",style="solid", color="black", weight=3]; 17705[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM (FiniteMap.Branch ywz14470 ywz14471 ywz14472 ywz14473 ywz14474) (Pos (Succ ywz1441)))",fontsize=16,color="black",shape="box"];17705 -> 17742[label="",style="solid", color="black", weight=3]; 21688[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 ywz1880 ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (compare (Pos (Succ ywz1877)) ywz1880 == GT))",fontsize=16,color="black",shape="box"];21688 -> 21715[label="",style="solid", color="black", weight=3]; 21689[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM FiniteMap.EmptyFM (Pos (Succ ywz1877)))",fontsize=16,color="black",shape="box"];21689 -> 21716[label="",style="solid", color="black", weight=3]; 21690[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM (FiniteMap.Branch ywz18830 ywz18831 ywz18832 ywz18833 ywz18834) (Pos (Succ ywz1877)))",fontsize=16,color="black",shape="box"];21690 -> 21717[label="",style="solid", color="black", weight=3]; 21903[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Pos ywz18940) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (primCmpInt (Pos (Succ ywz1891)) (Pos ywz18940) == GT))",fontsize=16,color="black",shape="box"];21903 -> 21959[label="",style="solid", color="black", weight=3]; 21904[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Neg ywz18940) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (primCmpInt (Pos (Succ ywz1891)) (Neg ywz18940) == GT))",fontsize=16,color="black",shape="box"];21904 -> 21960[label="",style="solid", color="black", weight=3]; 21905[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 Nothing",fontsize=16,color="black",shape="box"];21905 -> 21961[label="",style="solid", color="black", weight=3]; 21906 -> 21630[label="",style="dashed", color="red", weight=0]; 21906[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM2 ywz18970 ywz18971 ywz18972 ywz18973 ywz18974 (Pos (Succ ywz1891)) (Pos (Succ ywz1891) < ywz18970))",fontsize=16,color="magenta"];21906 -> 21962[label="",style="dashed", color="magenta", weight=3]; 21906 -> 21963[label="",style="dashed", color="magenta", weight=3]; 21906 -> 21964[label="",style="dashed", color="magenta", weight=3]; 21906 -> 21965[label="",style="dashed", color="magenta", weight=3]; 21906 -> 21966[label="",style="dashed", color="magenta", weight=3]; 21906 -> 21967[label="",style="dashed", color="magenta", weight=3]; 22790[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 ywz2034 ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (primCmpInt (Pos Zero) ywz2034 == GT))",fontsize=16,color="burlywood",shape="box"];25643[label="ywz2034/Pos ywz20340",fontsize=10,color="white",style="solid",shape="box"];22790 -> 25643[label="",style="solid", color="burlywood", weight=9]; 25643 -> 22832[label="",style="solid", color="burlywood", weight=3]; 25644[label="ywz2034/Neg ywz20340",fontsize=10,color="white",style="solid",shape="box"];22790 -> 25644[label="",style="solid", color="burlywood", weight=9]; 25644 -> 22833[label="",style="solid", color="burlywood", weight=3]; 22791[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos Zero))",fontsize=16,color="black",shape="box"];22791 -> 22834[label="",style="solid", color="black", weight=3]; 22792[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz20370 ywz20371 ywz20372 ywz20373 ywz20374) (Pos Zero))",fontsize=16,color="black",shape="box"];22792 -> 22835[label="",style="solid", color="black", weight=3]; 1343[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];1343 -> 1634[label="",style="solid", color="black", weight=3]; 22072[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 ywz1949 ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (primCmpInt (Pos Zero) ywz1949 == GT))",fontsize=16,color="burlywood",shape="box"];25645[label="ywz1949/Pos ywz19490",fontsize=10,color="white",style="solid",shape="box"];22072 -> 25645[label="",style="solid", color="burlywood", weight=9]; 25645 -> 22127[label="",style="solid", color="burlywood", weight=3]; 25646[label="ywz1949/Neg ywz19490",fontsize=10,color="white",style="solid",shape="box"];22072 -> 25646[label="",style="solid", color="burlywood", weight=9]; 25646 -> 22128[label="",style="solid", color="burlywood", weight=3]; 22073[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos Zero))",fontsize=16,color="black",shape="box"];22073 -> 22129[label="",style="solid", color="black", weight=3]; 22074[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz19520 ywz19521 ywz19522 ywz19523 ywz19524) (Pos Zero))",fontsize=16,color="black",shape="box"];22074 -> 22130[label="",style="solid", color="black", weight=3]; 1345[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];1345 -> 1636[label="",style="solid", color="black", weight=3]; 19945[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Pos ywz17020) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (primCmpInt (Neg (Succ ywz1699)) (Pos ywz17020) == GT))",fontsize=16,color="black",shape="box"];19945 -> 19975[label="",style="solid", color="black", weight=3]; 19946[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Neg ywz17020) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (primCmpInt (Neg (Succ ywz1699)) (Neg ywz17020) == GT))",fontsize=16,color="black",shape="box"];19946 -> 19976[label="",style="solid", color="black", weight=3]; 19947[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 Nothing",fontsize=16,color="black",shape="box"];19947 -> 19977[label="",style="solid", color="black", weight=3]; 19948 -> 19814[label="",style="dashed", color="red", weight=0]; 19948[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM2 ywz17050 ywz17051 ywz17052 ywz17053 ywz17054 (Neg (Succ ywz1699)) (Neg (Succ ywz1699) < ywz17050))",fontsize=16,color="magenta"];19948 -> 19978[label="",style="dashed", color="magenta", weight=3]; 19948 -> 19979[label="",style="dashed", color="magenta", weight=3]; 19948 -> 19980[label="",style="dashed", color="magenta", weight=3]; 19948 -> 19981[label="",style="dashed", color="magenta", weight=3]; 19948 -> 19982[label="",style="dashed", color="magenta", weight=3]; 19948 -> 19983[label="",style="dashed", color="magenta", weight=3]; 18083[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 ywz1480 ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (compare (Neg (Succ ywz1477)) ywz1480 == GT))",fontsize=16,color="black",shape="box"];18083 -> 18093[label="",style="solid", color="black", weight=3]; 18084[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg (Succ ywz1477)))",fontsize=16,color="black",shape="box"];18084 -> 18094[label="",style="solid", color="black", weight=3]; 18085[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM (FiniteMap.Branch ywz14830 ywz14831 ywz14832 ywz14833 ywz14834) (Neg (Succ ywz1477)))",fontsize=16,color="black",shape="box"];18085 -> 18095[label="",style="solid", color="black", weight=3]; 20644[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 ywz1789 ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (compare (Neg (Succ ywz1786)) ywz1789 == GT))",fontsize=16,color="black",shape="box"];20644 -> 20746[label="",style="solid", color="black", weight=3]; 20645[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM FiniteMap.EmptyFM (Neg (Succ ywz1786)))",fontsize=16,color="black",shape="box"];20645 -> 20747[label="",style="solid", color="black", weight=3]; 20646[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM (FiniteMap.Branch ywz17920 ywz17921 ywz17922 ywz17923 ywz17924) (Neg (Succ ywz1786)))",fontsize=16,color="black",shape="box"];20646 -> 20748[label="",style="solid", color="black", weight=3]; 22633[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 ywz2005 ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (primCmpInt (Neg Zero) ywz2005 == GT))",fontsize=16,color="burlywood",shape="box"];25647[label="ywz2005/Pos ywz20050",fontsize=10,color="white",style="solid",shape="box"];22633 -> 25647[label="",style="solid", color="burlywood", weight=9]; 25647 -> 22698[label="",style="solid", color="burlywood", weight=3]; 25648[label="ywz2005/Neg ywz20050",fontsize=10,color="white",style="solid",shape="box"];22633 -> 25648[label="",style="solid", color="burlywood", weight=9]; 25648 -> 22699[label="",style="solid", color="burlywood", weight=3]; 22634[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg Zero))",fontsize=16,color="black",shape="box"];22634 -> 22700[label="",style="solid", color="black", weight=3]; 22635[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz20080 ywz20081 ywz20082 ywz20083 ywz20084) (Neg Zero))",fontsize=16,color="black",shape="box"];22635 -> 22701[label="",style="solid", color="black", weight=3]; 1357[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];1357 -> 1649[label="",style="solid", color="black", weight=3]; 25162[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 ywz2383 ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (primCmpInt (Neg Zero) ywz2383 == GT))",fontsize=16,color="burlywood",shape="box"];25649[label="ywz2383/Pos ywz23830",fontsize=10,color="white",style="solid",shape="box"];25162 -> 25649[label="",style="solid", color="burlywood", weight=9]; 25649 -> 25177[label="",style="solid", color="burlywood", weight=3]; 25650[label="ywz2383/Neg ywz23830",fontsize=10,color="white",style="solid",shape="box"];25162 -> 25650[label="",style="solid", color="burlywood", weight=9]; 25650 -> 25178[label="",style="solid", color="burlywood", weight=3]; 25163[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg Zero))",fontsize=16,color="black",shape="box"];25163 -> 25179[label="",style="solid", color="black", weight=3]; 25164[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz23860 ywz23861 ywz23862 ywz23863 ywz23864) (Neg Zero))",fontsize=16,color="black",shape="box"];25164 -> 25180[label="",style="solid", color="black", weight=3]; 1359[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];1359 -> 1651[label="",style="solid", color="black", weight=3]; 1954[label="primPlusNat (primPlusNat (primPlusNat (primPlusNat Zero (Succ ywz7200)) (Succ ywz7200)) (Succ ywz7200)) (Succ ywz7200)",fontsize=16,color="black",shape="box"];1954 -> 2000[label="",style="solid", color="black", weight=3]; 15608[label="ywz1237",fontsize=16,color="green",shape="box"];15609[label="Pos Zero",fontsize=16,color="green",shape="box"];15610[label="ywz12382",fontsize=16,color="green",shape="box"];14239[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz115700) (Succ ywz115400) == GT)",fontsize=16,color="black",shape="box"];14239 -> 14303[label="",style="solid", color="black", weight=3]; 14240[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz115700) Zero == GT)",fontsize=16,color="black",shape="box"];14240 -> 14304[label="",style="solid", color="black", weight=3]; 14241[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 True",fontsize=16,color="black",shape="box"];14241 -> 14305[label="",style="solid", color="black", weight=3]; 14242 -> 14182[label="",style="dashed", color="red", weight=0]; 14242[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat Zero (Succ ywz115400) == GT)",fontsize=16,color="magenta"];14242 -> 14306[label="",style="dashed", color="magenta", weight=3]; 14242 -> 14307[label="",style="dashed", color="magenta", weight=3]; 14243[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (EQ == GT)",fontsize=16,color="black",shape="triangle"];14243 -> 14308[label="",style="solid", color="black", weight=3]; 14244 -> 14176[label="",style="dashed", color="red", weight=0]; 14244[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (GT == GT)",fontsize=16,color="magenta"];14245 -> 14243[label="",style="dashed", color="red", weight=0]; 14245[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (EQ == GT)",fontsize=16,color="magenta"];14246[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 False",fontsize=16,color="black",shape="triangle"];14246 -> 14309[label="",style="solid", color="black", weight=3]; 14247[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz115400) (Succ ywz115700) == GT)",fontsize=16,color="black",shape="box"];14247 -> 14310[label="",style="solid", color="black", weight=3]; 14248[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat Zero (Succ ywz115700) == GT)",fontsize=16,color="black",shape="box"];14248 -> 14311[label="",style="solid", color="black", weight=3]; 14249 -> 14181[label="",style="dashed", color="red", weight=0]; 14249[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (LT == GT)",fontsize=16,color="magenta"];14250 -> 14243[label="",style="dashed", color="red", weight=0]; 14250[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (EQ == GT)",fontsize=16,color="magenta"];14251 -> 14175[label="",style="dashed", color="red", weight=0]; 14251[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz115400) Zero == GT)",fontsize=16,color="magenta"];14251 -> 14312[label="",style="dashed", color="magenta", weight=3]; 14251 -> 14313[label="",style="dashed", color="magenta", weight=3]; 14252 -> 14243[label="",style="dashed", color="red", weight=0]; 14252[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (EQ == GT)",fontsize=16,color="magenta"];20556[label="ywz427",fontsize=16,color="green",shape="box"];20557[label="ywz430",fontsize=16,color="green",shape="box"];20558[label="Succ ywz432",fontsize=16,color="green",shape="box"];20559[label="ywz428",fontsize=16,color="green",shape="box"];20560[label="ywz431",fontsize=16,color="green",shape="box"];20561[label="ywz429",fontsize=16,color="green",shape="box"];20562[label="Succ ywz427",fontsize=16,color="green",shape="box"];20563[label="ywz432",fontsize=16,color="green",shape="box"];20555[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (primCmpNat ywz1815 ywz1816 == GT)",fontsize=16,color="burlywood",shape="triangle"];25651[label="ywz1815/Succ ywz18150",fontsize=10,color="white",style="solid",shape="box"];20555 -> 25651[label="",style="solid", color="burlywood", weight=9]; 25651 -> 20647[label="",style="solid", color="burlywood", weight=3]; 25652[label="ywz1815/Zero",fontsize=10,color="white",style="solid",shape="box"];20555 -> 25652[label="",style="solid", color="burlywood", weight=9]; 25652 -> 20648[label="",style="solid", color="burlywood", weight=3]; 1282[label="ywz444",fontsize=16,color="green",shape="box"];1283[label="ywz442",fontsize=16,color="green",shape="box"];1284[label="ywz441",fontsize=16,color="green",shape="box"];1285[label="ywz443",fontsize=16,color="green",shape="box"];1286[label="ywz440",fontsize=16,color="green",shape="box"];1287[label="Pos (Succ ywz5000)",fontsize=16,color="green",shape="box"];975 -> 767[label="",style="dashed", color="red", weight=0]; 975[label="FiniteMap.splitLT ywz44 (Pos (Succ ywz5000))",fontsize=16,color="magenta"];974[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz15 (Neg ywz400) ywz41",fontsize=16,color="burlywood",shape="triangle"];25653[label="ywz15/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];974 -> 25653[label="",style="solid", color="burlywood", weight=9]; 25653 -> 1117[label="",style="solid", color="burlywood", weight=3]; 25654[label="ywz15/FiniteMap.Branch ywz150 ywz151 ywz152 ywz153 ywz154",fontsize=10,color="white",style="solid",shape="box"];974 -> 25654[label="",style="solid", color="burlywood", weight=9]; 25654 -> 1118[label="",style="solid", color="burlywood", weight=3]; 976 -> 83[label="",style="dashed", color="red", weight=0]; 976[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];977[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];977 -> 1119[label="",style="solid", color="black", weight=3]; 978[label="FiniteMap.mkVBalBranch (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (FiniteMap.Branch ywz130 ywz131 ywz132 ywz133 ywz134)",fontsize=16,color="black",shape="box"];978 -> 1120[label="",style="solid", color="black", weight=3]; 979[label="ywz444",fontsize=16,color="green",shape="box"];980[label="ywz442",fontsize=16,color="green",shape="box"];981[label="ywz441",fontsize=16,color="green",shape="box"];982[label="ywz443",fontsize=16,color="green",shape="box"];983[label="ywz440",fontsize=16,color="green",shape="box"];984[label="Pos (Succ ywz5000)",fontsize=16,color="green",shape="box"];985[label="FiniteMap.addToFM ywz10 (Neg (Succ ywz4000)) ywz41",fontsize=16,color="black",shape="triangle"];985 -> 1121[label="",style="solid", color="black", weight=3]; 986[label="FiniteMap.mkVBalBranch4 (Neg (Succ ywz4000)) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];986 -> 1122[label="",style="solid", color="black", weight=3]; 987[label="FiniteMap.mkVBalBranch3 (Neg (Succ ywz4000)) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (FiniteMap.Branch ywz100 ywz101 ywz102 ywz103 ywz104)",fontsize=16,color="black",shape="box"];987 -> 1123[label="",style="solid", color="black", weight=3]; 20658[label="ywz437",fontsize=16,color="green",shape="box"];20659[label="ywz438",fontsize=16,color="green",shape="box"];20660[label="ywz439",fontsize=16,color="green",shape="box"];20661[label="Succ ywz436",fontsize=16,color="green",shape="box"];20662[label="Succ ywz441",fontsize=16,color="green",shape="box"];20663[label="ywz441",fontsize=16,color="green",shape="box"];20664[label="ywz436",fontsize=16,color="green",shape="box"];20665[label="ywz440",fontsize=16,color="green",shape="box"];20657[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (primCmpNat ywz1824 ywz1825 == GT)",fontsize=16,color="burlywood",shape="triangle"];25655[label="ywz1824/Succ ywz18240",fontsize=10,color="white",style="solid",shape="box"];20657 -> 25655[label="",style="solid", color="burlywood", weight=9]; 25655 -> 20749[label="",style="solid", color="burlywood", weight=3]; 25656[label="ywz1824/Zero",fontsize=10,color="white",style="solid",shape="box"];20657 -> 25656[label="",style="solid", color="burlywood", weight=9]; 25656 -> 20750[label="",style="solid", color="burlywood", weight=3]; 997[label="ywz44",fontsize=16,color="green",shape="box"];21031[label="FiniteMap.splitGT0 (Pos (Succ ywz1827)) ywz1828 ywz1829 ywz1830 ywz1831 (Pos (Succ ywz1832)) True",fontsize=16,color="black",shape="box"];21031 -> 21079[label="",style="solid", color="black", weight=3]; 21032[label="ywz1831",fontsize=16,color="green",shape="box"];21033[label="ywz1828",fontsize=16,color="green",shape="box"];21034[label="Succ ywz1827",fontsize=16,color="green",shape="box"];21035 -> 165[label="",style="dashed", color="red", weight=0]; 21035[label="FiniteMap.splitGT ywz1830 (Pos (Succ ywz1832))",fontsize=16,color="magenta"];21035 -> 21080[label="",style="dashed", color="magenta", weight=3]; 21035 -> 21081[label="",style="dashed", color="magenta", weight=3]; 1007[label="ywz43",fontsize=16,color="green",shape="box"];1008[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz44 (Pos ywz400) ywz41",fontsize=16,color="burlywood",shape="triangle"];25657[label="ywz44/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];1008 -> 25657[label="",style="solid", color="burlywood", weight=9]; 25657 -> 1146[label="",style="solid", color="burlywood", weight=3]; 25658[label="ywz44/FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=10,color="white",style="solid",shape="box"];1008 -> 25658[label="",style="solid", color="burlywood", weight=9]; 25658 -> 1147[label="",style="solid", color="burlywood", weight=3]; 1009 -> 905[label="",style="dashed", color="red", weight=0]; 1009[label="FiniteMap.addToFM (FiniteMap.Branch ywz120 ywz121 ywz122 ywz123 ywz124) (Pos ywz400) ywz41",fontsize=16,color="magenta"];1009 -> 1148[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13641[label="",style="dashed", color="red", weight=0]; 1010[label="FiniteMap.mkVBalBranch3MkVBalBranch2 ywz120 ywz121 ywz122 ywz123 ywz124 ywz440 ywz441 ywz442 ywz443 ywz444 (Pos ywz400) ywz41 ywz120 ywz121 ywz122 ywz123 ywz124 ywz440 ywz441 ywz442 ywz443 ywz444 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz120 ywz121 ywz122 ywz123 ywz124 ywz440 ywz441 ywz442 ywz443 ywz444 < FiniteMap.mkVBalBranch3Size_r ywz120 ywz121 ywz122 ywz123 ywz124 ywz440 ywz441 ywz442 ywz443 ywz444)",fontsize=16,color="magenta"];1010 -> 13820[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13821[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13822[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13823[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13824[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13825[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13826[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13827[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13828[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13829[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13830[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13831[label="",style="dashed", color="magenta", weight=3]; 1010 -> 13832[label="",style="dashed", color="magenta", weight=3]; 21115[label="FiniteMap.splitGT0 (Neg (Succ ywz1837)) ywz1838 ywz1839 ywz1840 ywz1841 (Neg (Succ ywz1842)) True",fontsize=16,color="black",shape="box"];21115 -> 21334[label="",style="solid", color="black", weight=3]; 21116[label="ywz1838",fontsize=16,color="green",shape="box"];21117 -> 760[label="",style="dashed", color="red", weight=0]; 21117[label="FiniteMap.splitGT ywz1840 (Neg (Succ ywz1842))",fontsize=16,color="magenta"];21117 -> 21335[label="",style="dashed", color="magenta", weight=3]; 21117 -> 21336[label="",style="dashed", color="magenta", weight=3]; 21118[label="ywz1841",fontsize=16,color="green",shape="box"];21119[label="ywz1837",fontsize=16,color="green",shape="box"];1020[label="FiniteMap.mkVBalBranch (Neg Zero) ywz41 FiniteMap.EmptyFM ywz44",fontsize=16,color="black",shape="box"];1020 -> 1161[label="",style="solid", color="black", weight=3]; 1021[label="FiniteMap.mkVBalBranch (Neg Zero) ywz41 (FiniteMap.Branch ywz140 ywz141 ywz142 ywz143 ywz144) ywz44",fontsize=16,color="burlywood",shape="box"];25659[label="ywz44/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];1021 -> 25659[label="",style="solid", color="burlywood", weight=9]; 25659 -> 1162[label="",style="solid", color="burlywood", weight=3]; 25660[label="ywz44/FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=10,color="white",style="solid",shape="box"];1021 -> 25660[label="",style="solid", color="burlywood", weight=9]; 25660 -> 1163[label="",style="solid", color="burlywood", weight=3]; 17147 -> 16963[label="",style="dashed", color="red", weight=0]; 17147[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (primCmpNat ywz14190 ywz14200 == GT)",fontsize=16,color="magenta"];17147 -> 17200[label="",style="dashed", color="magenta", weight=3]; 17147 -> 17201[label="",style="dashed", color="magenta", weight=3]; 17148[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (GT == GT)",fontsize=16,color="black",shape="box"];17148 -> 17202[label="",style="solid", color="black", weight=3]; 17149[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (LT == GT)",fontsize=16,color="black",shape="box"];17149 -> 17203[label="",style="solid", color="black", weight=3]; 17150[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 (EQ == GT)",fontsize=16,color="black",shape="box"];17150 -> 17204[label="",style="solid", color="black", weight=3]; 15559[label="ywz744",fontsize=16,color="green",shape="box"];15560[label="Pos (Succ ywz5000)",fontsize=16,color="green",shape="box"];15561[label="FiniteMap.mkBalBranch6 (Pos Zero) ywz741 ywz743 ywz1247",fontsize=16,color="black",shape="box"];15561 -> 15601[label="",style="solid", color="black", weight=3]; 15573[label="ywz743",fontsize=16,color="green",shape="box"];15574[label="ywz1243",fontsize=16,color="green",shape="box"];15575[label="ywz1243",fontsize=16,color="green",shape="box"];15576[label="Neg ywz7400",fontsize=16,color="green",shape="box"];15577[label="ywz741",fontsize=16,color="green",shape="box"];15578 -> 10999[label="",style="dashed", color="red", weight=0]; 15578[label="FiniteMap.mkBalBranch6Size_l ywz1243 ywz743 (Neg ywz7400) ywz741 + FiniteMap.mkBalBranch6Size_r ywz1243 ywz743 (Neg ywz7400) ywz741 < Pos (Succ (Succ Zero))",fontsize=16,color="magenta"];15578 -> 15611[label="",style="dashed", color="magenta", weight=3]; 15578 -> 15612[label="",style="dashed", color="magenta", weight=3]; 15579[label="FiniteMap.Branch (Pos Zero) (FiniteMap.addToFM0 ywz741 ywz9) ywz742 ywz743 ywz744",fontsize=16,color="green",shape="box"];15579 -> 15613[label="",style="dashed", color="green", weight=3]; 15580 -> 15543[label="",style="dashed", color="red", weight=0]; 15580[label="FiniteMap.addToFM0 ywz741 ywz9",fontsize=16,color="magenta"];15581 -> 15543[label="",style="dashed", color="red", weight=0]; 15581[label="FiniteMap.addToFM0 ywz741 ywz9",fontsize=16,color="magenta"];15582[label="ywz9",fontsize=16,color="green",shape="box"];16553 -> 16422[label="",style="dashed", color="red", weight=0]; 16553[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (primCmpNat ywz13680 ywz13690 == GT)",fontsize=16,color="magenta"];16553 -> 16589[label="",style="dashed", color="magenta", weight=3]; 16553 -> 16590[label="",style="dashed", color="magenta", weight=3]; 16554[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (GT == GT)",fontsize=16,color="black",shape="box"];16554 -> 16591[label="",style="solid", color="black", weight=3]; 16555[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (LT == GT)",fontsize=16,color="black",shape="box"];16555 -> 16592[label="",style="solid", color="black", weight=3]; 16556[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 (EQ == GT)",fontsize=16,color="black",shape="box"];16556 -> 16593[label="",style="solid", color="black", weight=3]; 15588[label="FiniteMap.Branch (Neg (Succ ywz5000)) (FiniteMap.addToFM0 ywz741 ywz9) ywz742 ywz743 ywz744",fontsize=16,color="green",shape="box"];15588 -> 15621[label="",style="dashed", color="green", weight=3]; 15589 -> 15543[label="",style="dashed", color="red", weight=0]; 15589[label="FiniteMap.addToFM0 ywz741 ywz9",fontsize=16,color="magenta"];15590 -> 15543[label="",style="dashed", color="red", weight=0]; 15590[label="FiniteMap.addToFM0 ywz741 ywz9",fontsize=16,color="magenta"];15591[label="ywz744",fontsize=16,color="green",shape="box"];15592[label="Neg Zero",fontsize=16,color="green",shape="box"];15593 -> 15543[label="",style="dashed", color="red", weight=0]; 15593[label="FiniteMap.addToFM0 ywz741 ywz9",fontsize=16,color="magenta"];17740[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 ywz1444 ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (primCmpInt (Pos (Succ ywz1441)) ywz1444 == GT))",fontsize=16,color="burlywood",shape="box"];25661[label="ywz1444/Pos ywz14440",fontsize=10,color="white",style="solid",shape="box"];17740 -> 25661[label="",style="solid", color="burlywood", weight=9]; 25661 -> 17751[label="",style="solid", color="burlywood", weight=3]; 25662[label="ywz1444/Neg ywz14440",fontsize=10,color="white",style="solid",shape="box"];17740 -> 25662[label="",style="solid", color="burlywood", weight=9]; 25662 -> 17752[label="",style="solid", color="burlywood", weight=3]; 17741[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos (Succ ywz1441)))",fontsize=16,color="black",shape="box"];17741 -> 17753[label="",style="solid", color="black", weight=3]; 17742[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz14470 ywz14471 ywz14472 ywz14473 ywz14474) (Pos (Succ ywz1441)))",fontsize=16,color="black",shape="box"];17742 -> 17754[label="",style="solid", color="black", weight=3]; 21715[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 ywz1880 ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (primCmpInt (Pos (Succ ywz1877)) ywz1880 == GT))",fontsize=16,color="burlywood",shape="box"];25663[label="ywz1880/Pos ywz18800",fontsize=10,color="white",style="solid",shape="box"];21715 -> 25663[label="",style="solid", color="burlywood", weight=9]; 25663 -> 21757[label="",style="solid", color="burlywood", weight=3]; 25664[label="ywz1880/Neg ywz18800",fontsize=10,color="white",style="solid",shape="box"];21715 -> 25664[label="",style="solid", color="burlywood", weight=9]; 25664 -> 21758[label="",style="solid", color="burlywood", weight=3]; 21716[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Pos (Succ ywz1877)))",fontsize=16,color="black",shape="box"];21716 -> 21759[label="",style="solid", color="black", weight=3]; 21717[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz18830 ywz18831 ywz18832 ywz18833 ywz18834) (Pos (Succ ywz1877)))",fontsize=16,color="black",shape="box"];21717 -> 21760[label="",style="solid", color="black", weight=3]; 21959[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Pos ywz18940) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (primCmpNat (Succ ywz1891) ywz18940 == GT))",fontsize=16,color="burlywood",shape="box"];25665[label="ywz18940/Succ ywz189400",fontsize=10,color="white",style="solid",shape="box"];21959 -> 25665[label="",style="solid", color="burlywood", weight=9]; 25665 -> 21998[label="",style="solid", color="burlywood", weight=3]; 25666[label="ywz18940/Zero",fontsize=10,color="white",style="solid",shape="box"];21959 -> 25666[label="",style="solid", color="burlywood", weight=9]; 25666 -> 21999[label="",style="solid", color="burlywood", weight=3]; 21960[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Neg ywz18940) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (GT == GT))",fontsize=16,color="black",shape="box"];21960 -> 22000[label="",style="solid", color="black", weight=3]; 21961[label="ywz1892",fontsize=16,color="green",shape="box"];21962[label="ywz18973",fontsize=16,color="green",shape="box"];21963[label="ywz18972",fontsize=16,color="green",shape="box"];21964 -> 10999[label="",style="dashed", color="red", weight=0]; 21964[label="Pos (Succ ywz1891) < ywz18970",fontsize=16,color="magenta"];21964 -> 22001[label="",style="dashed", color="magenta", weight=3]; 21964 -> 22002[label="",style="dashed", color="magenta", weight=3]; 21965[label="ywz18970",fontsize=16,color="green",shape="box"];21966[label="ywz18971",fontsize=16,color="green",shape="box"];21967[label="ywz18974",fontsize=16,color="green",shape="box"];22832[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Pos ywz20340) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (primCmpInt (Pos Zero) (Pos ywz20340) == GT))",fontsize=16,color="burlywood",shape="box"];25667[label="ywz20340/Succ ywz203400",fontsize=10,color="white",style="solid",shape="box"];22832 -> 25667[label="",style="solid", color="burlywood", weight=9]; 25667 -> 22876[label="",style="solid", color="burlywood", weight=3]; 25668[label="ywz20340/Zero",fontsize=10,color="white",style="solid",shape="box"];22832 -> 25668[label="",style="solid", color="burlywood", weight=9]; 25668 -> 22877[label="",style="solid", color="burlywood", weight=3]; 22833[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Neg ywz20340) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (primCmpInt (Pos Zero) (Neg ywz20340) == GT))",fontsize=16,color="burlywood",shape="box"];25669[label="ywz20340/Succ ywz203400",fontsize=10,color="white",style="solid",shape="box"];22833 -> 25669[label="",style="solid", color="burlywood", weight=9]; 25669 -> 22878[label="",style="solid", color="burlywood", weight=3]; 25670[label="ywz20340/Zero",fontsize=10,color="white",style="solid",shape="box"];22833 -> 25670[label="",style="solid", color="burlywood", weight=9]; 25670 -> 22879[label="",style="solid", color="burlywood", weight=3]; 22834[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 Nothing",fontsize=16,color="black",shape="box"];22834 -> 22880[label="",style="solid", color="black", weight=3]; 22835 -> 22575[label="",style="dashed", color="red", weight=0]; 22835[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM2 ywz20370 ywz20371 ywz20372 ywz20373 ywz20374 (Pos Zero) (Pos Zero < ywz20370))",fontsize=16,color="magenta"];22835 -> 22881[label="",style="dashed", color="magenta", weight=3]; 22835 -> 22882[label="",style="dashed", color="magenta", weight=3]; 22835 -> 22883[label="",style="dashed", color="magenta", weight=3]; 22835 -> 22884[label="",style="dashed", color="magenta", weight=3]; 22835 -> 22885[label="",style="dashed", color="magenta", weight=3]; 22835 -> 22886[label="",style="dashed", color="magenta", weight=3]; 1634[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False)",fontsize=16,color="black",shape="box"];1634 -> 1776[label="",style="solid", color="black", weight=3]; 22127[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Pos ywz19490) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (primCmpInt (Pos Zero) (Pos ywz19490) == GT))",fontsize=16,color="burlywood",shape="box"];25671[label="ywz19490/Succ ywz194900",fontsize=10,color="white",style="solid",shape="box"];22127 -> 25671[label="",style="solid", color="burlywood", weight=9]; 25671 -> 22244[label="",style="solid", color="burlywood", weight=3]; 25672[label="ywz19490/Zero",fontsize=10,color="white",style="solid",shape="box"];22127 -> 25672[label="",style="solid", color="burlywood", weight=9]; 25672 -> 22245[label="",style="solid", color="burlywood", weight=3]; 22128[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Neg ywz19490) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (primCmpInt (Pos Zero) (Neg ywz19490) == GT))",fontsize=16,color="burlywood",shape="box"];25673[label="ywz19490/Succ ywz194900",fontsize=10,color="white",style="solid",shape="box"];22128 -> 25673[label="",style="solid", color="burlywood", weight=9]; 25673 -> 22246[label="",style="solid", color="burlywood", weight=3]; 25674[label="ywz19490/Zero",fontsize=10,color="white",style="solid",shape="box"];22128 -> 25674[label="",style="solid", color="burlywood", weight=9]; 25674 -> 22247[label="",style="solid", color="burlywood", weight=3]; 22129[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 Nothing",fontsize=16,color="black",shape="box"];22129 -> 22248[label="",style="solid", color="black", weight=3]; 22130 -> 21916[label="",style="dashed", color="red", weight=0]; 22130[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM2 ywz19520 ywz19521 ywz19522 ywz19523 ywz19524 (Pos Zero) (Pos Zero < ywz19520))",fontsize=16,color="magenta"];22130 -> 22249[label="",style="dashed", color="magenta", weight=3]; 22130 -> 22250[label="",style="dashed", color="magenta", weight=3]; 22130 -> 22251[label="",style="dashed", color="magenta", weight=3]; 22130 -> 22252[label="",style="dashed", color="magenta", weight=3]; 22130 -> 22253[label="",style="dashed", color="magenta", weight=3]; 22130 -> 22254[label="",style="dashed", color="magenta", weight=3]; 1636[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) False)",fontsize=16,color="black",shape="box"];1636 -> 1778[label="",style="solid", color="black", weight=3]; 19975[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Pos ywz17020) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (LT == GT))",fontsize=16,color="black",shape="box"];19975 -> 19990[label="",style="solid", color="black", weight=3]; 19976[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Neg ywz17020) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (primCmpNat ywz17020 (Succ ywz1699) == GT))",fontsize=16,color="burlywood",shape="box"];25675[label="ywz17020/Succ ywz170200",fontsize=10,color="white",style="solid",shape="box"];19976 -> 25675[label="",style="solid", color="burlywood", weight=9]; 25675 -> 19991[label="",style="solid", color="burlywood", weight=3]; 25676[label="ywz17020/Zero",fontsize=10,color="white",style="solid",shape="box"];19976 -> 25676[label="",style="solid", color="burlywood", weight=9]; 25676 -> 19992[label="",style="solid", color="burlywood", weight=3]; 19977[label="ywz1700",fontsize=16,color="green",shape="box"];19978[label="ywz17052",fontsize=16,color="green",shape="box"];19979[label="ywz17054",fontsize=16,color="green",shape="box"];19980[label="ywz17053",fontsize=16,color="green",shape="box"];19981 -> 10999[label="",style="dashed", color="red", weight=0]; 19981[label="Neg (Succ ywz1699) < ywz17050",fontsize=16,color="magenta"];19981 -> 19993[label="",style="dashed", color="magenta", weight=3]; 19981 -> 19994[label="",style="dashed", color="magenta", weight=3]; 19982[label="ywz17050",fontsize=16,color="green",shape="box"];19983[label="ywz17051",fontsize=16,color="green",shape="box"];18093[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 ywz1480 ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (primCmpInt (Neg (Succ ywz1477)) ywz1480 == GT))",fontsize=16,color="burlywood",shape="box"];25677[label="ywz1480/Pos ywz14800",fontsize=10,color="white",style="solid",shape="box"];18093 -> 25677[label="",style="solid", color="burlywood", weight=9]; 25677 -> 18103[label="",style="solid", color="burlywood", weight=3]; 25678[label="ywz1480/Neg ywz14800",fontsize=10,color="white",style="solid",shape="box"];18093 -> 25678[label="",style="solid", color="burlywood", weight=9]; 25678 -> 18104[label="",style="solid", color="burlywood", weight=3]; 18094[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg (Succ ywz1477)))",fontsize=16,color="black",shape="box"];18094 -> 18105[label="",style="solid", color="black", weight=3]; 18095[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz14830 ywz14831 ywz14832 ywz14833 ywz14834) (Neg (Succ ywz1477)))",fontsize=16,color="black",shape="box"];18095 -> 18106[label="",style="solid", color="black", weight=3]; 20746[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 ywz1789 ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (primCmpInt (Neg (Succ ywz1786)) ywz1789 == GT))",fontsize=16,color="burlywood",shape="box"];25679[label="ywz1789/Pos ywz17890",fontsize=10,color="white",style="solid",shape="box"];20746 -> 25679[label="",style="solid", color="burlywood", weight=9]; 25679 -> 20885[label="",style="solid", color="burlywood", weight=3]; 25680[label="ywz1789/Neg ywz17890",fontsize=10,color="white",style="solid",shape="box"];20746 -> 25680[label="",style="solid", color="burlywood", weight=9]; 25680 -> 20886[label="",style="solid", color="burlywood", weight=3]; 20747[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM4 FiniteMap.EmptyFM (Neg (Succ ywz1786)))",fontsize=16,color="black",shape="box"];20747 -> 20887[label="",style="solid", color="black", weight=3]; 20748[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM3 (FiniteMap.Branch ywz17920 ywz17921 ywz17922 ywz17923 ywz17924) (Neg (Succ ywz1786)))",fontsize=16,color="black",shape="box"];20748 -> 20888[label="",style="solid", color="black", weight=3]; 22698[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Pos ywz20050) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (primCmpInt (Neg Zero) (Pos ywz20050) == GT))",fontsize=16,color="burlywood",shape="box"];25681[label="ywz20050/Succ ywz200500",fontsize=10,color="white",style="solid",shape="box"];22698 -> 25681[label="",style="solid", color="burlywood", weight=9]; 25681 -> 22745[label="",style="solid", color="burlywood", weight=3]; 25682[label="ywz20050/Zero",fontsize=10,color="white",style="solid",shape="box"];22698 -> 25682[label="",style="solid", color="burlywood", weight=9]; 25682 -> 22746[label="",style="solid", color="burlywood", weight=3]; 22699[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Neg ywz20050) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (primCmpInt (Neg Zero) (Neg ywz20050) == GT))",fontsize=16,color="burlywood",shape="box"];25683[label="ywz20050/Succ ywz200500",fontsize=10,color="white",style="solid",shape="box"];22699 -> 25683[label="",style="solid", color="burlywood", weight=9]; 25683 -> 22747[label="",style="solid", color="burlywood", weight=3]; 25684[label="ywz20050/Zero",fontsize=10,color="white",style="solid",shape="box"];22699 -> 25684[label="",style="solid", color="burlywood", weight=9]; 25684 -> 22748[label="",style="solid", color="burlywood", weight=3]; 22700[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 Nothing",fontsize=16,color="black",shape="box"];22700 -> 22749[label="",style="solid", color="black", weight=3]; 22701 -> 22320[label="",style="dashed", color="red", weight=0]; 22701[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM2 ywz20080 ywz20081 ywz20082 ywz20083 ywz20084 (Neg Zero) (Neg Zero < ywz20080))",fontsize=16,color="magenta"];22701 -> 22750[label="",style="dashed", color="magenta", weight=3]; 22701 -> 22751[label="",style="dashed", color="magenta", weight=3]; 22701 -> 22752[label="",style="dashed", color="magenta", weight=3]; 22701 -> 22753[label="",style="dashed", color="magenta", weight=3]; 22701 -> 22754[label="",style="dashed", color="magenta", weight=3]; 22701 -> 22755[label="",style="dashed", color="magenta", weight=3]; 1649[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False)",fontsize=16,color="black",shape="box"];1649 -> 1792[label="",style="solid", color="black", weight=3]; 25177[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Pos ywz23830) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (primCmpInt (Neg Zero) (Pos ywz23830) == GT))",fontsize=16,color="burlywood",shape="box"];25685[label="ywz23830/Succ ywz238300",fontsize=10,color="white",style="solid",shape="box"];25177 -> 25685[label="",style="solid", color="burlywood", weight=9]; 25685 -> 25204[label="",style="solid", color="burlywood", weight=3]; 25686[label="ywz23830/Zero",fontsize=10,color="white",style="solid",shape="box"];25177 -> 25686[label="",style="solid", color="burlywood", weight=9]; 25686 -> 25205[label="",style="solid", color="burlywood", weight=3]; 25178[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Neg ywz23830) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (primCmpInt (Neg Zero) (Neg ywz23830) == GT))",fontsize=16,color="burlywood",shape="box"];25687[label="ywz23830/Succ ywz238300",fontsize=10,color="white",style="solid",shape="box"];25178 -> 25687[label="",style="solid", color="burlywood", weight=9]; 25687 -> 25206[label="",style="solid", color="burlywood", weight=3]; 25688[label="ywz23830/Zero",fontsize=10,color="white",style="solid",shape="box"];25178 -> 25688[label="",style="solid", color="burlywood", weight=9]; 25688 -> 25207[label="",style="solid", color="burlywood", weight=3]; 25179[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 Nothing",fontsize=16,color="black",shape="box"];25179 -> 25208[label="",style="solid", color="black", weight=3]; 25180 -> 24654[label="",style="dashed", color="red", weight=0]; 25180[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM2 ywz23860 ywz23861 ywz23862 ywz23863 ywz23864 (Neg Zero) (Neg Zero < ywz23860))",fontsize=16,color="magenta"];25180 -> 25209[label="",style="dashed", color="magenta", weight=3]; 25180 -> 25210[label="",style="dashed", color="magenta", weight=3]; 25180 -> 25211[label="",style="dashed", color="magenta", weight=3]; 25180 -> 25212[label="",style="dashed", color="magenta", weight=3]; 25180 -> 25213[label="",style="dashed", color="magenta", weight=3]; 25180 -> 25214[label="",style="dashed", color="magenta", weight=3]; 1651[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM1 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) False)",fontsize=16,color="black",shape="box"];1651 -> 1794[label="",style="solid", color="black", weight=3]; 2000[label="primPlusNat (primPlusNat (primPlusNat (Succ ywz7200) (Succ ywz7200)) (Succ ywz7200)) (Succ ywz7200)",fontsize=16,color="black",shape="box"];2000 -> 2011[label="",style="solid", color="black", weight=3]; 14303[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat ywz115700 ywz115400 == GT)",fontsize=16,color="burlywood",shape="triangle"];25689[label="ywz115700/Succ ywz1157000",fontsize=10,color="white",style="solid",shape="box"];14303 -> 25689[label="",style="solid", color="burlywood", weight=9]; 25689 -> 14364[label="",style="solid", color="burlywood", weight=3]; 25690[label="ywz115700/Zero",fontsize=10,color="white",style="solid",shape="box"];14303 -> 25690[label="",style="solid", color="burlywood", weight=9]; 25690 -> 14365[label="",style="solid", color="burlywood", weight=3]; 14304 -> 14176[label="",style="dashed", color="red", weight=0]; 14304[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (GT == GT)",fontsize=16,color="magenta"];14305[label="FiniteMap.mkBalBranch6MkBalBranch0 ywz1007 ywz73 ywz70 ywz71 ywz73 ywz1006 ywz1006",fontsize=16,color="burlywood",shape="box"];25691[label="ywz1006/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];14305 -> 25691[label="",style="solid", color="burlywood", weight=9]; 25691 -> 14366[label="",style="solid", color="burlywood", weight=3]; 25692[label="ywz1006/FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064",fontsize=10,color="white",style="solid",shape="box"];14305 -> 25692[label="",style="solid", color="burlywood", weight=9]; 25692 -> 14367[label="",style="solid", color="burlywood", weight=3]; 14306[label="ywz115400",fontsize=16,color="green",shape="box"];14307[label="Zero",fontsize=16,color="green",shape="box"];14308 -> 14246[label="",style="dashed", color="red", weight=0]; 14308[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 False",fontsize=16,color="magenta"];14309 -> 14368[label="",style="dashed", color="red", weight=0]; 14309[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (FiniteMap.mkBalBranch6Size_l ywz1007 ywz73 ywz70 ywz71 > FiniteMap.sIZE_RATIO * FiniteMap.mkBalBranch6Size_r ywz1007 ywz73 ywz70 ywz71)",fontsize=16,color="magenta"];14309 -> 14369[label="",style="dashed", color="magenta", weight=3]; 14309 -> 14370[label="",style="dashed", color="magenta", weight=3]; 14310 -> 14303[label="",style="dashed", color="red", weight=0]; 14310[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat ywz115400 ywz115700 == GT)",fontsize=16,color="magenta"];14310 -> 14377[label="",style="dashed", color="magenta", weight=3]; 14310 -> 14378[label="",style="dashed", color="magenta", weight=3]; 14311 -> 14181[label="",style="dashed", color="red", weight=0]; 14311[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (LT == GT)",fontsize=16,color="magenta"];14312[label="ywz115400",fontsize=16,color="green",shape="box"];14313[label="Zero",fontsize=16,color="green",shape="box"];20647[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (primCmpNat (Succ ywz18150) ywz1816 == GT)",fontsize=16,color="burlywood",shape="box"];25693[label="ywz1816/Succ ywz18160",fontsize=10,color="white",style="solid",shape="box"];20647 -> 25693[label="",style="solid", color="burlywood", weight=9]; 25693 -> 20751[label="",style="solid", color="burlywood", weight=3]; 25694[label="ywz1816/Zero",fontsize=10,color="white",style="solid",shape="box"];20647 -> 25694[label="",style="solid", color="burlywood", weight=9]; 25694 -> 20752[label="",style="solid", color="burlywood", weight=3]; 20648[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (primCmpNat Zero ywz1816 == GT)",fontsize=16,color="burlywood",shape="box"];25695[label="ywz1816/Succ ywz18160",fontsize=10,color="white",style="solid",shape="box"];20648 -> 25695[label="",style="solid", color="burlywood", weight=9]; 25695 -> 20753[label="",style="solid", color="burlywood", weight=3]; 25696[label="ywz1816/Zero",fontsize=10,color="white",style="solid",shape="box"];20648 -> 25696[label="",style="solid", color="burlywood", weight=9]; 25696 -> 20754[label="",style="solid", color="burlywood", weight=3]; 1117[label="FiniteMap.addToFM_C FiniteMap.addToFM0 FiniteMap.EmptyFM (Neg ywz400) ywz41",fontsize=16,color="black",shape="box"];1117 -> 1242[label="",style="solid", color="black", weight=3]; 1118[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch ywz150 ywz151 ywz152 ywz153 ywz154) (Neg ywz400) ywz41",fontsize=16,color="black",shape="box"];1118 -> 1243[label="",style="solid", color="black", weight=3]; 1119[label="FiniteMap.mkVBalBranch4 (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) FiniteMap.EmptyFM",fontsize=16,color="black",shape="triangle"];1119 -> 1288[label="",style="solid", color="black", weight=3]; 1120[label="FiniteMap.mkVBalBranch3 (Neg ywz400) ywz41 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (FiniteMap.Branch ywz130 ywz131 ywz132 ywz133 ywz134)",fontsize=16,color="black",shape="triangle"];1120 -> 1289[label="",style="solid", color="black", weight=3]; 1121 -> 974[label="",style="dashed", color="red", weight=0]; 1121[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz10 (Neg (Succ ywz4000)) ywz41",fontsize=16,color="magenta"];1121 -> 1290[label="",style="dashed", color="magenta", weight=3]; 1121 -> 1291[label="",style="dashed", color="magenta", weight=3]; 1122 -> 985[label="",style="dashed", color="red", weight=0]; 1122[label="FiniteMap.addToFM (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Neg (Succ ywz4000)) ywz41",fontsize=16,color="magenta"];1122 -> 1292[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13641[label="",style="dashed", color="red", weight=0]; 1123[label="FiniteMap.mkVBalBranch3MkVBalBranch2 ywz430 ywz431 ywz432 ywz433 ywz434 ywz100 ywz101 ywz102 ywz103 ywz104 (Neg (Succ ywz4000)) ywz41 ywz430 ywz431 ywz432 ywz433 ywz434 ywz100 ywz101 ywz102 ywz103 ywz104 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz430 ywz431 ywz432 ywz433 ywz434 ywz100 ywz101 ywz102 ywz103 ywz104 < FiniteMap.mkVBalBranch3Size_r ywz430 ywz431 ywz432 ywz433 ywz434 ywz100 ywz101 ywz102 ywz103 ywz104)",fontsize=16,color="magenta"];1123 -> 13833[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13834[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13835[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13836[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13837[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13838[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13839[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13840[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13841[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13842[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13843[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13844[label="",style="dashed", color="magenta", weight=3]; 1123 -> 13845[label="",style="dashed", color="magenta", weight=3]; 20749[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (primCmpNat (Succ ywz18240) ywz1825 == GT)",fontsize=16,color="burlywood",shape="box"];25697[label="ywz1825/Succ ywz18250",fontsize=10,color="white",style="solid",shape="box"];20749 -> 25697[label="",style="solid", color="burlywood", weight=9]; 25697 -> 20889[label="",style="solid", color="burlywood", weight=3]; 25698[label="ywz1825/Zero",fontsize=10,color="white",style="solid",shape="box"];20749 -> 25698[label="",style="solid", color="burlywood", weight=9]; 25698 -> 20890[label="",style="solid", color="burlywood", weight=3]; 20750[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (primCmpNat Zero ywz1825 == GT)",fontsize=16,color="burlywood",shape="box"];25699[label="ywz1825/Succ ywz18250",fontsize=10,color="white",style="solid",shape="box"];20750 -> 25699[label="",style="solid", color="burlywood", weight=9]; 25699 -> 20891[label="",style="solid", color="burlywood", weight=3]; 25700[label="ywz1825/Zero",fontsize=10,color="white",style="solid",shape="box"];20750 -> 25700[label="",style="solid", color="burlywood", weight=9]; 25700 -> 20892[label="",style="solid", color="burlywood", weight=3]; 21079[label="ywz1831",fontsize=16,color="green",shape="box"];21080[label="ywz1830",fontsize=16,color="green",shape="box"];21081[label="ywz1832",fontsize=16,color="green",shape="box"];1146[label="FiniteMap.addToFM_C FiniteMap.addToFM0 FiniteMap.EmptyFM (Pos ywz400) ywz41",fontsize=16,color="black",shape="box"];1146 -> 1316[label="",style="solid", color="black", weight=3]; 1147[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos ywz400) ywz41",fontsize=16,color="black",shape="box"];1147 -> 1317[label="",style="solid", color="black", weight=3]; 1148[label="FiniteMap.Branch ywz120 ywz121 ywz122 ywz123 ywz124",fontsize=16,color="green",shape="box"];13820[label="ywz123",fontsize=16,color="green",shape="box"];13821[label="ywz442",fontsize=16,color="green",shape="box"];13822[label="ywz441",fontsize=16,color="green",shape="box"];13823[label="Pos ywz400",fontsize=16,color="green",shape="box"];13824[label="ywz121",fontsize=16,color="green",shape="box"];13825[label="ywz440",fontsize=16,color="green",shape="box"];13826[label="ywz444",fontsize=16,color="green",shape="box"];13827[label="ywz120",fontsize=16,color="green",shape="box"];13828[label="ywz122",fontsize=16,color="green",shape="box"];13829[label="ywz124",fontsize=16,color="green",shape="box"];13830[label="ywz41",fontsize=16,color="green",shape="box"];13831 -> 10999[label="",style="dashed", color="red", weight=0]; 13831[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz120 ywz121 ywz122 ywz123 ywz124 ywz440 ywz441 ywz442 ywz443 ywz444 < FiniteMap.mkVBalBranch3Size_r ywz120 ywz121 ywz122 ywz123 ywz124 ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=16,color="magenta"];13831 -> 14092[label="",style="dashed", color="magenta", weight=3]; 13831 -> 14093[label="",style="dashed", color="magenta", weight=3]; 13832[label="ywz443",fontsize=16,color="green",shape="box"];21334[label="ywz1841",fontsize=16,color="green",shape="box"];21335[label="ywz1842",fontsize=16,color="green",shape="box"];21336[label="ywz1840",fontsize=16,color="green",shape="box"];1161[label="FiniteMap.mkVBalBranch5 (Neg Zero) ywz41 FiniteMap.EmptyFM ywz44",fontsize=16,color="black",shape="box"];1161 -> 1331[label="",style="solid", color="black", weight=3]; 1162[label="FiniteMap.mkVBalBranch (Neg Zero) ywz41 (FiniteMap.Branch ywz140 ywz141 ywz142 ywz143 ywz144) FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];1162 -> 1332[label="",style="solid", color="black", weight=3]; 1163[label="FiniteMap.mkVBalBranch (Neg Zero) ywz41 (FiniteMap.Branch ywz140 ywz141 ywz142 ywz143 ywz144) (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444)",fontsize=16,color="black",shape="box"];1163 -> 1333[label="",style="solid", color="black", weight=3]; 17200[label="ywz14190",fontsize=16,color="green",shape="box"];17201[label="ywz14200",fontsize=16,color="green",shape="box"];17202[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 True",fontsize=16,color="black",shape="box"];17202 -> 17227[label="",style="solid", color="black", weight=3]; 17203[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 False",fontsize=16,color="black",shape="triangle"];17203 -> 17228[label="",style="solid", color="black", weight=3]; 17204 -> 17203[label="",style="dashed", color="red", weight=0]; 17204[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 False",fontsize=16,color="magenta"];15601 -> 13158[label="",style="dashed", color="red", weight=0]; 15601[label="FiniteMap.mkBalBranch6MkBalBranch5 ywz1247 ywz743 (Pos Zero) ywz741 (Pos Zero) ywz741 ywz743 ywz1247 (FiniteMap.mkBalBranch6Size_l ywz1247 ywz743 (Pos Zero) ywz741 + FiniteMap.mkBalBranch6Size_r ywz1247 ywz743 (Pos Zero) ywz741 < Pos (Succ (Succ Zero)))",fontsize=16,color="magenta"];15601 -> 15630[label="",style="dashed", color="magenta", weight=3]; 15601 -> 15631[label="",style="dashed", color="magenta", weight=3]; 15601 -> 15632[label="",style="dashed", color="magenta", weight=3]; 15601 -> 15633[label="",style="dashed", color="magenta", weight=3]; 15601 -> 15634[label="",style="dashed", color="magenta", weight=3]; 15601 -> 15635[label="",style="dashed", color="magenta", weight=3]; 15611 -> 12612[label="",style="dashed", color="red", weight=0]; 15611[label="FiniteMap.mkBalBranch6Size_l ywz1243 ywz743 (Neg ywz7400) ywz741 + FiniteMap.mkBalBranch6Size_r ywz1243 ywz743 (Neg ywz7400) ywz741",fontsize=16,color="magenta"];15611 -> 15636[label="",style="dashed", color="magenta", weight=3]; 15611 -> 15637[label="",style="dashed", color="magenta", weight=3]; 15612[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];15613 -> 15543[label="",style="dashed", color="red", weight=0]; 15613[label="FiniteMap.addToFM0 ywz741 ywz9",fontsize=16,color="magenta"];16589[label="ywz13690",fontsize=16,color="green",shape="box"];16590[label="ywz13680",fontsize=16,color="green",shape="box"];16591[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 True",fontsize=16,color="black",shape="box"];16591 -> 16608[label="",style="solid", color="black", weight=3]; 16592[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 False",fontsize=16,color="black",shape="triangle"];16592 -> 16609[label="",style="solid", color="black", weight=3]; 16593 -> 16592[label="",style="dashed", color="red", weight=0]; 16593[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 False",fontsize=16,color="magenta"];15621 -> 15543[label="",style="dashed", color="red", weight=0]; 15621[label="FiniteMap.addToFM0 ywz741 ywz9",fontsize=16,color="magenta"];17751[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Pos ywz14440) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (primCmpInt (Pos (Succ ywz1441)) (Pos ywz14440) == GT))",fontsize=16,color="black",shape="box"];17751 -> 17802[label="",style="solid", color="black", weight=3]; 17752[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Neg ywz14440) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (primCmpInt (Pos (Succ ywz1441)) (Neg ywz14440) == GT))",fontsize=16,color="black",shape="box"];17752 -> 17803[label="",style="solid", color="black", weight=3]; 17753[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 Nothing",fontsize=16,color="black",shape="box"];17753 -> 17804[label="",style="solid", color="black", weight=3]; 17754 -> 17540[label="",style="dashed", color="red", weight=0]; 17754[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM2 ywz14470 ywz14471 ywz14472 ywz14473 ywz14474 (Pos (Succ ywz1441)) (Pos (Succ ywz1441) < ywz14470))",fontsize=16,color="magenta"];17754 -> 17805[label="",style="dashed", color="magenta", weight=3]; 17754 -> 17806[label="",style="dashed", color="magenta", weight=3]; 17754 -> 17807[label="",style="dashed", color="magenta", weight=3]; 17754 -> 17808[label="",style="dashed", color="magenta", weight=3]; 17754 -> 17809[label="",style="dashed", color="magenta", weight=3]; 17754 -> 17810[label="",style="dashed", color="magenta", weight=3]; 21757[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Pos ywz18800) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (primCmpInt (Pos (Succ ywz1877)) (Pos ywz18800) == GT))",fontsize=16,color="black",shape="box"];21757 -> 21907[label="",style="solid", color="black", weight=3]; 21758[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Neg ywz18800) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (primCmpInt (Pos (Succ ywz1877)) (Neg ywz18800) == GT))",fontsize=16,color="black",shape="box"];21758 -> 21908[label="",style="solid", color="black", weight=3]; 21759[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 Nothing",fontsize=16,color="black",shape="box"];21759 -> 21909[label="",style="solid", color="black", weight=3]; 21760 -> 21600[label="",style="dashed", color="red", weight=0]; 21760[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM2 ywz18830 ywz18831 ywz18832 ywz18833 ywz18834 (Pos (Succ ywz1877)) (Pos (Succ ywz1877) < ywz18830))",fontsize=16,color="magenta"];21760 -> 21910[label="",style="dashed", color="magenta", weight=3]; 21760 -> 21911[label="",style="dashed", color="magenta", weight=3]; 21760 -> 21912[label="",style="dashed", color="magenta", weight=3]; 21760 -> 21913[label="",style="dashed", color="magenta", weight=3]; 21760 -> 21914[label="",style="dashed", color="magenta", weight=3]; 21760 -> 21915[label="",style="dashed", color="magenta", weight=3]; 21998[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Pos (Succ ywz189400)) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (primCmpNat (Succ ywz1891) (Succ ywz189400) == GT))",fontsize=16,color="black",shape="box"];21998 -> 22044[label="",style="solid", color="black", weight=3]; 21999[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Pos Zero) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (primCmpNat (Succ ywz1891) Zero == GT))",fontsize=16,color="black",shape="box"];21999 -> 22045[label="",style="solid", color="black", weight=3]; 22000[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Neg ywz18940) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) True)",fontsize=16,color="black",shape="box"];22000 -> 22046[label="",style="solid", color="black", weight=3]; 22001[label="Pos (Succ ywz1891)",fontsize=16,color="green",shape="box"];22002[label="ywz18970",fontsize=16,color="green",shape="box"];22876[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Pos (Succ ywz203400)) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ ywz203400)) == GT))",fontsize=16,color="black",shape="box"];22876 -> 23068[label="",style="solid", color="black", weight=3]; 22877[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Pos Zero) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT))",fontsize=16,color="black",shape="box"];22877 -> 23069[label="",style="solid", color="black", weight=3]; 22878[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Neg (Succ ywz203400)) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ ywz203400)) == GT))",fontsize=16,color="black",shape="box"];22878 -> 23070[label="",style="solid", color="black", weight=3]; 22879[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Neg Zero) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT))",fontsize=16,color="black",shape="box"];22879 -> 23071[label="",style="solid", color="black", weight=3]; 22880[label="ywz2032",fontsize=16,color="green",shape="box"];22881[label="ywz20370",fontsize=16,color="green",shape="box"];22882 -> 10999[label="",style="dashed", color="red", weight=0]; 22882[label="Pos Zero < ywz20370",fontsize=16,color="magenta"];22882 -> 23072[label="",style="dashed", color="magenta", weight=3]; 22882 -> 23073[label="",style="dashed", color="magenta", weight=3]; 22883[label="ywz20373",fontsize=16,color="green",shape="box"];22884[label="ywz20371",fontsize=16,color="green",shape="box"];22885[label="ywz20372",fontsize=16,color="green",shape="box"];22886[label="ywz20374",fontsize=16,color="green",shape="box"];1776[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];1776 -> 1914[label="",style="solid", color="black", weight=3]; 22244[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Pos (Succ ywz194900)) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (primCmpInt (Pos Zero) (Pos (Succ ywz194900)) == GT))",fontsize=16,color="black",shape="box"];22244 -> 22350[label="",style="solid", color="black", weight=3]; 22245[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Pos Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (primCmpInt (Pos Zero) (Pos Zero) == GT))",fontsize=16,color="black",shape="box"];22245 -> 22351[label="",style="solid", color="black", weight=3]; 22246[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Neg (Succ ywz194900)) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (primCmpInt (Pos Zero) (Neg (Succ ywz194900)) == GT))",fontsize=16,color="black",shape="box"];22246 -> 22352[label="",style="solid", color="black", weight=3]; 22247[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Neg Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (primCmpInt (Pos Zero) (Neg Zero) == GT))",fontsize=16,color="black",shape="box"];22247 -> 22353[label="",style="solid", color="black", weight=3]; 22248[label="ywz1947",fontsize=16,color="green",shape="box"];22249[label="ywz19524",fontsize=16,color="green",shape="box"];22250 -> 10999[label="",style="dashed", color="red", weight=0]; 22250[label="Pos Zero < ywz19520",fontsize=16,color="magenta"];22250 -> 22354[label="",style="dashed", color="magenta", weight=3]; 22250 -> 22355[label="",style="dashed", color="magenta", weight=3]; 22251[label="ywz19520",fontsize=16,color="green",shape="box"];22252[label="ywz19522",fontsize=16,color="green",shape="box"];22253[label="ywz19521",fontsize=16,color="green",shape="box"];22254[label="ywz19523",fontsize=16,color="green",shape="box"];1778[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];1778 -> 1917[label="",style="solid", color="black", weight=3]; 19990[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Pos ywz17020) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) False)",fontsize=16,color="black",shape="box"];19990 -> 20001[label="",style="solid", color="black", weight=3]; 19991[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Neg (Succ ywz170200)) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (primCmpNat (Succ ywz170200) (Succ ywz1699) == GT))",fontsize=16,color="black",shape="box"];19991 -> 20002[label="",style="solid", color="black", weight=3]; 19992[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Neg Zero) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (primCmpNat Zero (Succ ywz1699) == GT))",fontsize=16,color="black",shape="box"];19992 -> 20003[label="",style="solid", color="black", weight=3]; 19993[label="Neg (Succ ywz1699)",fontsize=16,color="green",shape="box"];19994[label="ywz17050",fontsize=16,color="green",shape="box"];18103[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Pos ywz14800) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (primCmpInt (Neg (Succ ywz1477)) (Pos ywz14800) == GT))",fontsize=16,color="black",shape="box"];18103 -> 18116[label="",style="solid", color="black", weight=3]; 18104[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Neg ywz14800) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (primCmpInt (Neg (Succ ywz1477)) (Neg ywz14800) == GT))",fontsize=16,color="black",shape="box"];18104 -> 18117[label="",style="solid", color="black", weight=3]; 18105[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 Nothing",fontsize=16,color="black",shape="box"];18105 -> 18118[label="",style="solid", color="black", weight=3]; 18106 -> 18018[label="",style="dashed", color="red", weight=0]; 18106[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM2 ywz14830 ywz14831 ywz14832 ywz14833 ywz14834 (Neg (Succ ywz1477)) (Neg (Succ ywz1477) < ywz14830))",fontsize=16,color="magenta"];18106 -> 18119[label="",style="dashed", color="magenta", weight=3]; 18106 -> 18120[label="",style="dashed", color="magenta", weight=3]; 18106 -> 18121[label="",style="dashed", color="magenta", weight=3]; 18106 -> 18122[label="",style="dashed", color="magenta", weight=3]; 18106 -> 18123[label="",style="dashed", color="magenta", weight=3]; 18106 -> 18124[label="",style="dashed", color="magenta", weight=3]; 20885[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Pos ywz17890) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (primCmpInt (Neg (Succ ywz1786)) (Pos ywz17890) == GT))",fontsize=16,color="black",shape="box"];20885 -> 21036[label="",style="solid", color="black", weight=3]; 20886[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Neg ywz17890) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (primCmpInt (Neg (Succ ywz1786)) (Neg ywz17890) == GT))",fontsize=16,color="black",shape="box"];20886 -> 21037[label="",style="solid", color="black", weight=3]; 20887[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 Nothing",fontsize=16,color="black",shape="box"];20887 -> 21038[label="",style="solid", color="black", weight=3]; 20888 -> 20444[label="",style="dashed", color="red", weight=0]; 20888[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM2 ywz17920 ywz17921 ywz17922 ywz17923 ywz17924 (Neg (Succ ywz1786)) (Neg (Succ ywz1786) < ywz17920))",fontsize=16,color="magenta"];20888 -> 21039[label="",style="dashed", color="magenta", weight=3]; 20888 -> 21040[label="",style="dashed", color="magenta", weight=3]; 20888 -> 21041[label="",style="dashed", color="magenta", weight=3]; 20888 -> 21042[label="",style="dashed", color="magenta", weight=3]; 20888 -> 21043[label="",style="dashed", color="magenta", weight=3]; 20888 -> 21044[label="",style="dashed", color="magenta", weight=3]; 22745[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Pos (Succ ywz200500)) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ ywz200500)) == GT))",fontsize=16,color="black",shape="box"];22745 -> 22793[label="",style="solid", color="black", weight=3]; 22746[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Pos Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT))",fontsize=16,color="black",shape="box"];22746 -> 22794[label="",style="solid", color="black", weight=3]; 22747[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Neg (Succ ywz200500)) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ ywz200500)) == GT))",fontsize=16,color="black",shape="box"];22747 -> 22795[label="",style="solid", color="black", weight=3]; 22748[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Neg Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT))",fontsize=16,color="black",shape="box"];22748 -> 22796[label="",style="solid", color="black", weight=3]; 22749[label="ywz2003",fontsize=16,color="green",shape="box"];22750[label="ywz20080",fontsize=16,color="green",shape="box"];22751 -> 10999[label="",style="dashed", color="red", weight=0]; 22751[label="Neg Zero < ywz20080",fontsize=16,color="magenta"];22751 -> 22797[label="",style="dashed", color="magenta", weight=3]; 22751 -> 22798[label="",style="dashed", color="magenta", weight=3]; 22752[label="ywz20083",fontsize=16,color="green",shape="box"];22753[label="ywz20082",fontsize=16,color="green",shape="box"];22754[label="ywz20081",fontsize=16,color="green",shape="box"];22755[label="ywz20084",fontsize=16,color="green",shape="box"];1792[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];1792 -> 1932[label="",style="solid", color="black", weight=3]; 25204[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Pos (Succ ywz238300)) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (primCmpInt (Neg Zero) (Pos (Succ ywz238300)) == GT))",fontsize=16,color="black",shape="box"];25204 -> 25227[label="",style="solid", color="black", weight=3]; 25205[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Pos Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (primCmpInt (Neg Zero) (Pos Zero) == GT))",fontsize=16,color="black",shape="box"];25205 -> 25228[label="",style="solid", color="black", weight=3]; 25206[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Neg (Succ ywz238300)) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (primCmpInt (Neg Zero) (Neg (Succ ywz238300)) == GT))",fontsize=16,color="black",shape="box"];25206 -> 25229[label="",style="solid", color="black", weight=3]; 25207[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Neg Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (primCmpInt (Neg Zero) (Neg Zero) == GT))",fontsize=16,color="black",shape="box"];25207 -> 25230[label="",style="solid", color="black", weight=3]; 25208[label="ywz2381",fontsize=16,color="green",shape="box"];25209[label="ywz23864",fontsize=16,color="green",shape="box"];25210[label="ywz23861",fontsize=16,color="green",shape="box"];25211[label="ywz23862",fontsize=16,color="green",shape="box"];25212[label="ywz23863",fontsize=16,color="green",shape="box"];25213 -> 10999[label="",style="dashed", color="red", weight=0]; 25213[label="Neg Zero < ywz23860",fontsize=16,color="magenta"];25213 -> 25231[label="",style="dashed", color="magenta", weight=3]; 25213 -> 25232[label="",style="dashed", color="magenta", weight=3]; 25214[label="ywz23860",fontsize=16,color="green",shape="box"];1794[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];1794 -> 1934[label="",style="solid", color="black", weight=3]; 2011[label="primPlusNat (primPlusNat (Succ (Succ (primPlusNat ywz7200 ywz7200))) (Succ ywz7200)) (Succ ywz7200)",fontsize=16,color="black",shape="box"];2011 -> 2023[label="",style="solid", color="black", weight=3]; 14364[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz1157000) ywz115400 == GT)",fontsize=16,color="burlywood",shape="box"];25701[label="ywz115400/Succ ywz1154000",fontsize=10,color="white",style="solid",shape="box"];14364 -> 25701[label="",style="solid", color="burlywood", weight=9]; 25701 -> 14379[label="",style="solid", color="burlywood", weight=3]; 25702[label="ywz115400/Zero",fontsize=10,color="white",style="solid",shape="box"];14364 -> 25702[label="",style="solid", color="burlywood", weight=9]; 25702 -> 14380[label="",style="solid", color="burlywood", weight=3]; 14365[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat Zero ywz115400 == GT)",fontsize=16,color="burlywood",shape="box"];25703[label="ywz115400/Succ ywz1154000",fontsize=10,color="white",style="solid",shape="box"];14365 -> 25703[label="",style="solid", color="burlywood", weight=9]; 25703 -> 14381[label="",style="solid", color="burlywood", weight=3]; 25704[label="ywz115400/Zero",fontsize=10,color="white",style="solid",shape="box"];14365 -> 25704[label="",style="solid", color="burlywood", weight=9]; 25704 -> 14382[label="",style="solid", color="burlywood", weight=3]; 14366[label="FiniteMap.mkBalBranch6MkBalBranch0 ywz1007 ywz73 ywz70 ywz71 ywz73 FiniteMap.EmptyFM FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];14366 -> 14383[label="",style="solid", color="black", weight=3]; 14367[label="FiniteMap.mkBalBranch6MkBalBranch0 ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064) (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064)",fontsize=16,color="black",shape="box"];14367 -> 14384[label="",style="solid", color="black", weight=3]; 14369 -> 12141[label="",style="dashed", color="red", weight=0]; 14369[label="FiniteMap.sIZE_RATIO * FiniteMap.mkBalBranch6Size_r ywz1007 ywz73 ywz70 ywz71",fontsize=16,color="magenta"];14369 -> 14385[label="",style="dashed", color="magenta", weight=3]; 14370 -> 13476[label="",style="dashed", color="red", weight=0]; 14370[label="FiniteMap.mkBalBranch6Size_l ywz1007 ywz73 ywz70 ywz71",fontsize=16,color="magenta"];14370 -> 14386[label="",style="dashed", color="magenta", weight=3]; 14370 -> 14387[label="",style="dashed", color="magenta", weight=3]; 14370 -> 14388[label="",style="dashed", color="magenta", weight=3]; 14370 -> 14389[label="",style="dashed", color="magenta", weight=3]; 14368[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (ywz1184 > ywz1183)",fontsize=16,color="black",shape="triangle"];14368 -> 14390[label="",style="solid", color="black", weight=3]; 14377[label="ywz115400",fontsize=16,color="green",shape="box"];14378[label="ywz115700",fontsize=16,color="green",shape="box"];20751[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (primCmpNat (Succ ywz18150) (Succ ywz18160) == GT)",fontsize=16,color="black",shape="box"];20751 -> 20893[label="",style="solid", color="black", weight=3]; 20752[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (primCmpNat (Succ ywz18150) Zero == GT)",fontsize=16,color="black",shape="box"];20752 -> 20894[label="",style="solid", color="black", weight=3]; 20753[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (primCmpNat Zero (Succ ywz18160) == GT)",fontsize=16,color="black",shape="box"];20753 -> 20895[label="",style="solid", color="black", weight=3]; 20754[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];20754 -> 20896[label="",style="solid", color="black", weight=3]; 1242[label="FiniteMap.addToFM_C4 FiniteMap.addToFM0 FiniteMap.EmptyFM (Neg ywz400) ywz41",fontsize=16,color="black",shape="box"];1242 -> 1408[label="",style="solid", color="black", weight=3]; 1243[label="FiniteMap.addToFM_C3 FiniteMap.addToFM0 (FiniteMap.Branch ywz150 ywz151 ywz152 ywz153 ywz154) (Neg ywz400) ywz41",fontsize=16,color="black",shape="box"];1243 -> 1409[label="",style="solid", color="black", weight=3]; 1288[label="FiniteMap.addToFM (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Neg ywz400) ywz41",fontsize=16,color="black",shape="box"];1288 -> 1562[label="",style="solid", color="black", weight=3]; 1289 -> 13641[label="",style="dashed", color="red", weight=0]; 1289[label="FiniteMap.mkVBalBranch3MkVBalBranch2 ywz430 ywz431 ywz432 ywz433 ywz434 ywz130 ywz131 ywz132 ywz133 ywz134 (Neg ywz400) ywz41 ywz430 ywz431 ywz432 ywz433 ywz434 ywz130 ywz131 ywz132 ywz133 ywz134 (FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz430 ywz431 ywz432 ywz433 ywz434 ywz130 ywz131 ywz132 ywz133 ywz134 < FiniteMap.mkVBalBranch3Size_r ywz430 ywz431 ywz432 ywz433 ywz434 ywz130 ywz131 ywz132 ywz133 ywz134)",fontsize=16,color="magenta"];1289 -> 13859[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13860[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13861[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13862[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13863[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13864[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13865[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13866[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13867[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13868[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13869[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13870[label="",style="dashed", color="magenta", weight=3]; 1289 -> 13871[label="",style="dashed", color="magenta", weight=3]; 1290[label="ywz10",fontsize=16,color="green",shape="box"];1291[label="Succ ywz4000",fontsize=16,color="green",shape="box"];1292[label="FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434",fontsize=16,color="green",shape="box"];13833[label="ywz433",fontsize=16,color="green",shape="box"];13834[label="ywz102",fontsize=16,color="green",shape="box"];13835[label="ywz101",fontsize=16,color="green",shape="box"];13836[label="Neg (Succ ywz4000)",fontsize=16,color="green",shape="box"];13837[label="ywz431",fontsize=16,color="green",shape="box"];13838[label="ywz100",fontsize=16,color="green",shape="box"];13839[label="ywz104",fontsize=16,color="green",shape="box"];13840[label="ywz430",fontsize=16,color="green",shape="box"];13841[label="ywz432",fontsize=16,color="green",shape="box"];13842[label="ywz434",fontsize=16,color="green",shape="box"];13843[label="ywz41",fontsize=16,color="green",shape="box"];13844 -> 10999[label="",style="dashed", color="red", weight=0]; 13844[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz430 ywz431 ywz432 ywz433 ywz434 ywz100 ywz101 ywz102 ywz103 ywz104 < FiniteMap.mkVBalBranch3Size_r ywz430 ywz431 ywz432 ywz433 ywz434 ywz100 ywz101 ywz102 ywz103 ywz104",fontsize=16,color="magenta"];13844 -> 14094[label="",style="dashed", color="magenta", weight=3]; 13844 -> 14095[label="",style="dashed", color="magenta", weight=3]; 13845[label="ywz103",fontsize=16,color="green",shape="box"];20889[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (primCmpNat (Succ ywz18240) (Succ ywz18250) == GT)",fontsize=16,color="black",shape="box"];20889 -> 21045[label="",style="solid", color="black", weight=3]; 20890[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (primCmpNat (Succ ywz18240) Zero == GT)",fontsize=16,color="black",shape="box"];20890 -> 21046[label="",style="solid", color="black", weight=3]; 20891[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (primCmpNat Zero (Succ ywz18250) == GT)",fontsize=16,color="black",shape="box"];20891 -> 21047[label="",style="solid", color="black", weight=3]; 20892[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];20892 -> 21048[label="",style="solid", color="black", weight=3]; 1316[label="FiniteMap.addToFM_C4 FiniteMap.addToFM0 FiniteMap.EmptyFM (Pos ywz400) ywz41",fontsize=16,color="black",shape="box"];1316 -> 1589[label="",style="solid", color="black", weight=3]; 1317[label="FiniteMap.addToFM_C3 FiniteMap.addToFM0 (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444) (Pos ywz400) ywz41",fontsize=16,color="black",shape="box"];1317 -> 1590[label="",style="solid", color="black", weight=3]; 14092 -> 12141[label="",style="dashed", color="red", weight=0]; 14092[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz120 ywz121 ywz122 ywz123 ywz124 ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=16,color="magenta"];14092 -> 14142[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14089[label="",style="dashed", color="red", weight=0]; 14093[label="FiniteMap.mkVBalBranch3Size_r ywz120 ywz121 ywz122 ywz123 ywz124 ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=16,color="magenta"];14093 -> 14143[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14144[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14145[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14146[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14147[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14148[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14149[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14150[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14151[label="",style="dashed", color="magenta", weight=3]; 14093 -> 14152[label="",style="dashed", color="magenta", weight=3]; 1331[label="FiniteMap.addToFM ywz44 (Neg Zero) ywz41",fontsize=16,color="black",shape="box"];1331 -> 1605[label="",style="solid", color="black", weight=3]; 1332 -> 1119[label="",style="dashed", color="red", weight=0]; 1332[label="FiniteMap.mkVBalBranch4 (Neg Zero) ywz41 (FiniteMap.Branch ywz140 ywz141 ywz142 ywz143 ywz144) FiniteMap.EmptyFM",fontsize=16,color="magenta"];1332 -> 1606[label="",style="dashed", color="magenta", weight=3]; 1332 -> 1607[label="",style="dashed", color="magenta", weight=3]; 1332 -> 1608[label="",style="dashed", color="magenta", weight=3]; 1332 -> 1609[label="",style="dashed", color="magenta", weight=3]; 1332 -> 1610[label="",style="dashed", color="magenta", weight=3]; 1332 -> 1611[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1120[label="",style="dashed", color="red", weight=0]; 1333[label="FiniteMap.mkVBalBranch3 (Neg Zero) ywz41 (FiniteMap.Branch ywz140 ywz141 ywz142 ywz143 ywz144) (FiniteMap.Branch ywz440 ywz441 ywz442 ywz443 ywz444)",fontsize=16,color="magenta"];1333 -> 1612[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1613[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1614[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1615[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1616[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1617[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1618[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1619[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1620[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1621[label="",style="dashed", color="magenta", weight=3]; 1333 -> 1622[label="",style="dashed", color="magenta", weight=3]; 17227 -> 17250[label="",style="dashed", color="red", weight=0]; 17227[label="FiniteMap.mkBalBranch (Pos (Succ ywz1412)) ywz1413 ywz1415 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz1416 (Pos (Succ ywz1417)) ywz1418)",fontsize=16,color="magenta"];17227 -> 17251[label="",style="dashed", color="magenta", weight=3]; 17228[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 otherwise",fontsize=16,color="black",shape="box"];17228 -> 17252[label="",style="solid", color="black", weight=3]; 15630[label="ywz743",fontsize=16,color="green",shape="box"];15631[label="ywz1247",fontsize=16,color="green",shape="box"];15632[label="ywz1247",fontsize=16,color="green",shape="box"];15633[label="Pos Zero",fontsize=16,color="green",shape="box"];15634[label="ywz741",fontsize=16,color="green",shape="box"];15635 -> 10999[label="",style="dashed", color="red", weight=0]; 15635[label="FiniteMap.mkBalBranch6Size_l ywz1247 ywz743 (Pos Zero) ywz741 + FiniteMap.mkBalBranch6Size_r ywz1247 ywz743 (Pos Zero) ywz741 < Pos (Succ (Succ Zero))",fontsize=16,color="magenta"];15635 -> 15664[label="",style="dashed", color="magenta", weight=3]; 15635 -> 15665[label="",style="dashed", color="magenta", weight=3]; 15636 -> 13476[label="",style="dashed", color="red", weight=0]; 15636[label="FiniteMap.mkBalBranch6Size_l ywz1243 ywz743 (Neg ywz7400) ywz741",fontsize=16,color="magenta"];15636 -> 15666[label="",style="dashed", color="magenta", weight=3]; 15636 -> 15667[label="",style="dashed", color="magenta", weight=3]; 15636 -> 15668[label="",style="dashed", color="magenta", weight=3]; 15636 -> 15669[label="",style="dashed", color="magenta", weight=3]; 15637 -> 13515[label="",style="dashed", color="red", weight=0]; 15637[label="FiniteMap.mkBalBranch6Size_r ywz1243 ywz743 (Neg ywz7400) ywz741",fontsize=16,color="magenta"];15637 -> 15670[label="",style="dashed", color="magenta", weight=3]; 15637 -> 15671[label="",style="dashed", color="magenta", weight=3]; 15637 -> 15672[label="",style="dashed", color="magenta", weight=3]; 15637 -> 15673[label="",style="dashed", color="magenta", weight=3]; 16608 -> 15478[label="",style="dashed", color="red", weight=0]; 16608[label="FiniteMap.mkBalBranch (Neg (Succ ywz1361)) ywz1362 ywz1364 (FiniteMap.addToFM_C FiniteMap.addToFM0 ywz1365 (Neg (Succ ywz1366)) ywz1367)",fontsize=16,color="magenta"];16608 -> 16620[label="",style="dashed", color="magenta", weight=3]; 16608 -> 16621[label="",style="dashed", color="magenta", weight=3]; 16608 -> 16622[label="",style="dashed", color="magenta", weight=3]; 16608 -> 16623[label="",style="dashed", color="magenta", weight=3]; 16609[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 otherwise",fontsize=16,color="black",shape="box"];16609 -> 16624[label="",style="solid", color="black", weight=3]; 17802[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Pos ywz14440) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (primCmpNat (Succ ywz1441) ywz14440 == GT))",fontsize=16,color="burlywood",shape="box"];25705[label="ywz14440/Succ ywz144400",fontsize=10,color="white",style="solid",shape="box"];17802 -> 25705[label="",style="solid", color="burlywood", weight=9]; 25705 -> 17838[label="",style="solid", color="burlywood", weight=3]; 25706[label="ywz14440/Zero",fontsize=10,color="white",style="solid",shape="box"];17802 -> 25706[label="",style="solid", color="burlywood", weight=9]; 25706 -> 17839[label="",style="solid", color="burlywood", weight=3]; 17803[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Neg ywz14440) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (GT == GT))",fontsize=16,color="black",shape="box"];17803 -> 17840[label="",style="solid", color="black", weight=3]; 17804[label="ywz1442",fontsize=16,color="green",shape="box"];17805[label="ywz14473",fontsize=16,color="green",shape="box"];17806[label="ywz14474",fontsize=16,color="green",shape="box"];17807[label="ywz14471",fontsize=16,color="green",shape="box"];17808[label="ywz14470",fontsize=16,color="green",shape="box"];17809[label="ywz14472",fontsize=16,color="green",shape="box"];17810 -> 10999[label="",style="dashed", color="red", weight=0]; 17810[label="Pos (Succ ywz1441) < ywz14470",fontsize=16,color="magenta"];17810 -> 17841[label="",style="dashed", color="magenta", weight=3]; 17810 -> 17842[label="",style="dashed", color="magenta", weight=3]; 21907[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Pos ywz18800) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (primCmpNat (Succ ywz1877) ywz18800 == GT))",fontsize=16,color="burlywood",shape="box"];25707[label="ywz18800/Succ ywz188000",fontsize=10,color="white",style="solid",shape="box"];21907 -> 25707[label="",style="solid", color="burlywood", weight=9]; 25707 -> 21968[label="",style="solid", color="burlywood", weight=3]; 25708[label="ywz18800/Zero",fontsize=10,color="white",style="solid",shape="box"];21907 -> 25708[label="",style="solid", color="burlywood", weight=9]; 25708 -> 21969[label="",style="solid", color="burlywood", weight=3]; 21908[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Neg ywz18800) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (GT == GT))",fontsize=16,color="black",shape="box"];21908 -> 21970[label="",style="solid", color="black", weight=3]; 21909[label="ywz1878",fontsize=16,color="green",shape="box"];21910[label="ywz18833",fontsize=16,color="green",shape="box"];21911[label="ywz18830",fontsize=16,color="green",shape="box"];21912 -> 10999[label="",style="dashed", color="red", weight=0]; 21912[label="Pos (Succ ywz1877) < ywz18830",fontsize=16,color="magenta"];21912 -> 21971[label="",style="dashed", color="magenta", weight=3]; 21912 -> 21972[label="",style="dashed", color="magenta", weight=3]; 21913[label="ywz18831",fontsize=16,color="green",shape="box"];21914[label="ywz18832",fontsize=16,color="green",shape="box"];21915[label="ywz18834",fontsize=16,color="green",shape="box"];22044 -> 24110[label="",style="dashed", color="red", weight=0]; 22044[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Pos (Succ ywz189400)) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (primCmpNat ywz1891 ywz189400 == GT))",fontsize=16,color="magenta"];22044 -> 24111[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24112[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24113[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24114[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24115[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24116[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24117[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24118[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24119[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24120[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24121[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24122[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24123[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24124[label="",style="dashed", color="magenta", weight=3]; 22044 -> 24125[label="",style="dashed", color="magenta", weight=3]; 22045[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Pos Zero) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) (GT == GT))",fontsize=16,color="black",shape="box"];22045 -> 22077[label="",style="solid", color="black", weight=3]; 22046 -> 21687[label="",style="dashed", color="red", weight=0]; 22046[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM ywz1898 (Pos (Succ ywz1891)))",fontsize=16,color="magenta"];22046 -> 22078[label="",style="dashed", color="magenta", weight=3]; 23068[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Pos (Succ ywz203400)) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (primCmpNat Zero (Succ ywz203400) == GT))",fontsize=16,color="black",shape="box"];23068 -> 23136[label="",style="solid", color="black", weight=3]; 23069[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Pos Zero) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];23069 -> 23137[label="",style="solid", color="black", weight=3]; 23070[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Neg (Succ ywz203400)) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (GT == GT))",fontsize=16,color="black",shape="box"];23070 -> 23138[label="",style="solid", color="black", weight=3]; 23071[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Neg Zero) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];23071 -> 23139[label="",style="solid", color="black", weight=3]; 23072[label="Pos Zero",fontsize=16,color="green",shape="box"];23073[label="ywz20370",fontsize=16,color="green",shape="box"];1914[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True)",fontsize=16,color="black",shape="box"];1914 -> 2170[label="",style="solid", color="black", weight=3]; 22350[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Pos (Succ ywz194900)) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (primCmpNat Zero (Succ ywz194900) == GT))",fontsize=16,color="black",shape="box"];22350 -> 22417[label="",style="solid", color="black", weight=3]; 22351[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Pos Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];22351 -> 22418[label="",style="solid", color="black", weight=3]; 22352[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Neg (Succ ywz194900)) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (GT == GT))",fontsize=16,color="black",shape="box"];22352 -> 22419[label="",style="solid", color="black", weight=3]; 22353[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Neg Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];22353 -> 22420[label="",style="solid", color="black", weight=3]; 22354[label="Pos Zero",fontsize=16,color="green",shape="box"];22355[label="ywz19520",fontsize=16,color="green",shape="box"];1917[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Pos Zero) True)",fontsize=16,color="black",shape="box"];1917 -> 2173[label="",style="solid", color="black", weight=3]; 20001[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM0 (Pos ywz17020) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) otherwise)",fontsize=16,color="black",shape="box"];20001 -> 20022[label="",style="solid", color="black", weight=3]; 20002 -> 22917[label="",style="dashed", color="red", weight=0]; 20002[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Neg (Succ ywz170200)) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (primCmpNat ywz170200 ywz1699 == GT))",fontsize=16,color="magenta"];20002 -> 22918[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22919[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22920[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22921[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22922[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22923[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22924[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22925[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22926[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22927[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22928[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22929[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22930[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22931[label="",style="dashed", color="magenta", weight=3]; 20002 -> 22932[label="",style="dashed", color="magenta", weight=3]; 20003[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Neg Zero) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) (LT == GT))",fontsize=16,color="black",shape="box"];20003 -> 20025[label="",style="solid", color="black", weight=3]; 18116[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Pos ywz14800) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (LT == GT))",fontsize=16,color="black",shape="box"];18116 -> 18147[label="",style="solid", color="black", weight=3]; 18117[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Neg ywz14800) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (primCmpNat ywz14800 (Succ ywz1477) == GT))",fontsize=16,color="burlywood",shape="box"];25709[label="ywz14800/Succ ywz148000",fontsize=10,color="white",style="solid",shape="box"];18117 -> 25709[label="",style="solid", color="burlywood", weight=9]; 25709 -> 18148[label="",style="solid", color="burlywood", weight=3]; 25710[label="ywz14800/Zero",fontsize=10,color="white",style="solid",shape="box"];18117 -> 25710[label="",style="solid", color="burlywood", weight=9]; 25710 -> 18149[label="",style="solid", color="burlywood", weight=3]; 18118[label="ywz1478",fontsize=16,color="green",shape="box"];18119[label="ywz14830",fontsize=16,color="green",shape="box"];18120 -> 10999[label="",style="dashed", color="red", weight=0]; 18120[label="Neg (Succ ywz1477) < ywz14830",fontsize=16,color="magenta"];18120 -> 18150[label="",style="dashed", color="magenta", weight=3]; 18120 -> 18151[label="",style="dashed", color="magenta", weight=3]; 18121[label="ywz14832",fontsize=16,color="green",shape="box"];18122[label="ywz14831",fontsize=16,color="green",shape="box"];18123[label="ywz14833",fontsize=16,color="green",shape="box"];18124[label="ywz14834",fontsize=16,color="green",shape="box"];21036[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Pos ywz17890) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (LT == GT))",fontsize=16,color="black",shape="box"];21036 -> 21082[label="",style="solid", color="black", weight=3]; 21037[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Neg ywz17890) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (primCmpNat ywz17890 (Succ ywz1786) == GT))",fontsize=16,color="burlywood",shape="box"];25711[label="ywz17890/Succ ywz178900",fontsize=10,color="white",style="solid",shape="box"];21037 -> 25711[label="",style="solid", color="burlywood", weight=9]; 25711 -> 21083[label="",style="solid", color="burlywood", weight=3]; 25712[label="ywz17890/Zero",fontsize=10,color="white",style="solid",shape="box"];21037 -> 25712[label="",style="solid", color="burlywood", weight=9]; 25712 -> 21084[label="",style="solid", color="burlywood", weight=3]; 21038[label="ywz1787",fontsize=16,color="green",shape="box"];21039 -> 10999[label="",style="dashed", color="red", weight=0]; 21039[label="Neg (Succ ywz1786) < ywz17920",fontsize=16,color="magenta"];21039 -> 21085[label="",style="dashed", color="magenta", weight=3]; 21039 -> 21086[label="",style="dashed", color="magenta", weight=3]; 21040[label="ywz17920",fontsize=16,color="green",shape="box"];21041[label="ywz17921",fontsize=16,color="green",shape="box"];21042[label="ywz17923",fontsize=16,color="green",shape="box"];21043[label="ywz17922",fontsize=16,color="green",shape="box"];21044[label="ywz17924",fontsize=16,color="green",shape="box"];22793[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Pos (Succ ywz200500)) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (LT == GT))",fontsize=16,color="black",shape="box"];22793 -> 22836[label="",style="solid", color="black", weight=3]; 22794[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Pos Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];22794 -> 22837[label="",style="solid", color="black", weight=3]; 22795[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Neg (Succ ywz200500)) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (primCmpNat (Succ ywz200500) Zero == GT))",fontsize=16,color="black",shape="box"];22795 -> 22838[label="",style="solid", color="black", weight=3]; 22796[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Neg Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];22796 -> 22839[label="",style="solid", color="black", weight=3]; 22797[label="Neg Zero",fontsize=16,color="green",shape="box"];22798[label="ywz20080",fontsize=16,color="green",shape="box"];1932[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM0 (Pos Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True)",fontsize=16,color="black",shape="box"];1932 -> 2194[label="",style="solid", color="black", weight=3]; 25227[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Pos (Succ ywz238300)) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (LT == GT))",fontsize=16,color="black",shape="box"];25227 -> 25250[label="",style="solid", color="black", weight=3]; 25228[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Pos Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];25228 -> 25251[label="",style="solid", color="black", weight=3]; 25229[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Neg (Succ ywz238300)) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (primCmpNat (Succ ywz238300) Zero == GT))",fontsize=16,color="black",shape="box"];25229 -> 25252[label="",style="solid", color="black", weight=3]; 25230[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Neg Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (EQ == GT))",fontsize=16,color="black",shape="box"];25230 -> 25253[label="",style="solid", color="black", weight=3]; 25231[label="Neg Zero",fontsize=16,color="green",shape="box"];25232[label="ywz23860",fontsize=16,color="green",shape="box"];1934[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (FiniteMap.lookupFM0 (Neg Zero) ywz41 ywz42 ywz43 ywz44 (Neg Zero) True)",fontsize=16,color="black",shape="box"];1934 -> 2196[label="",style="solid", color="black", weight=3]; 2023[label="primPlusNat (Succ (Succ (primPlusNat (Succ (primPlusNat ywz7200 ywz7200)) ywz7200))) (Succ ywz7200)",fontsize=16,color="black",shape="box"];2023 -> 2046[label="",style="solid", color="black", weight=3]; 14379[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz1157000) (Succ ywz1154000) == GT)",fontsize=16,color="black",shape="box"];14379 -> 14443[label="",style="solid", color="black", weight=3]; 14380[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz1157000) Zero == GT)",fontsize=16,color="black",shape="box"];14380 -> 14444[label="",style="solid", color="black", weight=3]; 14381[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat Zero (Succ ywz1154000) == GT)",fontsize=16,color="black",shape="box"];14381 -> 14445[label="",style="solid", color="black", weight=3]; 14382[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat Zero Zero == GT)",fontsize=16,color="black",shape="box"];14382 -> 14446[label="",style="solid", color="black", weight=3]; 14383[label="error []",fontsize=16,color="red",shape="box"];14384[label="FiniteMap.mkBalBranch6MkBalBranch02 ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064) (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064)",fontsize=16,color="black",shape="box"];14384 -> 14447[label="",style="solid", color="black", weight=3]; 14385 -> 13515[label="",style="dashed", color="red", weight=0]; 14385[label="FiniteMap.mkBalBranch6Size_r ywz1007 ywz73 ywz70 ywz71",fontsize=16,color="magenta"];14385 -> 14448[label="",style="dashed", color="magenta", weight=3]; 14385 -> 14449[label="",style="dashed", color="magenta", weight=3]; 14385 -> 14450[label="",style="dashed", color="magenta", weight=3]; 14385 -> 14451[label="",style="dashed", color="magenta", weight=3]; 14386[label="ywz1007",fontsize=16,color="green",shape="box"];14387[label="ywz70",fontsize=16,color="green",shape="box"];14388[label="ywz71",fontsize=16,color="green",shape="box"];14389[label="ywz73",fontsize=16,color="green",shape="box"];14390[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (compare ywz1184 ywz1183 == GT)",fontsize=16,color="black",shape="box"];14390 -> 14452[label="",style="solid", color="black", weight=3]; 20893 -> 20555[label="",style="dashed", color="red", weight=0]; 20893[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (primCmpNat ywz18150 ywz18160 == GT)",fontsize=16,color="magenta"];20893 -> 21049[label="",style="dashed", color="magenta", weight=3]; 20893 -> 21050[label="",style="dashed", color="magenta", weight=3]; 20894[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (GT == GT)",fontsize=16,color="black",shape="box"];20894 -> 21051[label="",style="solid", color="black", weight=3]; 20895[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (LT == GT)",fontsize=16,color="black",shape="box"];20895 -> 21052[label="",style="solid", color="black", weight=3]; 20896[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) (EQ == GT)",fontsize=16,color="black",shape="box"];20896 -> 21053[label="",style="solid", color="black", weight=3]; 1408[label="FiniteMap.unitFM (Neg ywz400) ywz41",fontsize=16,color="black",shape="box"];1408 -> 1686[label="",style="solid", color="black", weight=3]; 1409 -> 14543[label="",style="dashed", color="red", weight=0]; 1409[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 ywz150 ywz151 ywz152 ywz153 ywz154 (Neg ywz400) ywz41 (Neg ywz400 < ywz150)",fontsize=16,color="magenta"];1409 -> 14941[label="",style="dashed", color="magenta", weight=3]; 1409 -> 14942[label="",style="dashed", color="magenta", weight=3]; 1409 -> 14943[label="",style="dashed", color="magenta", weight=3]; 1409 -> 14944[label="",style="dashed", color="magenta", weight=3]; 1409 -> 14945[label="",style="dashed", color="magenta", weight=3]; 1409 -> 14946[label="",style="dashed", color="magenta", weight=3]; 1409 -> 14947[label="",style="dashed", color="magenta", weight=3]; 1409 -> 14948[label="",style="dashed", color="magenta", weight=3]; 1562 -> 974[label="",style="dashed", color="red", weight=0]; 1562[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434) (Neg ywz400) ywz41",fontsize=16,color="magenta"];1562 -> 1714[label="",style="dashed", color="magenta", weight=3]; 13859[label="ywz433",fontsize=16,color="green",shape="box"];13860[label="ywz132",fontsize=16,color="green",shape="box"];13861[label="ywz131",fontsize=16,color="green",shape="box"];13862[label="Neg ywz400",fontsize=16,color="green",shape="box"];13863[label="ywz431",fontsize=16,color="green",shape="box"];13864[label="ywz130",fontsize=16,color="green",shape="box"];13865[label="ywz134",fontsize=16,color="green",shape="box"];13866[label="ywz430",fontsize=16,color="green",shape="box"];13867[label="ywz432",fontsize=16,color="green",shape="box"];13868[label="ywz434",fontsize=16,color="green",shape="box"];13869[label="ywz41",fontsize=16,color="green",shape="box"];13870 -> 10999[label="",style="dashed", color="red", weight=0]; 13870[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz430 ywz431 ywz432 ywz433 ywz434 ywz130 ywz131 ywz132 ywz133 ywz134 < FiniteMap.mkVBalBranch3Size_r ywz430 ywz431 ywz432 ywz433 ywz434 ywz130 ywz131 ywz132 ywz133 ywz134",fontsize=16,color="magenta"];13870 -> 14096[label="",style="dashed", color="magenta", weight=3]; 13870 -> 14097[label="",style="dashed", color="magenta", weight=3]; 13871[label="ywz133",fontsize=16,color="green",shape="box"];14094 -> 12141[label="",style="dashed", color="red", weight=0]; 14094[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz430 ywz431 ywz432 ywz433 ywz434 ywz100 ywz101 ywz102 ywz103 ywz104",fontsize=16,color="magenta"];14094 -> 14153[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14089[label="",style="dashed", color="red", weight=0]; 14095[label="FiniteMap.mkVBalBranch3Size_r ywz430 ywz431 ywz432 ywz433 ywz434 ywz100 ywz101 ywz102 ywz103 ywz104",fontsize=16,color="magenta"];14095 -> 14154[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14155[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14156[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14157[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14158[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14159[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14160[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14161[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14162[label="",style="dashed", color="magenta", weight=3]; 14095 -> 14163[label="",style="dashed", color="magenta", weight=3]; 21045 -> 20657[label="",style="dashed", color="red", weight=0]; 21045[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (primCmpNat ywz18240 ywz18250 == GT)",fontsize=16,color="magenta"];21045 -> 21087[label="",style="dashed", color="magenta", weight=3]; 21045 -> 21088[label="",style="dashed", color="magenta", weight=3]; 21046[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (GT == GT)",fontsize=16,color="black",shape="box"];21046 -> 21089[label="",style="solid", color="black", weight=3]; 21047[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (LT == GT)",fontsize=16,color="black",shape="box"];21047 -> 21090[label="",style="solid", color="black", weight=3]; 21048[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) (EQ == GT)",fontsize=16,color="black",shape="box"];21048 -> 21091[label="",style="solid", color="black", weight=3]; 1589[label="FiniteMap.unitFM (Pos ywz400) ywz41",fontsize=16,color="black",shape="box"];1589 -> 1745[label="",style="solid", color="black", weight=3]; 1590 -> 14543[label="",style="dashed", color="red", weight=0]; 1590[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 ywz440 ywz441 ywz442 ywz443 ywz444 (Pos ywz400) ywz41 (Pos ywz400 < ywz440)",fontsize=16,color="magenta"];1590 -> 14949[label="",style="dashed", color="magenta", weight=3]; 1590 -> 14950[label="",style="dashed", color="magenta", weight=3]; 1590 -> 14951[label="",style="dashed", color="magenta", weight=3]; 1590 -> 14952[label="",style="dashed", color="magenta", weight=3]; 1590 -> 14953[label="",style="dashed", color="magenta", weight=3]; 1590 -> 14954[label="",style="dashed", color="magenta", weight=3]; 1590 -> 14955[label="",style="dashed", color="magenta", weight=3]; 1590 -> 14956[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14138[label="",style="dashed", color="red", weight=0]; 14142[label="FiniteMap.mkVBalBranch3Size_l ywz120 ywz121 ywz122 ywz123 ywz124 ywz440 ywz441 ywz442 ywz443 ywz444",fontsize=16,color="magenta"];14142 -> 14209[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14210[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14211[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14212[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14213[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14214[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14215[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14216[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14217[label="",style="dashed", color="magenta", weight=3]; 14142 -> 14218[label="",style="dashed", color="magenta", weight=3]; 14143[label="ywz123",fontsize=16,color="green",shape="box"];14144[label="ywz440",fontsize=16,color="green",shape="box"];14145[label="ywz442",fontsize=16,color="green",shape="box"];14146[label="ywz441",fontsize=16,color="green",shape="box"];14147[label="ywz444",fontsize=16,color="green",shape="box"];14148[label="ywz443",fontsize=16,color="green",shape="box"];14149[label="ywz124",fontsize=16,color="green",shape="box"];14150[label="ywz120",fontsize=16,color="green",shape="box"];14151[label="ywz121",fontsize=16,color="green",shape="box"];14152[label="ywz122",fontsize=16,color="green",shape="box"];1605 -> 974[label="",style="dashed", color="red", weight=0]; 1605[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz44 (Neg Zero) ywz41",fontsize=16,color="magenta"];1605 -> 1761[label="",style="dashed", color="magenta", weight=3]; 1605 -> 1762[label="",style="dashed", color="magenta", weight=3]; 1606[label="ywz141",fontsize=16,color="green",shape="box"];1607[label="ywz140",fontsize=16,color="green",shape="box"];1608[label="ywz142",fontsize=16,color="green",shape="box"];1609[label="ywz143",fontsize=16,color="green",shape="box"];1610[label="Zero",fontsize=16,color="green",shape="box"];1611[label="ywz144",fontsize=16,color="green",shape="box"];1612[label="ywz141",fontsize=16,color="green",shape="box"];1613[label="ywz442",fontsize=16,color="green",shape="box"];1614[label="ywz444",fontsize=16,color="green",shape="box"];1615[label="ywz140",fontsize=16,color="green",shape="box"];1616[label="ywz142",fontsize=16,color="green",shape="box"];1617[label="ywz143",fontsize=16,color="green",shape="box"];1618[label="Zero",fontsize=16,color="green",shape="box"];1619[label="ywz144",fontsize=16,color="green",shape="box"];1620[label="ywz441",fontsize=16,color="green",shape="box"];1621[label="ywz443",fontsize=16,color="green",shape="box"];1622[label="ywz440",fontsize=16,color="green",shape="box"];17251 -> 15167[label="",style="dashed", color="red", weight=0]; 17251[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz1416 (Pos (Succ ywz1417)) ywz1418",fontsize=16,color="magenta"];17251 -> 17253[label="",style="dashed", color="magenta", weight=3]; 17251 -> 17254[label="",style="dashed", color="magenta", weight=3]; 17251 -> 17255[label="",style="dashed", color="magenta", weight=3]; 17250[label="FiniteMap.mkBalBranch (Pos (Succ ywz1412)) ywz1413 ywz1415 ywz1434",fontsize=16,color="black",shape="triangle"];17250 -> 17256[label="",style="solid", color="black", weight=3]; 17252[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Pos (Succ ywz1412)) ywz1413 ywz1414 ywz1415 ywz1416 (Pos (Succ ywz1417)) ywz1418 True",fontsize=16,color="black",shape="box"];17252 -> 17495[label="",style="solid", color="black", weight=3]; 15664 -> 12612[label="",style="dashed", color="red", weight=0]; 15664[label="FiniteMap.mkBalBranch6Size_l ywz1247 ywz743 (Pos Zero) ywz741 + FiniteMap.mkBalBranch6Size_r ywz1247 ywz743 (Pos Zero) ywz741",fontsize=16,color="magenta"];15664 -> 15702[label="",style="dashed", color="magenta", weight=3]; 15664 -> 15703[label="",style="dashed", color="magenta", weight=3]; 15665[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];15666[label="ywz1243",fontsize=16,color="green",shape="box"];15667[label="Neg ywz7400",fontsize=16,color="green",shape="box"];15668[label="ywz741",fontsize=16,color="green",shape="box"];15669[label="ywz743",fontsize=16,color="green",shape="box"];15670[label="ywz1243",fontsize=16,color="green",shape="box"];15671[label="Neg ywz7400",fontsize=16,color="green",shape="box"];15672[label="ywz741",fontsize=16,color="green",shape="box"];15673[label="ywz743",fontsize=16,color="green",shape="box"];16620[label="ywz1362",fontsize=16,color="green",shape="box"];16621[label="ywz1364",fontsize=16,color="green",shape="box"];16622[label="Succ ywz1361",fontsize=16,color="green",shape="box"];16623 -> 15167[label="",style="dashed", color="red", weight=0]; 16623[label="FiniteMap.addToFM_C FiniteMap.addToFM0 ywz1365 (Neg (Succ ywz1366)) ywz1367",fontsize=16,color="magenta"];16623 -> 16627[label="",style="dashed", color="magenta", weight=3]; 16623 -> 16628[label="",style="dashed", color="magenta", weight=3]; 16623 -> 16629[label="",style="dashed", color="magenta", weight=3]; 16624[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 (Neg (Succ ywz1361)) ywz1362 ywz1363 ywz1364 ywz1365 (Neg (Succ ywz1366)) ywz1367 True",fontsize=16,color="black",shape="box"];16624 -> 16630[label="",style="solid", color="black", weight=3]; 17838[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Pos (Succ ywz144400)) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (primCmpNat (Succ ywz1441) (Succ ywz144400) == GT))",fontsize=16,color="black",shape="box"];17838 -> 18001[label="",style="solid", color="black", weight=3]; 17839[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Pos Zero) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (primCmpNat (Succ ywz1441) Zero == GT))",fontsize=16,color="black",shape="box"];17839 -> 18002[label="",style="solid", color="black", weight=3]; 17840[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Neg ywz14440) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) True)",fontsize=16,color="black",shape="box"];17840 -> 18003[label="",style="solid", color="black", weight=3]; 17841[label="Pos (Succ ywz1441)",fontsize=16,color="green",shape="box"];17842[label="ywz14470",fontsize=16,color="green",shape="box"];21968[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Pos (Succ ywz188000)) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (primCmpNat (Succ ywz1877) (Succ ywz188000) == GT))",fontsize=16,color="black",shape="box"];21968 -> 22003[label="",style="solid", color="black", weight=3]; 21969[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Pos Zero) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (primCmpNat (Succ ywz1877) Zero == GT))",fontsize=16,color="black",shape="box"];21969 -> 22004[label="",style="solid", color="black", weight=3]; 21970[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Neg ywz18800) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) True)",fontsize=16,color="black",shape="box"];21970 -> 22005[label="",style="solid", color="black", weight=3]; 21971[label="Pos (Succ ywz1877)",fontsize=16,color="green",shape="box"];21972[label="ywz18830",fontsize=16,color="green",shape="box"];24111[label="ywz1891",fontsize=16,color="green",shape="box"];24112[label="ywz1892",fontsize=16,color="green",shape="box"];24113[label="ywz1898",fontsize=16,color="green",shape="box"];24114[label="ywz1893",fontsize=16,color="green",shape="box"];24115[label="ywz1897",fontsize=16,color="green",shape="box"];24116[label="ywz189400",fontsize=16,color="green",shape="box"];24117[label="ywz1895",fontsize=16,color="green",shape="box"];24118[label="ywz1896",fontsize=16,color="green",shape="box"];24119[label="ywz1887",fontsize=16,color="green",shape="box"];24120[label="ywz1891",fontsize=16,color="green",shape="box"];24121[label="ywz1889",fontsize=16,color="green",shape="box"];24122[label="ywz1888",fontsize=16,color="green",shape="box"];24123[label="ywz1890",fontsize=16,color="green",shape="box"];24124[label="ywz1886",fontsize=16,color="green",shape="box"];24125[label="ywz189400",fontsize=16,color="green",shape="box"];24110[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (primCmpNat ywz2319 ywz2320 == GT))",fontsize=16,color="burlywood",shape="triangle"];25713[label="ywz2319/Succ ywz23190",fontsize=10,color="white",style="solid",shape="box"];24110 -> 25713[label="",style="solid", color="burlywood", weight=9]; 25713 -> 24261[label="",style="solid", color="burlywood", weight=3]; 25714[label="ywz2319/Zero",fontsize=10,color="white",style="solid",shape="box"];24110 -> 25714[label="",style="solid", color="burlywood", weight=9]; 25714 -> 24262[label="",style="solid", color="burlywood", weight=3]; 22077[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM1 (Pos Zero) ywz1895 ywz1896 ywz1897 ywz1898 (Pos (Succ ywz1891)) True)",fontsize=16,color="black",shape="box"];22077 -> 22135[label="",style="solid", color="black", weight=3]; 22078[label="ywz1898",fontsize=16,color="green",shape="box"];23136[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Pos (Succ ywz203400)) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) (LT == GT))",fontsize=16,color="black",shape="box"];23136 -> 23196[label="",style="solid", color="black", weight=3]; 23137[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Pos Zero) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) False)",fontsize=16,color="black",shape="box"];23137 -> 23197[label="",style="solid", color="black", weight=3]; 23138[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Neg (Succ ywz203400)) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) True)",fontsize=16,color="black",shape="box"];23138 -> 23198[label="",style="solid", color="black", weight=3]; 23139[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM1 (Neg Zero) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) False)",fontsize=16,color="black",shape="box"];23139 -> 23199[label="",style="solid", color="black", weight=3]; 2170[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (Just ywz41)",fontsize=16,color="black",shape="box"];2170 -> 2417[label="",style="solid", color="black", weight=3]; 22417[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Pos (Succ ywz194900)) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) (LT == GT))",fontsize=16,color="black",shape="box"];22417 -> 22636[label="",style="solid", color="black", weight=3]; 22418[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Pos Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) False)",fontsize=16,color="black",shape="box"];22418 -> 22637[label="",style="solid", color="black", weight=3]; 22419[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Neg (Succ ywz194900)) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) True)",fontsize=16,color="black",shape="box"];22419 -> 22638[label="",style="solid", color="black", weight=3]; 22420[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM1 (Neg Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) False)",fontsize=16,color="black",shape="box"];22420 -> 22639[label="",style="solid", color="black", weight=3]; 2173[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Pos Zero) ywz51 ywz3 ywz51 ywz3 (Just ywz41)",fontsize=16,color="black",shape="box"];2173 -> 2420[label="",style="solid", color="black", weight=3]; 20022[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM0 (Pos ywz17020) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) True)",fontsize=16,color="black",shape="box"];20022 -> 20052[label="",style="solid", color="black", weight=3]; 22918[label="ywz170200",fontsize=16,color="green",shape="box"];22919[label="ywz1695",fontsize=16,color="green",shape="box"];22920[label="ywz1694",fontsize=16,color="green",shape="box"];22921[label="ywz1697",fontsize=16,color="green",shape="box"];22922[label="ywz1699",fontsize=16,color="green",shape="box"];22923[label="ywz1704",fontsize=16,color="green",shape="box"];22924[label="ywz1700",fontsize=16,color="green",shape="box"];22925[label="ywz1705",fontsize=16,color="green",shape="box"];22926[label="ywz170200",fontsize=16,color="green",shape="box"];22927[label="ywz1698",fontsize=16,color="green",shape="box"];22928[label="ywz1703",fontsize=16,color="green",shape="box"];22929[label="ywz1706",fontsize=16,color="green",shape="box"];22930[label="ywz1696",fontsize=16,color="green",shape="box"];22931[label="ywz1699",fontsize=16,color="green",shape="box"];22932[label="ywz1701",fontsize=16,color="green",shape="box"];22917[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (primCmpNat ywz2103 ywz2104 == GT))",fontsize=16,color="burlywood",shape="triangle"];25715[label="ywz2103/Succ ywz21030",fontsize=10,color="white",style="solid",shape="box"];22917 -> 25715[label="",style="solid", color="burlywood", weight=9]; 25715 -> 23074[label="",style="solid", color="burlywood", weight=3]; 25716[label="ywz2103/Zero",fontsize=10,color="white",style="solid",shape="box"];22917 -> 25716[label="",style="solid", color="burlywood", weight=9]; 25716 -> 23075[label="",style="solid", color="burlywood", weight=3]; 20025[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM1 (Neg Zero) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) False)",fontsize=16,color="black",shape="box"];20025 -> 20057[label="",style="solid", color="black", weight=3]; 18147[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Pos ywz14800) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) False)",fontsize=16,color="black",shape="box"];18147 -> 18161[label="",style="solid", color="black", weight=3]; 18148[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Neg (Succ ywz148000)) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (primCmpNat (Succ ywz148000) (Succ ywz1477) == GT))",fontsize=16,color="black",shape="box"];18148 -> 18162[label="",style="solid", color="black", weight=3]; 18149[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Neg Zero) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (primCmpNat Zero (Succ ywz1477) == GT))",fontsize=16,color="black",shape="box"];18149 -> 18163[label="",style="solid", color="black", weight=3]; 18150[label="Neg (Succ ywz1477)",fontsize=16,color="green",shape="box"];18151[label="ywz14830",fontsize=16,color="green",shape="box"];21082[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Pos ywz17890) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) False)",fontsize=16,color="black",shape="box"];21082 -> 21120[label="",style="solid", color="black", weight=3]; 21083[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Neg (Succ ywz178900)) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (primCmpNat (Succ ywz178900) (Succ ywz1786) == GT))",fontsize=16,color="black",shape="box"];21083 -> 21121[label="",style="solid", color="black", weight=3]; 21084[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Neg Zero) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (primCmpNat Zero (Succ ywz1786) == GT))",fontsize=16,color="black",shape="box"];21084 -> 21122[label="",style="solid", color="black", weight=3]; 21085[label="Neg (Succ ywz1786)",fontsize=16,color="green",shape="box"];21086[label="ywz17920",fontsize=16,color="green",shape="box"];22836[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Pos (Succ ywz200500)) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) False)",fontsize=16,color="black",shape="box"];22836 -> 22887[label="",style="solid", color="black", weight=3]; 22837[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Pos Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) False)",fontsize=16,color="black",shape="box"];22837 -> 22888[label="",style="solid", color="black", weight=3]; 22838[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Neg (Succ ywz200500)) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) (GT == GT))",fontsize=16,color="black",shape="box"];22838 -> 22889[label="",style="solid", color="black", weight=3]; 22839[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Neg Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) False)",fontsize=16,color="black",shape="box"];22839 -> 22890[label="",style="solid", color="black", weight=3]; 2194[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (Just ywz41)",fontsize=16,color="black",shape="box"];2194 -> 2442[label="",style="solid", color="black", weight=3]; 25250[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Pos (Succ ywz238300)) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) False)",fontsize=16,color="black",shape="box"];25250 -> 25269[label="",style="solid", color="black", weight=3]; 25251[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Pos Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) False)",fontsize=16,color="black",shape="box"];25251 -> 25270[label="",style="solid", color="black", weight=3]; 25252[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Neg (Succ ywz238300)) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) (GT == GT))",fontsize=16,color="black",shape="box"];25252 -> 25271[label="",style="solid", color="black", weight=3]; 25253[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Neg Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) False)",fontsize=16,color="black",shape="box"];25253 -> 25272[label="",style="solid", color="black", weight=3]; 2196[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz41 ywz42 ywz43 ywz44) (Neg Zero) ywz51 ywz3 ywz51 ywz3 (Just ywz41)",fontsize=16,color="black",shape="box"];2196 -> 2445[label="",style="solid", color="black", weight=3]; 2046[label="Succ (Succ (primPlusNat (Succ (primPlusNat (Succ (primPlusNat ywz7200 ywz7200)) ywz7200)) ywz7200))",fontsize=16,color="green",shape="box"];2046 -> 2059[label="",style="dashed", color="green", weight=3]; 14443 -> 14303[label="",style="dashed", color="red", weight=0]; 14443[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat ywz1157000 ywz1154000 == GT)",fontsize=16,color="magenta"];14443 -> 14482[label="",style="dashed", color="magenta", weight=3]; 14443 -> 14483[label="",style="dashed", color="magenta", weight=3]; 14444 -> 14176[label="",style="dashed", color="red", weight=0]; 14444[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (GT == GT)",fontsize=16,color="magenta"];14445 -> 14181[label="",style="dashed", color="red", weight=0]; 14445[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (LT == GT)",fontsize=16,color="magenta"];14446 -> 14243[label="",style="dashed", color="red", weight=0]; 14446[label="FiniteMap.mkBalBranch6MkBalBranch4 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (EQ == GT)",fontsize=16,color="magenta"];14447 -> 14484[label="",style="dashed", color="red", weight=0]; 14447[label="FiniteMap.mkBalBranch6MkBalBranch01 ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064) ywz10060 ywz10061 ywz10062 ywz10063 ywz10064 (FiniteMap.sizeFM ywz10063 < Pos (Succ (Succ Zero)) * FiniteMap.sizeFM ywz10064)",fontsize=16,color="magenta"];14447 -> 14485[label="",style="dashed", color="magenta", weight=3]; 14448[label="ywz1007",fontsize=16,color="green",shape="box"];14449[label="ywz70",fontsize=16,color="green",shape="box"];14450[label="ywz71",fontsize=16,color="green",shape="box"];14451[label="ywz73",fontsize=16,color="green",shape="box"];14452[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt ywz1184 ywz1183 == GT)",fontsize=16,color="burlywood",shape="box"];25717[label="ywz1184/Pos ywz11840",fontsize=10,color="white",style="solid",shape="box"];14452 -> 25717[label="",style="solid", color="burlywood", weight=9]; 25717 -> 14494[label="",style="solid", color="burlywood", weight=3]; 25718[label="ywz1184/Neg ywz11840",fontsize=10,color="white",style="solid",shape="box"];14452 -> 25718[label="",style="solid", color="burlywood", weight=9]; 25718 -> 14495[label="",style="solid", color="burlywood", weight=3]; 21049[label="ywz18150",fontsize=16,color="green",shape="box"];21050[label="ywz18160",fontsize=16,color="green",shape="box"];21051[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) True",fontsize=16,color="black",shape="box"];21051 -> 21092[label="",style="solid", color="black", weight=3]; 21052[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) False",fontsize=16,color="black",shape="triangle"];21052 -> 21093[label="",style="solid", color="black", weight=3]; 21053 -> 21052[label="",style="dashed", color="red", weight=0]; 21053[label="FiniteMap.splitLT1 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) False",fontsize=16,color="magenta"];1686[label="FiniteMap.Branch (Neg ywz400) ywz41 (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];1686 -> 1832[label="",style="dashed", color="green", weight=3]; 1686 -> 1833[label="",style="dashed", color="green", weight=3]; 14941[label="ywz151",fontsize=16,color="green",shape="box"];14942[label="ywz153",fontsize=16,color="green",shape="box"];14943[label="ywz150",fontsize=16,color="green",shape="box"];14944[label="ywz152",fontsize=16,color="green",shape="box"];14945[label="ywz154",fontsize=16,color="green",shape="box"];14946[label="ywz41",fontsize=16,color="green",shape="box"];14947 -> 10999[label="",style="dashed", color="red", weight=0]; 14947[label="Neg ywz400 < ywz150",fontsize=16,color="magenta"];14947 -> 15008[label="",style="dashed", color="magenta", weight=3]; 14947 -> 15009[label="",style="dashed", color="magenta", weight=3]; 14948[label="Neg ywz400",fontsize=16,color="green",shape="box"];1714[label="FiniteMap.Branch ywz430 ywz431 ywz432 ywz433 ywz434",fontsize=16,color="green",shape="box"];14096 -> 12141[label="",style="dashed", color="red", weight=0]; 14096[label="FiniteMap.sIZE_RATIO * FiniteMap.mkVBalBranch3Size_l ywz430 ywz431 ywz432 ywz433 ywz434 ywz130 ywz131 ywz132 ywz133 ywz134",fontsize=16,color="magenta"];14096 -> 14164[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14089[label="",style="dashed", color="red", weight=0]; 14097[label="FiniteMap.mkVBalBranch3Size_r ywz430 ywz431 ywz432 ywz433 ywz434 ywz130 ywz131 ywz132 ywz133 ywz134",fontsize=16,color="magenta"];14097 -> 14165[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14166[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14167[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14168[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14169[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14170[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14171[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14172[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14173[label="",style="dashed", color="magenta", weight=3]; 14097 -> 14174[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14138[label="",style="dashed", color="red", weight=0]; 14153[label="FiniteMap.mkVBalBranch3Size_l ywz430 ywz431 ywz432 ywz433 ywz434 ywz100 ywz101 ywz102 ywz103 ywz104",fontsize=16,color="magenta"];14153 -> 14219[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14220[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14221[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14222[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14223[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14224[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14225[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14226[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14227[label="",style="dashed", color="magenta", weight=3]; 14153 -> 14228[label="",style="dashed", color="magenta", weight=3]; 14154[label="ywz433",fontsize=16,color="green",shape="box"];14155[label="ywz100",fontsize=16,color="green",shape="box"];14156[label="ywz102",fontsize=16,color="green",shape="box"];14157[label="ywz101",fontsize=16,color="green",shape="box"];14158[label="ywz104",fontsize=16,color="green",shape="box"];14159[label="ywz103",fontsize=16,color="green",shape="box"];14160[label="ywz434",fontsize=16,color="green",shape="box"];14161[label="ywz430",fontsize=16,color="green",shape="box"];14162[label="ywz431",fontsize=16,color="green",shape="box"];14163[label="ywz432",fontsize=16,color="green",shape="box"];21087[label="ywz18240",fontsize=16,color="green",shape="box"];21088[label="ywz18250",fontsize=16,color="green",shape="box"];21089[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) True",fontsize=16,color="black",shape="box"];21089 -> 21123[label="",style="solid", color="black", weight=3]; 21090[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) False",fontsize=16,color="black",shape="triangle"];21090 -> 21124[label="",style="solid", color="black", weight=3]; 21091 -> 21090[label="",style="dashed", color="red", weight=0]; 21091[label="FiniteMap.splitLT1 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) False",fontsize=16,color="magenta"];1745[label="FiniteMap.Branch (Pos ywz400) ywz41 (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];1745 -> 1885[label="",style="dashed", color="green", weight=3]; 1745 -> 1886[label="",style="dashed", color="green", weight=3]; 14949[label="ywz441",fontsize=16,color="green",shape="box"];14950[label="ywz443",fontsize=16,color="green",shape="box"];14951[label="ywz440",fontsize=16,color="green",shape="box"];14952[label="ywz442",fontsize=16,color="green",shape="box"];14953[label="ywz444",fontsize=16,color="green",shape="box"];14954[label="ywz41",fontsize=16,color="green",shape="box"];14955 -> 10999[label="",style="dashed", color="red", weight=0]; 14955[label="Pos ywz400 < ywz440",fontsize=16,color="magenta"];14955 -> 15010[label="",style="dashed", color="magenta", weight=3]; 14955 -> 15011[label="",style="dashed", color="magenta", weight=3]; 14956[label="Pos ywz400",fontsize=16,color="green",shape="box"];14209[label="ywz123",fontsize=16,color="green",shape="box"];14210[label="ywz440",fontsize=16,color="green",shape="box"];14211[label="ywz442",fontsize=16,color="green",shape="box"];14212[label="ywz441",fontsize=16,color="green",shape="box"];14213[label="ywz444",fontsize=16,color="green",shape="box"];14214[label="ywz443",fontsize=16,color="green",shape="box"];14215[label="ywz124",fontsize=16,color="green",shape="box"];14216[label="ywz120",fontsize=16,color="green",shape="box"];14217[label="ywz121",fontsize=16,color="green",shape="box"];14218[label="ywz122",fontsize=16,color="green",shape="box"];1761[label="ywz44",fontsize=16,color="green",shape="box"];1762[label="Zero",fontsize=16,color="green",shape="box"];17253[label="ywz1416",fontsize=16,color="green",shape="box"];17254[label="ywz1418",fontsize=16,color="green",shape="box"];17255[label="Pos (Succ ywz1417)",fontsize=16,color="green",shape="box"];17256[label="FiniteMap.mkBalBranch6 (Pos (Succ ywz1412)) ywz1413 ywz1415 ywz1434",fontsize=16,color="black",shape="box"];17256 -> 17496[label="",style="solid", color="black", weight=3]; 17495[label="FiniteMap.Branch (Pos (Succ ywz1417)) (FiniteMap.addToFM0 ywz1413 ywz1418) ywz1414 ywz1415 ywz1416",fontsize=16,color="green",shape="box"];17495 -> 17533[label="",style="dashed", color="green", weight=3]; 15702 -> 13476[label="",style="dashed", color="red", weight=0]; 15702[label="FiniteMap.mkBalBranch6Size_l ywz1247 ywz743 (Pos Zero) ywz741",fontsize=16,color="magenta"];15702 -> 15727[label="",style="dashed", color="magenta", weight=3]; 15702 -> 15728[label="",style="dashed", color="magenta", weight=3]; 15702 -> 15729[label="",style="dashed", color="magenta", weight=3]; 15702 -> 15730[label="",style="dashed", color="magenta", weight=3]; 15703 -> 13515[label="",style="dashed", color="red", weight=0]; 15703[label="FiniteMap.mkBalBranch6Size_r ywz1247 ywz743 (Pos Zero) ywz741",fontsize=16,color="magenta"];15703 -> 15731[label="",style="dashed", color="magenta", weight=3]; 15703 -> 15732[label="",style="dashed", color="magenta", weight=3]; 15703 -> 15733[label="",style="dashed", color="magenta", weight=3]; 15703 -> 15734[label="",style="dashed", color="magenta", weight=3]; 16627[label="ywz1365",fontsize=16,color="green",shape="box"];16628[label="ywz1367",fontsize=16,color="green",shape="box"];16629[label="Neg (Succ ywz1366)",fontsize=16,color="green",shape="box"];16630[label="FiniteMap.Branch (Neg (Succ ywz1366)) (FiniteMap.addToFM0 ywz1362 ywz1367) ywz1363 ywz1364 ywz1365",fontsize=16,color="green",shape="box"];16630 -> 16637[label="",style="dashed", color="green", weight=3]; 18001 -> 24501[label="",style="dashed", color="red", weight=0]; 18001[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Pos (Succ ywz144400)) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (primCmpNat ywz1441 ywz144400 == GT))",fontsize=16,color="magenta"];18001 -> 24502[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24503[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24504[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24505[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24506[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24507[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24508[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24509[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24510[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24511[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24512[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24513[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24514[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24515[label="",style="dashed", color="magenta", weight=3]; 18001 -> 24516[label="",style="dashed", color="magenta", weight=3]; 18002[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Pos Zero) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) (GT == GT))",fontsize=16,color="black",shape="box"];18002 -> 18054[label="",style="solid", color="black", weight=3]; 18003 -> 17688[label="",style="dashed", color="red", weight=0]; 18003[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM ywz1448 (Pos (Succ ywz1441)))",fontsize=16,color="magenta"];18003 -> 18055[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24704[label="",style="dashed", color="red", weight=0]; 22003[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Pos (Succ ywz188000)) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (primCmpNat ywz1877 ywz188000 == GT))",fontsize=16,color="magenta"];22003 -> 24705[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24706[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24707[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24708[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24709[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24710[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24711[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24712[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24713[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24714[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24715[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24716[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24717[label="",style="dashed", color="magenta", weight=3]; 22003 -> 24718[label="",style="dashed", color="magenta", weight=3]; 22004[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Pos Zero) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) (GT == GT))",fontsize=16,color="black",shape="box"];22004 -> 22049[label="",style="solid", color="black", weight=3]; 22005 -> 21663[label="",style="dashed", color="red", weight=0]; 22005[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM ywz1884 (Pos (Succ ywz1877)))",fontsize=16,color="magenta"];22005 -> 22050[label="",style="dashed", color="magenta", weight=3]; 24261[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (primCmpNat (Succ ywz23190) ywz2320 == GT))",fontsize=16,color="burlywood",shape="box"];25719[label="ywz2320/Succ ywz23200",fontsize=10,color="white",style="solid",shape="box"];24261 -> 25719[label="",style="solid", color="burlywood", weight=9]; 25719 -> 24283[label="",style="solid", color="burlywood", weight=3]; 25720[label="ywz2320/Zero",fontsize=10,color="white",style="solid",shape="box"];24261 -> 25720[label="",style="solid", color="burlywood", weight=9]; 25720 -> 24284[label="",style="solid", color="burlywood", weight=3]; 24262[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (primCmpNat Zero ywz2320 == GT))",fontsize=16,color="burlywood",shape="box"];25721[label="ywz2320/Succ ywz23200",fontsize=10,color="white",style="solid",shape="box"];24262 -> 25721[label="",style="solid", color="burlywood", weight=9]; 25721 -> 24285[label="",style="solid", color="burlywood", weight=3]; 25722[label="ywz2320/Zero",fontsize=10,color="white",style="solid",shape="box"];24262 -> 25722[label="",style="solid", color="burlywood", weight=9]; 25722 -> 24286[label="",style="solid", color="burlywood", weight=3]; 22135 -> 21687[label="",style="dashed", color="red", weight=0]; 22135[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz1886) ywz1887 ywz1888 ywz1889 ywz1890) (Pos (Succ ywz1891)) ywz1892 ywz1893 ywz1892 ywz1893 (FiniteMap.lookupFM ywz1898 (Pos (Succ ywz1891)))",fontsize=16,color="magenta"];22135 -> 22259[label="",style="dashed", color="magenta", weight=3]; 23196[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 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(FiniteMap.lookupFM0 (Pos Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];22637 -> 22703[label="",style="solid", color="black", weight=3]; 22638 -> 21997[label="",style="dashed", color="red", weight=0]; 22638[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM ywz1953 (Pos Zero))",fontsize=16,color="magenta"];22638 -> 22704[label="",style="dashed", color="magenta", weight=3]; 22639[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM0 (Neg Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];22639 -> 22705[label="",style="solid", color="black", weight=3]; 2420[label="ywz3 ywz41 ywz51",fontsize=16,color="green",shape="box"];2420 -> 2607[label="",style="dashed", color="green", weight=3]; 2420 -> 2608[label="",style="dashed", color="green", weight=3]; 20052[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (Just ywz1703)",fontsize=16,color="black",shape="triangle"];20052 -> 20064[label="",style="solid", color="black", weight=3]; 23074[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (primCmpNat (Succ ywz21030) ywz2104 == GT))",fontsize=16,color="burlywood",shape="box"];25723[label="ywz2104/Succ ywz21040",fontsize=10,color="white",style="solid",shape="box"];23074 -> 25723[label="",style="solid", color="burlywood", weight=9]; 25723 -> 23140[label="",style="solid", color="burlywood", weight=3]; 25724[label="ywz2104/Zero",fontsize=10,color="white",style="solid",shape="box"];23074 -> 25724[label="",style="solid", color="burlywood", weight=9]; 25724 -> 23141[label="",style="solid", color="burlywood", weight=3]; 23075[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (primCmpNat Zero ywz2104 == GT))",fontsize=16,color="burlywood",shape="box"];25725[label="ywz2104/Succ ywz21040",fontsize=10,color="white",style="solid",shape="box"];23075 -> 25725[label="",style="solid", color="burlywood", weight=9]; 25725 -> 23142[label="",style="solid", color="burlywood", weight=3]; 25726[label="ywz2104/Zero",fontsize=10,color="white",style="solid",shape="box"];23075 -> 25726[label="",style="solid", color="burlywood", weight=9]; 25726 -> 23143[label="",style="solid", color="burlywood", weight=3]; 20057[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM0 (Neg Zero) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) otherwise)",fontsize=16,color="black",shape="box"];20057 -> 20069[label="",style="solid", color="black", weight=3]; 18161[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM0 (Pos ywz14800) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) otherwise)",fontsize=16,color="black",shape="box"];18161 -> 18179[label="",style="solid", color="black", weight=3]; 18162 -> 24854[label="",style="dashed", color="red", weight=0]; 18162[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Neg (Succ 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color="magenta", weight=3]; 18162 -> 24868[label="",style="dashed", color="magenta", weight=3]; 18162 -> 24869[label="",style="dashed", color="magenta", weight=3]; 18163[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Neg Zero) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) (LT == GT))",fontsize=16,color="black",shape="box"];18163 -> 18182[label="",style="solid", color="black", weight=3]; 21120[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM0 (Pos ywz17890) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) otherwise)",fontsize=16,color="black",shape="box"];21120 -> 21337[label="",style="solid", color="black", weight=3]; 21121 -> 25021[label="",style="dashed", color="red", weight=0]; 21121[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Neg (Succ ywz178900)) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (primCmpNat ywz178900 ywz1786 == GT))",fontsize=16,color="magenta"];21121 -> 25022[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25023[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25024[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25025[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25026[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25027[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25028[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25029[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25030[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25031[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25032[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25033[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25034[label="",style="dashed", color="magenta", weight=3]; 21121 -> 25035[label="",style="dashed", color="magenta", weight=3]; 21122[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Neg Zero) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) (LT == GT))",fontsize=16,color="black",shape="box"];21122 -> 21340[label="",style="solid", color="black", weight=3]; 22887[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM0 (Pos (Succ ywz200500)) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];22887 -> 23076[label="",style="solid", color="black", weight=3]; 22888[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM0 (Pos Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];22888 -> 23077[label="",style="solid", color="black", weight=3]; 22889[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM1 (Neg (Succ ywz200500)) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) True)",fontsize=16,color="black",shape="box"];22889 -> 23078[label="",style="solid", color="black", weight=3]; 22890[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM0 (Neg Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];22890 -> 23079[label="",style="solid", color="black", weight=3]; 2442[label="ywz3 ywz41 ywz51",fontsize=16,color="green",shape="box"];2442 -> 2633[label="",style="dashed", color="green", weight=3]; 2442 -> 2634[label="",style="dashed", color="green", weight=3]; 25269[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM0 (Pos (Succ ywz238300)) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];25269 -> 25284[label="",style="solid", color="black", weight=3]; 25270[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM0 (Pos Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];25270 -> 25285[label="",style="solid", color="black", weight=3]; 25271[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM1 (Neg (Succ ywz238300)) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) True)",fontsize=16,color="black",shape="box"];25271 -> 25286[label="",style="solid", color="black", weight=3]; 25272[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM0 (Neg Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) otherwise)",fontsize=16,color="black",shape="box"];25272 -> 25287[label="",style="solid", color="black", weight=3]; 2445[label="ywz3 ywz41 ywz51",fontsize=16,color="green",shape="box"];2445 -> 2637[label="",style="dashed", color="green", weight=3]; 2445 -> 2638[label="",style="dashed", color="green", weight=3]; 2059[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat ywz7200 ywz7200)) ywz7200)) ywz7200",fontsize=16,color="burlywood",shape="triangle"];25727[label="ywz7200/Succ ywz72000",fontsize=10,color="white",style="solid",shape="box"];2059 -> 25727[label="",style="solid", color="burlywood", weight=9]; 25727 -> 2084[label="",style="solid", color="burlywood", weight=3]; 25728[label="ywz7200/Zero",fontsize=10,color="white",style="solid",shape="box"];2059 -> 25728[label="",style="solid", color="burlywood", weight=9]; 25728 -> 2085[label="",style="solid", color="burlywood", weight=3]; 14482[label="ywz1157000",fontsize=16,color="green",shape="box"];14483[label="ywz1154000",fontsize=16,color="green",shape="box"];14485 -> 10999[label="",style="dashed", color="red", weight=0]; 14485[label="FiniteMap.sizeFM ywz10063 < Pos (Succ (Succ Zero)) * FiniteMap.sizeFM ywz10064",fontsize=16,color="magenta"];14485 -> 14496[label="",style="dashed", color="magenta", weight=3]; 14485 -> 14497[label="",style="dashed", color="magenta", weight=3]; 14484[label="FiniteMap.mkBalBranch6MkBalBranch01 ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064) ywz10060 ywz10061 ywz10062 ywz10063 ywz10064 ywz1202",fontsize=16,color="burlywood",shape="triangle"];25729[label="ywz1202/False",fontsize=10,color="white",style="solid",shape="box"];14484 -> 25729[label="",style="solid", color="burlywood", weight=9]; 25729 -> 14498[label="",style="solid", color="burlywood", weight=3]; 25730[label="ywz1202/True",fontsize=10,color="white",style="solid",shape="box"];14484 -> 25730[label="",style="solid", color="burlywood", weight=9]; 25730 -> 14499[label="",style="solid", color="burlywood", weight=3]; 14494[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos ywz11840) ywz1183 == GT)",fontsize=16,color="burlywood",shape="box"];25731[label="ywz11840/Succ ywz118400",fontsize=10,color="white",style="solid",shape="box"];14494 -> 25731[label="",style="solid", color="burlywood", weight=9]; 25731 -> 15012[label="",style="solid", color="burlywood", weight=3]; 25732[label="ywz11840/Zero",fontsize=10,color="white",style="solid",shape="box"];14494 -> 25732[label="",style="solid", color="burlywood", weight=9]; 25732 -> 15013[label="",style="solid", color="burlywood", weight=3]; 14495[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg ywz11840) ywz1183 == GT)",fontsize=16,color="burlywood",shape="box"];25733[label="ywz11840/Succ ywz118400",fontsize=10,color="white",style="solid",shape="box"];14495 -> 25733[label="",style="solid", color="burlywood", weight=9]; 25733 -> 15014[label="",style="solid", color="burlywood", weight=3]; 25734[label="ywz11840/Zero",fontsize=10,color="white",style="solid",shape="box"];14495 -> 25734[label="",style="solid", color="burlywood", weight=9]; 25734 -> 15015[label="",style="solid", color="burlywood", weight=3]; 21092 -> 759[label="",style="dashed", color="red", weight=0]; 21092[label="FiniteMap.mkVBalBranch (Pos (Succ ywz1809)) ywz1810 ywz1812 (FiniteMap.splitLT ywz1813 (Pos (Succ ywz1814)))",fontsize=16,color="magenta"];21092 -> 21125[label="",style="dashed", color="magenta", weight=3]; 21092 -> 21126[label="",style="dashed", color="magenta", weight=3]; 21092 -> 21127[label="",style="dashed", color="magenta", weight=3]; 21092 -> 21128[label="",style="dashed", color="magenta", weight=3]; 21093[label="FiniteMap.splitLT0 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) otherwise",fontsize=16,color="black",shape="box"];21093 -> 21129[label="",style="solid", color="black", weight=3]; 1832 -> 83[label="",style="dashed", color="red", weight=0]; 1832[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];1833 -> 83[label="",style="dashed", color="red", weight=0]; 1833[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];15008[label="Neg ywz400",fontsize=16,color="green",shape="box"];15009[label="ywz150",fontsize=16,color="green",shape="box"];14164 -> 14138[label="",style="dashed", color="red", weight=0]; 14164[label="FiniteMap.mkVBalBranch3Size_l ywz430 ywz431 ywz432 ywz433 ywz434 ywz130 ywz131 ywz132 ywz133 ywz134",fontsize=16,color="magenta"];14164 -> 14229[label="",style="dashed", color="magenta", weight=3]; 14164 -> 14230[label="",style="dashed", color="magenta", weight=3]; 14164 -> 14231[label="",style="dashed", color="magenta", weight=3]; 14164 -> 14232[label="",style="dashed", color="magenta", weight=3]; 14164 -> 14233[label="",style="dashed", color="magenta", weight=3]; 14164 -> 14234[label="",style="dashed", color="magenta", weight=3]; 14164 -> 14235[label="",style="dashed", color="magenta", weight=3]; 14164 -> 14236[label="",style="dashed", color="magenta", weight=3]; 14164 -> 14237[label="",style="dashed", color="magenta", weight=3]; 14164 -> 14238[label="",style="dashed", color="magenta", weight=3]; 14165[label="ywz433",fontsize=16,color="green",shape="box"];14166[label="ywz130",fontsize=16,color="green",shape="box"];14167[label="ywz132",fontsize=16,color="green",shape="box"];14168[label="ywz131",fontsize=16,color="green",shape="box"];14169[label="ywz134",fontsize=16,color="green",shape="box"];14170[label="ywz133",fontsize=16,color="green",shape="box"];14171[label="ywz434",fontsize=16,color="green",shape="box"];14172[label="ywz430",fontsize=16,color="green",shape="box"];14173[label="ywz431",fontsize=16,color="green",shape="box"];14174[label="ywz432",fontsize=16,color="green",shape="box"];14219[label="ywz433",fontsize=16,color="green",shape="box"];14220[label="ywz100",fontsize=16,color="green",shape="box"];14221[label="ywz102",fontsize=16,color="green",shape="box"];14222[label="ywz101",fontsize=16,color="green",shape="box"];14223[label="ywz104",fontsize=16,color="green",shape="box"];14224[label="ywz103",fontsize=16,color="green",shape="box"];14225[label="ywz434",fontsize=16,color="green",shape="box"];14226[label="ywz430",fontsize=16,color="green",shape="box"];14227[label="ywz431",fontsize=16,color="green",shape="box"];14228[label="ywz432",fontsize=16,color="green",shape="box"];21123 -> 626[label="",style="dashed", color="red", weight=0]; 21123[label="FiniteMap.mkVBalBranch (Neg (Succ ywz1818)) ywz1819 ywz1821 (FiniteMap.splitLT ywz1822 (Neg (Succ ywz1823)))",fontsize=16,color="magenta"];21123 -> 21341[label="",style="dashed", color="magenta", weight=3]; 21123 -> 21342[label="",style="dashed", color="magenta", weight=3]; 21123 -> 21343[label="",style="dashed", color="magenta", weight=3]; 21123 -> 21344[label="",style="dashed", color="magenta", weight=3]; 21124[label="FiniteMap.splitLT0 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) otherwise",fontsize=16,color="black",shape="box"];21124 -> 21345[label="",style="solid", color="black", weight=3]; 1885 -> 83[label="",style="dashed", color="red", weight=0]; 1885[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];1886 -> 83[label="",style="dashed", color="red", weight=0]; 1886[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];15010[label="Pos ywz400",fontsize=16,color="green",shape="box"];15011[label="ywz440",fontsize=16,color="green",shape="box"];17496 -> 13158[label="",style="dashed", color="red", weight=0]; 17496[label="FiniteMap.mkBalBranch6MkBalBranch5 ywz1434 ywz1415 (Pos (Succ ywz1412)) ywz1413 (Pos (Succ ywz1412)) ywz1413 ywz1415 ywz1434 (FiniteMap.mkBalBranch6Size_l ywz1434 ywz1415 (Pos (Succ ywz1412)) ywz1413 + FiniteMap.mkBalBranch6Size_r ywz1434 ywz1415 (Pos (Succ ywz1412)) ywz1413 < Pos (Succ (Succ Zero)))",fontsize=16,color="magenta"];17496 -> 17534[label="",style="dashed", color="magenta", weight=3]; 17496 -> 17535[label="",style="dashed", color="magenta", weight=3]; 17496 -> 17536[label="",style="dashed", color="magenta", weight=3]; 17496 -> 17537[label="",style="dashed", color="magenta", weight=3]; 17496 -> 17538[label="",style="dashed", color="magenta", weight=3]; 17496 -> 17539[label="",style="dashed", color="magenta", weight=3]; 17533 -> 15543[label="",style="dashed", color="red", weight=0]; 17533[label="FiniteMap.addToFM0 ywz1413 ywz1418",fontsize=16,color="magenta"];17533 -> 17672[label="",style="dashed", color="magenta", weight=3]; 17533 -> 17673[label="",style="dashed", color="magenta", weight=3]; 15727[label="ywz1247",fontsize=16,color="green",shape="box"];15728[label="Pos Zero",fontsize=16,color="green",shape="box"];15729[label="ywz741",fontsize=16,color="green",shape="box"];15730[label="ywz743",fontsize=16,color="green",shape="box"];15731[label="ywz1247",fontsize=16,color="green",shape="box"];15732[label="Pos Zero",fontsize=16,color="green",shape="box"];15733[label="ywz741",fontsize=16,color="green",shape="box"];15734[label="ywz743",fontsize=16,color="green",shape="box"];16637 -> 15543[label="",style="dashed", color="red", weight=0]; 16637[label="FiniteMap.addToFM0 ywz1362 ywz1367",fontsize=16,color="magenta"];16637 -> 16653[label="",style="dashed", color="magenta", weight=3]; 16637 -> 16654[label="",style="dashed", color="magenta", weight=3]; 24502[label="ywz1438",fontsize=16,color="green",shape="box"];24503[label="ywz144400",fontsize=16,color="green",shape="box"];24504[label="ywz1437",fontsize=16,color="green",shape="box"];24505[label="ywz1446",fontsize=16,color="green",shape="box"];24506[label="ywz144400",fontsize=16,color="green",shape="box"];24507[label="ywz1441",fontsize=16,color="green",shape="box"];24508[label="ywz1447",fontsize=16,color="green",shape="box"];24509[label="ywz1439",fontsize=16,color="green",shape="box"];24510[label="ywz1442",fontsize=16,color="green",shape="box"];24511[label="ywz1445",fontsize=16,color="green",shape="box"];24512[label="ywz1441",fontsize=16,color="green",shape="box"];24513[label="ywz1443",fontsize=16,color="green",shape="box"];24514[label="ywz1436",fontsize=16,color="green",shape="box"];24515[label="ywz1440",fontsize=16,color="green",shape="box"];24516[label="ywz1448",fontsize=16,color="green",shape="box"];24501[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (primCmpNat ywz2402 ywz2403 == GT))",fontsize=16,color="burlywood",shape="triangle"];25735[label="ywz2402/Succ ywz24020",fontsize=10,color="white",style="solid",shape="box"];24501 -> 25735[label="",style="solid", color="burlywood", weight=9]; 25735 -> 24652[label="",style="solid", color="burlywood", weight=3]; 25736[label="ywz2402/Zero",fontsize=10,color="white",style="solid",shape="box"];24501 -> 25736[label="",style="solid", color="burlywood", weight=9]; 25736 -> 24653[label="",style="solid", color="burlywood", weight=3]; 18054[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM1 (Pos Zero) ywz1445 ywz1446 ywz1447 ywz1448 (Pos (Succ ywz1441)) True)",fontsize=16,color="black",shape="box"];18054 -> 18064[label="",style="solid", color="black", weight=3]; 18055[label="ywz1448",fontsize=16,color="green",shape="box"];24705[label="ywz1882",fontsize=16,color="green",shape="box"];24706[label="ywz1877",fontsize=16,color="green",shape="box"];24707[label="ywz1874",fontsize=16,color="green",shape="box"];24708[label="ywz1878",fontsize=16,color="green",shape="box"];24709[label="ywz1884",fontsize=16,color="green",shape="box"];24710[label="ywz1875",fontsize=16,color="green",shape="box"];24711[label="ywz1881",fontsize=16,color="green",shape="box"];24712[label="ywz1877",fontsize=16,color="green",shape="box"];24713[label="ywz1879",fontsize=16,color="green",shape="box"];24714[label="ywz1883",fontsize=16,color="green",shape="box"];24715[label="ywz1873",fontsize=16,color="green",shape="box"];24716[label="ywz1876",fontsize=16,color="green",shape="box"];24717[label="ywz188000",fontsize=16,color="green",shape="box"];24718[label="ywz188000",fontsize=16,color="green",shape="box"];24704[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (primCmpNat ywz2418 ywz2419 == GT))",fontsize=16,color="burlywood",shape="triangle"];25737[label="ywz2418/Succ ywz24180",fontsize=10,color="white",style="solid",shape="box"];24704 -> 25737[label="",style="solid", color="burlywood", weight=9]; 25737 -> 24847[label="",style="solid", color="burlywood", weight=3]; 25738[label="ywz2418/Zero",fontsize=10,color="white",style="solid",shape="box"];24704 -> 25738[label="",style="solid", color="burlywood", weight=9]; 25738 -> 24848[label="",style="solid", color="burlywood", weight=3]; 22049[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM1 (Pos Zero) ywz1881 ywz1882 ywz1883 ywz1884 (Pos (Succ ywz1877)) True)",fontsize=16,color="black",shape="box"];22049 -> 22083[label="",style="solid", color="black", weight=3]; 22050[label="ywz1884",fontsize=16,color="green",shape="box"];24283[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (primCmpNat (Succ ywz23190) (Succ ywz23200) == GT))",fontsize=16,color="black",shape="box"];24283 -> 24300[label="",style="solid", color="black", weight=3]; 24284[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (primCmpNat (Succ ywz23190) Zero == GT))",fontsize=16,color="black",shape="box"];24284 -> 24301[label="",style="solid", color="black", weight=3]; 24285[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (primCmpNat Zero (Succ ywz23200) == GT))",fontsize=16,color="black",shape="box"];24285 -> 24302[label="",style="solid", color="black", weight=3]; 24286[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];24286 -> 24303[label="",style="solid", color="black", weight=3]; 22259[label="ywz1898",fontsize=16,color="green",shape="box"];23234[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM0 (Pos (Succ ywz203400)) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];23234 -> 23269[label="",style="solid", color="black", weight=3]; 23235[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM0 (Pos Zero) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) True)",fontsize=16,color="black",shape="box"];23235 -> 23270[label="",style="solid", color="black", weight=3]; 23236[label="ywz2038",fontsize=16,color="green",shape="box"];23237[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM0 (Neg Zero) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) True)",fontsize=16,color="black",shape="box"];23237 -> 23271[label="",style="solid", color="black", weight=3]; 2603[label="ywz41",fontsize=16,color="green",shape="box"];2604[label="ywz51",fontsize=16,color="green",shape="box"];22702[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM0 (Pos (Succ ywz194900)) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) otherwise)",fontsize=16,color="black",shape="box"];22702 -> 22756[label="",style="solid", color="black", weight=3]; 22703[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM0 (Pos Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) True)",fontsize=16,color="black",shape="box"];22703 -> 22757[label="",style="solid", color="black", weight=3]; 22704[label="ywz1953",fontsize=16,color="green",shape="box"];22705[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM0 (Neg Zero) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) True)",fontsize=16,color="black",shape="box"];22705 -> 22758[label="",style="solid", color="black", weight=3]; 2607[label="ywz41",fontsize=16,color="green",shape="box"];2608[label="ywz51",fontsize=16,color="green",shape="box"];20064[label="ywz1701 ywz1703 ywz1700",fontsize=16,color="green",shape="box"];20064 -> 20076[label="",style="dashed", color="green", weight=3]; 20064 -> 20077[label="",style="dashed", color="green", weight=3]; 23140[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (primCmpNat (Succ ywz21030) (Succ ywz21040) == GT))",fontsize=16,color="black",shape="box"];23140 -> 23200[label="",style="solid", color="black", weight=3]; 23141[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (primCmpNat (Succ ywz21030) Zero == GT))",fontsize=16,color="black",shape="box"];23141 -> 23201[label="",style="solid", color="black", weight=3]; 23142[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (primCmpNat Zero (Succ ywz21040) == GT))",fontsize=16,color="black",shape="box"];23142 -> 23202[label="",style="solid", color="black", weight=3]; 23143[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];23143 -> 23203[label="",style="solid", color="black", weight=3]; 20069[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (FiniteMap.lookupFM0 (Neg Zero) ywz1703 ywz1704 ywz1705 ywz1706 (Neg (Succ ywz1699)) True)",fontsize=16,color="black",shape="box"];20069 -> 20083[label="",style="solid", color="black", weight=3]; 18179[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM0 (Pos ywz14800) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) True)",fontsize=16,color="black",shape="box"];18179 -> 18195[label="",style="solid", color="black", weight=3]; 24855[label="ywz148000",fontsize=16,color="green",shape="box"];24856[label="ywz1484",fontsize=16,color="green",shape="box"];24857[label="ywz1478",fontsize=16,color="green",shape="box"];24858[label="ywz1483",fontsize=16,color="green",shape="box"];24859[label="ywz1472",fontsize=16,color="green",shape="box"];24860[label="ywz1482",fontsize=16,color="green",shape="box"];24861[label="ywz1476",fontsize=16,color="green",shape="box"];24862[label="ywz1479",fontsize=16,color="green",shape="box"];24863[label="ywz1477",fontsize=16,color="green",shape="box"];24864[label="ywz1475",fontsize=16,color="green",shape="box"];24865[label="ywz1477",fontsize=16,color="green",shape="box"];24866[label="ywz1481",fontsize=16,color="green",shape="box"];24867[label="ywz148000",fontsize=16,color="green",shape="box"];24868[label="ywz1473",fontsize=16,color="green",shape="box"];24869[label="ywz1474",fontsize=16,color="green",shape="box"];24854[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (primCmpNat ywz2434 ywz2435 == GT))",fontsize=16,color="burlywood",shape="triangle"];25739[label="ywz2434/Succ ywz24340",fontsize=10,color="white",style="solid",shape="box"];24854 -> 25739[label="",style="solid", color="burlywood", weight=9]; 25739 -> 25008[label="",style="solid", color="burlywood", weight=3]; 25740[label="ywz2434/Zero",fontsize=10,color="white",style="solid",shape="box"];24854 -> 25740[label="",style="solid", color="burlywood", weight=9]; 25740 -> 25009[label="",style="solid", color="burlywood", weight=3]; 18182[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM1 (Neg Zero) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) False)",fontsize=16,color="black",shape="box"];18182 -> 18200[label="",style="solid", color="black", weight=3]; 21337[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM0 (Pos ywz17890) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) True)",fontsize=16,color="black",shape="box"];21337 -> 21591[label="",style="solid", color="black", weight=3]; 25022[label="ywz1791",fontsize=16,color="green",shape="box"];25023[label="ywz1784",fontsize=16,color="green",shape="box"];25024[label="ywz1785",fontsize=16,color="green",shape="box"];25025[label="ywz1792",fontsize=16,color="green",shape="box"];25026[label="ywz178900",fontsize=16,color="green",shape="box"];25027[label="ywz1788",fontsize=16,color="green",shape="box"];25028[label="ywz1790",fontsize=16,color="green",shape="box"];25029[label="ywz1786",fontsize=16,color="green",shape="box"];25030[label="ywz1793",fontsize=16,color="green",shape="box"];25031[label="ywz1783",fontsize=16,color="green",shape="box"];25032[label="ywz1782",fontsize=16,color="green",shape="box"];25033[label="ywz178900",fontsize=16,color="green",shape="box"];25034[label="ywz1787",fontsize=16,color="green",shape="box"];25035[label="ywz1786",fontsize=16,color="green",shape="box"];25021[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (primCmpNat ywz2449 ywz2450 == GT))",fontsize=16,color="burlywood",shape="triangle"];25741[label="ywz2449/Succ ywz24490",fontsize=10,color="white",style="solid",shape="box"];25021 -> 25741[label="",style="solid", color="burlywood", weight=9]; 25741 -> 25165[label="",style="solid", color="burlywood", weight=3]; 25742[label="ywz2449/Zero",fontsize=10,color="white",style="solid",shape="box"];25021 -> 25742[label="",style="solid", color="burlywood", weight=9]; 25742 -> 25166[label="",style="solid", color="burlywood", weight=3]; 21340[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM1 (Neg Zero) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) False)",fontsize=16,color="black",shape="box"];21340 -> 21596[label="",style="solid", color="black", weight=3]; 23076[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM0 (Pos (Succ ywz200500)) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) True)",fontsize=16,color="black",shape="box"];23076 -> 23144[label="",style="solid", color="black", weight=3]; 23077[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM0 (Pos Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) True)",fontsize=16,color="black",shape="box"];23077 -> 23145[label="",style="solid", color="black", weight=3]; 23078 -> 22416[label="",style="dashed", color="red", weight=0]; 23078[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM ywz2009 (Neg Zero))",fontsize=16,color="magenta"];23078 -> 23146[label="",style="dashed", color="magenta", weight=3]; 23079[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (FiniteMap.lookupFM0 (Neg Zero) ywz2006 ywz2007 ywz2008 ywz2009 (Neg Zero) True)",fontsize=16,color="black",shape="box"];23079 -> 23147[label="",style="solid", color="black", weight=3]; 2633[label="ywz41",fontsize=16,color="green",shape="box"];2634[label="ywz51",fontsize=16,color="green",shape="box"];25284[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM0 (Pos (Succ ywz238300)) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) True)",fontsize=16,color="black",shape="box"];25284 -> 25300[label="",style="solid", color="black", weight=3]; 25285[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM0 (Pos Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) True)",fontsize=16,color="black",shape="box"];25285 -> 25301[label="",style="solid", color="black", weight=3]; 25286 -> 24846[label="",style="dashed", color="red", weight=0]; 25286[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM ywz2387 (Neg Zero))",fontsize=16,color="magenta"];25286 -> 25302[label="",style="dashed", color="magenta", weight=3]; 25287[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (FiniteMap.lookupFM0 (Neg Zero) ywz2384 ywz2385 ywz2386 ywz2387 (Neg Zero) True)",fontsize=16,color="black",shape="box"];25287 -> 25303[label="",style="solid", color="black", weight=3]; 2637[label="ywz41",fontsize=16,color="green",shape="box"];2638[label="ywz51",fontsize=16,color="green",shape="box"];2084[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat (Succ ywz72000) (Succ ywz72000))) (Succ ywz72000))) (Succ ywz72000)",fontsize=16,color="black",shape="box"];2084 -> 2232[label="",style="solid", color="black", weight=3]; 2085[label="primPlusNat (Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)) Zero",fontsize=16,color="black",shape="box"];2085 -> 2233[label="",style="solid", color="black", weight=3]; 14496 -> 3313[label="",style="dashed", color="red", weight=0]; 14496[label="FiniteMap.sizeFM ywz10063",fontsize=16,color="magenta"];14496 -> 15016[label="",style="dashed", color="magenta", weight=3]; 14497 -> 15017[label="",style="dashed", color="red", weight=0]; 14497[label="Pos (Succ (Succ Zero)) * FiniteMap.sizeFM ywz10064",fontsize=16,color="magenta"];14497 -> 15018[label="",style="dashed", color="magenta", weight=3]; 14498[label="FiniteMap.mkBalBranch6MkBalBranch01 ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064) ywz10060 ywz10061 ywz10062 ywz10063 ywz10064 False",fontsize=16,color="black",shape="box"];14498 -> 15024[label="",style="solid", color="black", weight=3]; 14499[label="FiniteMap.mkBalBranch6MkBalBranch01 ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064) ywz10060 ywz10061 ywz10062 ywz10063 ywz10064 True",fontsize=16,color="black",shape="box"];14499 -> 15025[label="",style="solid", color="black", weight=3]; 15012[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos (Succ ywz118400)) ywz1183 == GT)",fontsize=16,color="burlywood",shape="box"];25743[label="ywz1183/Pos ywz11830",fontsize=10,color="white",style="solid",shape="box"];15012 -> 25743[label="",style="solid", color="burlywood", weight=9]; 25743 -> 15026[label="",style="solid", color="burlywood", weight=3]; 25744[label="ywz1183/Neg ywz11830",fontsize=10,color="white",style="solid",shape="box"];15012 -> 25744[label="",style="solid", color="burlywood", weight=9]; 25744 -> 15027[label="",style="solid", color="burlywood", weight=3]; 15013[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) ywz1183 == GT)",fontsize=16,color="burlywood",shape="box"];25745[label="ywz1183/Pos ywz11830",fontsize=10,color="white",style="solid",shape="box"];15013 -> 25745[label="",style="solid", color="burlywood", weight=9]; 25745 -> 15028[label="",style="solid", color="burlywood", weight=3]; 25746[label="ywz1183/Neg ywz11830",fontsize=10,color="white",style="solid",shape="box"];15013 -> 25746[label="",style="solid", color="burlywood", weight=9]; 25746 -> 15029[label="",style="solid", color="burlywood", weight=3]; 15014[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg (Succ ywz118400)) ywz1183 == GT)",fontsize=16,color="burlywood",shape="box"];25747[label="ywz1183/Pos ywz11830",fontsize=10,color="white",style="solid",shape="box"];15014 -> 25747[label="",style="solid", color="burlywood", weight=9]; 25747 -> 15030[label="",style="solid", color="burlywood", weight=3]; 25748[label="ywz1183/Neg ywz11830",fontsize=10,color="white",style="solid",shape="box"];15014 -> 25748[label="",style="solid", color="burlywood", weight=9]; 25748 -> 15031[label="",style="solid", color="burlywood", weight=3]; 15015[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) ywz1183 == GT)",fontsize=16,color="burlywood",shape="box"];25749[label="ywz1183/Pos ywz11830",fontsize=10,color="white",style="solid",shape="box"];15015 -> 25749[label="",style="solid", color="burlywood", weight=9]; 25749 -> 15032[label="",style="solid", color="burlywood", weight=3]; 25750[label="ywz1183/Neg ywz11830",fontsize=10,color="white",style="solid",shape="box"];15015 -> 25750[label="",style="solid", color="burlywood", weight=9]; 25750 -> 15033[label="",style="solid", color="burlywood", weight=3]; 21125 -> 767[label="",style="dashed", color="red", weight=0]; 21125[label="FiniteMap.splitLT ywz1813 (Pos (Succ ywz1814))",fontsize=16,color="magenta"];21125 -> 21346[label="",style="dashed", color="magenta", weight=3]; 21125 -> 21347[label="",style="dashed", color="magenta", weight=3]; 21126[label="ywz1810",fontsize=16,color="green",shape="box"];21127[label="Succ ywz1809",fontsize=16,color="green",shape="box"];21128[label="ywz1812",fontsize=16,color="green",shape="box"];21129[label="FiniteMap.splitLT0 (Pos (Succ ywz1809)) ywz1810 ywz1811 ywz1812 ywz1813 (Pos (Succ ywz1814)) True",fontsize=16,color="black",shape="box"];21129 -> 21348[label="",style="solid", color="black", weight=3]; 14229[label="ywz433",fontsize=16,color="green",shape="box"];14230[label="ywz130",fontsize=16,color="green",shape="box"];14231[label="ywz132",fontsize=16,color="green",shape="box"];14232[label="ywz131",fontsize=16,color="green",shape="box"];14233[label="ywz134",fontsize=16,color="green",shape="box"];14234[label="ywz133",fontsize=16,color="green",shape="box"];14235[label="ywz434",fontsize=16,color="green",shape="box"];14236[label="ywz430",fontsize=16,color="green",shape="box"];14237[label="ywz431",fontsize=16,color="green",shape="box"];14238[label="ywz432",fontsize=16,color="green",shape="box"];21341[label="ywz1819",fontsize=16,color="green",shape="box"];21342[label="ywz1821",fontsize=16,color="green",shape="box"];21343 -> 156[label="",style="dashed", color="red", weight=0]; 21343[label="FiniteMap.splitLT ywz1822 (Neg (Succ ywz1823))",fontsize=16,color="magenta"];21343 -> 21597[label="",style="dashed", color="magenta", weight=3]; 21343 -> 21598[label="",style="dashed", color="magenta", weight=3]; 21344[label="ywz1818",fontsize=16,color="green",shape="box"];21345[label="FiniteMap.splitLT0 (Neg (Succ ywz1818)) ywz1819 ywz1820 ywz1821 ywz1822 (Neg (Succ ywz1823)) True",fontsize=16,color="black",shape="box"];21345 -> 21599[label="",style="solid", color="black", weight=3]; 17534[label="ywz1415",fontsize=16,color="green",shape="box"];17535[label="ywz1434",fontsize=16,color="green",shape="box"];17536[label="ywz1434",fontsize=16,color="green",shape="box"];17537[label="Pos (Succ ywz1412)",fontsize=16,color="green",shape="box"];17538[label="ywz1413",fontsize=16,color="green",shape="box"];17539 -> 10999[label="",style="dashed", color="red", weight=0]; 17539[label="FiniteMap.mkBalBranch6Size_l ywz1434 ywz1415 (Pos (Succ ywz1412)) ywz1413 + FiniteMap.mkBalBranch6Size_r ywz1434 ywz1415 (Pos (Succ ywz1412)) ywz1413 < Pos (Succ (Succ Zero))",fontsize=16,color="magenta"];17539 -> 17674[label="",style="dashed", color="magenta", weight=3]; 17539 -> 17675[label="",style="dashed", color="magenta", weight=3]; 17672[label="ywz1413",fontsize=16,color="green",shape="box"];17673[label="ywz1418",fontsize=16,color="green",shape="box"];16653[label="ywz1362",fontsize=16,color="green",shape="box"];16654[label="ywz1367",fontsize=16,color="green",shape="box"];24652[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (primCmpNat (Succ ywz24020) ywz2403 == GT))",fontsize=16,color="burlywood",shape="box"];25751[label="ywz2403/Succ ywz24030",fontsize=10,color="white",style="solid",shape="box"];24652 -> 25751[label="",style="solid", color="burlywood", weight=9]; 25751 -> 24699[label="",style="solid", color="burlywood", weight=3]; 25752[label="ywz2403/Zero",fontsize=10,color="white",style="solid",shape="box"];24652 -> 25752[label="",style="solid", color="burlywood", weight=9]; 25752 -> 24700[label="",style="solid", color="burlywood", weight=3]; 24653[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (primCmpNat Zero ywz2403 == GT))",fontsize=16,color="burlywood",shape="box"];25753[label="ywz2403/Succ ywz24030",fontsize=10,color="white",style="solid",shape="box"];24653 -> 25753[label="",style="solid", color="burlywood", weight=9]; 25753 -> 24701[label="",style="solid", color="burlywood", weight=3]; 25754[label="ywz2403/Zero",fontsize=10,color="white",style="solid",shape="box"];24653 -> 25754[label="",style="solid", color="burlywood", weight=9]; 25754 -> 24702[label="",style="solid", color="burlywood", weight=3]; 18064 -> 17688[label="",style="dashed", color="red", weight=0]; 18064[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1436)) ywz1437 ywz1438 ywz1439 ywz1440) (Pos (Succ ywz1441)) ywz1442 ywz1443 ywz1442 ywz1443 (FiniteMap.lookupFM ywz1448 (Pos (Succ ywz1441)))",fontsize=16,color="magenta"];18064 -> 18090[label="",style="dashed", color="magenta", weight=3]; 24847[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (primCmpNat (Succ ywz24180) ywz2419 == GT))",fontsize=16,color="burlywood",shape="box"];25755[label="ywz2419/Succ ywz24190",fontsize=10,color="white",style="solid",shape="box"];24847 -> 25755[label="",style="solid", color="burlywood", weight=9]; 25755 -> 25010[label="",style="solid", color="burlywood", weight=3]; 25756[label="ywz2419/Zero",fontsize=10,color="white",style="solid",shape="box"];24847 -> 25756[label="",style="solid", color="burlywood", weight=9]; 25756 -> 25011[label="",style="solid", color="burlywood", weight=3]; 24848[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (primCmpNat Zero ywz2419 == GT))",fontsize=16,color="burlywood",shape="box"];25757[label="ywz2419/Succ ywz24190",fontsize=10,color="white",style="solid",shape="box"];24848 -> 25757[label="",style="solid", color="burlywood", weight=9]; 25757 -> 25012[label="",style="solid", color="burlywood", weight=3]; 25758[label="ywz2419/Zero",fontsize=10,color="white",style="solid",shape="box"];24848 -> 25758[label="",style="solid", color="burlywood", weight=9]; 25758 -> 25013[label="",style="solid", color="burlywood", weight=3]; 22083 -> 21663[label="",style="dashed", color="red", weight=0]; 22083[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz1873 ywz1874 ywz1875 ywz1876) (Pos (Succ ywz1877)) ywz1878 ywz1879 ywz1878 ywz1879 (FiniteMap.lookupFM ywz1884 (Pos (Succ ywz1877)))",fontsize=16,color="magenta"];22083 -> 22140[label="",style="dashed", color="magenta", weight=3]; 24300 -> 24110[label="",style="dashed", color="red", weight=0]; 24300[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (primCmpNat ywz23190 ywz23200 == GT))",fontsize=16,color="magenta"];24300 -> 24317[label="",style="dashed", color="magenta", weight=3]; 24300 -> 24318[label="",style="dashed", color="magenta", weight=3]; 24301[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (GT == GT))",fontsize=16,color="black",shape="box"];24301 -> 24319[label="",style="solid", color="black", weight=3]; 24302[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (LT == GT))",fontsize=16,color="black",shape="box"];24302 -> 24320[label="",style="solid", color="black", weight=3]; 24303[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) (EQ == GT))",fontsize=16,color="black",shape="box"];24303 -> 24321[label="",style="solid", color="black", weight=3]; 23269[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (FiniteMap.lookupFM0 (Pos (Succ ywz203400)) ywz2035 ywz2036 ywz2037 ywz2038 (Pos Zero) True)",fontsize=16,color="black",shape="box"];23269 -> 23289[label="",style="solid", color="black", weight=3]; 23270[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (Just ywz2035)",fontsize=16,color="black",shape="triangle"];23270 -> 23290[label="",style="solid", color="black", weight=3]; 23271 -> 23270[label="",style="dashed", color="red", weight=0]; 23271[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (Just ywz2035)",fontsize=16,color="magenta"];22756[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (FiniteMap.lookupFM0 (Pos (Succ ywz194900)) ywz1950 ywz1951 ywz1952 ywz1953 (Pos Zero) True)",fontsize=16,color="black",shape="box"];22756 -> 22799[label="",style="solid", color="black", weight=3]; 22757[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (Just ywz1950)",fontsize=16,color="black",shape="triangle"];22757 -> 22800[label="",style="solid", color="black", weight=3]; 22758 -> 22757[label="",style="dashed", color="red", weight=0]; 22758[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (Just ywz1950)",fontsize=16,color="magenta"];20076[label="ywz1703",fontsize=16,color="green",shape="box"];20077[label="ywz1700",fontsize=16,color="green",shape="box"];23200 -> 22917[label="",style="dashed", color="red", weight=0]; 23200[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (primCmpNat ywz21030 ywz21040 == GT))",fontsize=16,color="magenta"];23200 -> 23238[label="",style="dashed", color="magenta", weight=3]; 23200 -> 23239[label="",style="dashed", color="magenta", weight=3]; 23201[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (GT == GT))",fontsize=16,color="black",shape="box"];23201 -> 23240[label="",style="solid", color="black", weight=3]; 23202[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (LT == GT))",fontsize=16,color="black",shape="box"];23202 -> 23241[label="",style="solid", color="black", weight=3]; 23203[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) (EQ == GT))",fontsize=16,color="black",shape="box"];23203 -> 23242[label="",style="solid", color="black", weight=3]; 20083 -> 20052[label="",style="dashed", color="red", weight=0]; 20083[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz1694) ywz1695 ywz1696 ywz1697 ywz1698) (Neg (Succ ywz1699)) ywz1700 ywz1701 ywz1700 ywz1701 (Just ywz1703)",fontsize=16,color="magenta"];18195[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (Just ywz1481)",fontsize=16,color="black",shape="triangle"];18195 -> 18253[label="",style="solid", color="black", weight=3]; 25008[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (primCmpNat (Succ ywz24340) ywz2435 == GT))",fontsize=16,color="burlywood",shape="box"];25759[label="ywz2435/Succ ywz24350",fontsize=10,color="white",style="solid",shape="box"];25008 -> 25759[label="",style="solid", color="burlywood", weight=9]; 25759 -> 25167[label="",style="solid", color="burlywood", weight=3]; 25760[label="ywz2435/Zero",fontsize=10,color="white",style="solid",shape="box"];25008 -> 25760[label="",style="solid", color="burlywood", weight=9]; 25760 -> 25168[label="",style="solid", color="burlywood", weight=3]; 25009[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (primCmpNat Zero ywz2435 == GT))",fontsize=16,color="burlywood",shape="box"];25761[label="ywz2435/Succ ywz24350",fontsize=10,color="white",style="solid",shape="box"];25009 -> 25761[label="",style="solid", color="burlywood", weight=9]; 25761 -> 25169[label="",style="solid", color="burlywood", weight=3]; 25762[label="ywz2435/Zero",fontsize=10,color="white",style="solid",shape="box"];25009 -> 25762[label="",style="solid", color="burlywood", weight=9]; 25762 -> 25170[label="",style="solid", color="burlywood", weight=3]; 18200[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM0 (Neg Zero) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) otherwise)",fontsize=16,color="black",shape="box"];18200 -> 18258[label="",style="solid", color="black", weight=3]; 21591[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (Just ywz1790)",fontsize=16,color="black",shape="triangle"];21591 -> 21664[label="",style="solid", color="black", weight=3]; 25165[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (primCmpNat (Succ ywz24490) ywz2450 == GT))",fontsize=16,color="burlywood",shape="box"];25763[label="ywz2450/Succ ywz24500",fontsize=10,color="white",style="solid",shape="box"];25165 -> 25763[label="",style="solid", color="burlywood", weight=9]; 25763 -> 25181[label="",style="solid", color="burlywood", weight=3]; 25764[label="ywz2450/Zero",fontsize=10,color="white",style="solid",shape="box"];25165 -> 25764[label="",style="solid", color="burlywood", weight=9]; 25764 -> 25182[label="",style="solid", color="burlywood", weight=3]; 25166[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (primCmpNat Zero ywz2450 == GT))",fontsize=16,color="burlywood",shape="box"];25765[label="ywz2450/Succ ywz24500",fontsize=10,color="white",style="solid",shape="box"];25166 -> 25765[label="",style="solid", color="burlywood", weight=9]; 25765 -> 25183[label="",style="solid", color="burlywood", weight=3]; 25766[label="ywz2450/Zero",fontsize=10,color="white",style="solid",shape="box"];25166 -> 25766[label="",style="solid", color="burlywood", weight=9]; 25766 -> 25184[label="",style="solid", color="burlywood", weight=3]; 21596[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM0 (Neg Zero) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) otherwise)",fontsize=16,color="black",shape="box"];21596 -> 21669[label="",style="solid", color="black", weight=3]; 23144[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (Just ywz2006)",fontsize=16,color="black",shape="triangle"];23144 -> 23204[label="",style="solid", color="black", weight=3]; 23145 -> 23144[label="",style="dashed", color="red", weight=0]; 23145[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (Just ywz2006)",fontsize=16,color="magenta"];23146[label="ywz2009",fontsize=16,color="green",shape="box"];23147 -> 23144[label="",style="dashed", color="red", weight=0]; 23147[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz1998)) ywz1999 ywz2000 ywz2001 ywz2002) (Neg Zero) ywz2003 ywz2004 ywz2003 ywz2004 (Just ywz2006)",fontsize=16,color="magenta"];25300[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (Just ywz2384)",fontsize=16,color="black",shape="triangle"];25300 -> 25312[label="",style="solid", color="black", weight=3]; 25301 -> 25300[label="",style="dashed", color="red", weight=0]; 25301[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (Just ywz2384)",fontsize=16,color="magenta"];25302[label="ywz2387",fontsize=16,color="green",shape="box"];25303 -> 25300[label="",style="dashed", color="red", weight=0]; 25303[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2376)) ywz2377 ywz2378 ywz2379 ywz2380) (Neg Zero) ywz2381 ywz2382 ywz2381 ywz2382 (Just ywz2384)",fontsize=16,color="magenta"];2232[label="Succ (Succ (primPlusNat (primPlusNat (Succ (primPlusNat (Succ ywz72000) (Succ ywz72000))) (Succ ywz72000)) ywz72000))",fontsize=16,color="green",shape="box"];2232 -> 2491[label="",style="dashed", color="green", weight=3]; 2233[label="Succ (primPlusNat (Succ (primPlusNat Zero Zero)) Zero)",fontsize=16,color="green",shape="box"];2233 -> 2492[label="",style="dashed", color="green", weight=3]; 15016[label="ywz10063",fontsize=16,color="green",shape="box"];15018 -> 3313[label="",style="dashed", color="red", weight=0]; 15018[label="FiniteMap.sizeFM ywz10064",fontsize=16,color="magenta"];15018 -> 15034[label="",style="dashed", color="magenta", weight=3]; 15017[label="Pos (Succ (Succ Zero)) * ywz1209",fontsize=16,color="black",shape="triangle"];15017 -> 15035[label="",style="solid", color="black", weight=3]; 15024[label="FiniteMap.mkBalBranch6MkBalBranch00 ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064) ywz10060 ywz10061 ywz10062 ywz10063 ywz10064 otherwise",fontsize=16,color="black",shape="box"];15024 -> 15078[label="",style="solid", color="black", weight=3]; 15025[label="FiniteMap.mkBalBranch6Single_L ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064)",fontsize=16,color="black",shape="box"];15025 -> 15079[label="",style="solid", color="black", weight=3]; 15026[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos (Succ ywz118400)) (Pos ywz11830) == GT)",fontsize=16,color="black",shape="box"];15026 -> 15080[label="",style="solid", color="black", weight=3]; 15027[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos (Succ ywz118400)) (Neg ywz11830) == GT)",fontsize=16,color="black",shape="box"];15027 -> 15081[label="",style="solid", color="black", weight=3]; 15028[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Pos ywz11830) == GT)",fontsize=16,color="burlywood",shape="box"];25767[label="ywz11830/Succ ywz118300",fontsize=10,color="white",style="solid",shape="box"];15028 -> 25767[label="",style="solid", color="burlywood", weight=9]; 25767 -> 15082[label="",style="solid", color="burlywood", weight=3]; 25768[label="ywz11830/Zero",fontsize=10,color="white",style="solid",shape="box"];15028 -> 25768[label="",style="solid", color="burlywood", weight=9]; 25768 -> 15083[label="",style="solid", color="burlywood", weight=3]; 15029[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Neg ywz11830) == GT)",fontsize=16,color="burlywood",shape="box"];25769[label="ywz11830/Succ ywz118300",fontsize=10,color="white",style="solid",shape="box"];15029 -> 25769[label="",style="solid", color="burlywood", weight=9]; 25769 -> 15084[label="",style="solid", color="burlywood", weight=3]; 25770[label="ywz11830/Zero",fontsize=10,color="white",style="solid",shape="box"];15029 -> 25770[label="",style="solid", color="burlywood", weight=9]; 25770 -> 15085[label="",style="solid", color="burlywood", weight=3]; 15030[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg (Succ ywz118400)) (Pos ywz11830) == GT)",fontsize=16,color="black",shape="box"];15030 -> 15086[label="",style="solid", color="black", weight=3]; 15031[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg (Succ ywz118400)) (Neg ywz11830) == GT)",fontsize=16,color="black",shape="box"];15031 -> 15087[label="",style="solid", color="black", weight=3]; 15032[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Pos ywz11830) == GT)",fontsize=16,color="burlywood",shape="box"];25771[label="ywz11830/Succ ywz118300",fontsize=10,color="white",style="solid",shape="box"];15032 -> 25771[label="",style="solid", color="burlywood", weight=9]; 25771 -> 15088[label="",style="solid", color="burlywood", weight=3]; 25772[label="ywz11830/Zero",fontsize=10,color="white",style="solid",shape="box"];15032 -> 25772[label="",style="solid", color="burlywood", weight=9]; 25772 -> 15089[label="",style="solid", color="burlywood", weight=3]; 15033[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Neg ywz11830) == GT)",fontsize=16,color="burlywood",shape="box"];25773[label="ywz11830/Succ ywz118300",fontsize=10,color="white",style="solid",shape="box"];15033 -> 25773[label="",style="solid", color="burlywood", weight=9]; 25773 -> 15090[label="",style="solid", color="burlywood", weight=3]; 25774[label="ywz11830/Zero",fontsize=10,color="white",style="solid",shape="box"];15033 -> 25774[label="",style="solid", color="burlywood", weight=9]; 25774 -> 15091[label="",style="solid", color="burlywood", weight=3]; 21346[label="ywz1813",fontsize=16,color="green",shape="box"];21347[label="ywz1814",fontsize=16,color="green",shape="box"];21348[label="ywz1812",fontsize=16,color="green",shape="box"];21597[label="ywz1823",fontsize=16,color="green",shape="box"];21598[label="ywz1822",fontsize=16,color="green",shape="box"];21599[label="ywz1821",fontsize=16,color="green",shape="box"];17674 -> 12612[label="",style="dashed", color="red", weight=0]; 17674[label="FiniteMap.mkBalBranch6Size_l ywz1434 ywz1415 (Pos (Succ ywz1412)) ywz1413 + FiniteMap.mkBalBranch6Size_r ywz1434 ywz1415 (Pos (Succ ywz1412)) ywz1413",fontsize=16,color="magenta"];17674 -> 17689[label="",style="dashed", color="magenta", weight=3]; 17674 -> 17690[label="",style="dashed", color="magenta", weight=3]; 17675[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];24699[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (primCmpNat (Succ ywz24020) (Succ ywz24030) == GT))",fontsize=16,color="black",shape="box"];24699 -> 24849[label="",style="solid", color="black", weight=3]; 24700[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (primCmpNat (Succ ywz24020) Zero == GT))",fontsize=16,color="black",shape="box"];24700 -> 24850[label="",style="solid", color="black", weight=3]; 24701[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (primCmpNat Zero (Succ ywz24030) == GT))",fontsize=16,color="black",shape="box"];24701 -> 24851[label="",style="solid", color="black", weight=3]; 24702[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];24702 -> 24852[label="",style="solid", color="black", weight=3]; 18090[label="ywz1448",fontsize=16,color="green",shape="box"];25010[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (primCmpNat (Succ ywz24180) (Succ ywz24190) == GT))",fontsize=16,color="black",shape="box"];25010 -> 25171[label="",style="solid", color="black", weight=3]; 25011[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (primCmpNat (Succ ywz24180) Zero == GT))",fontsize=16,color="black",shape="box"];25011 -> 25172[label="",style="solid", color="black", weight=3]; 25012[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (primCmpNat Zero (Succ ywz24190) == GT))",fontsize=16,color="black",shape="box"];25012 -> 25173[label="",style="solid", color="black", weight=3]; 25013[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];25013 -> 25174[label="",style="solid", color="black", weight=3]; 22140[label="ywz1884",fontsize=16,color="green",shape="box"];24317[label="ywz23190",fontsize=16,color="green",shape="box"];24318[label="ywz23200",fontsize=16,color="green",shape="box"];24319[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) True)",fontsize=16,color="black",shape="box"];24319 -> 24335[label="",style="solid", color="black", weight=3]; 24320[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) False)",fontsize=16,color="black",shape="triangle"];24320 -> 24336[label="",style="solid", color="black", weight=3]; 24321 -> 24320[label="",style="dashed", color="red", weight=0]; 24321[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM1 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) False)",fontsize=16,color="magenta"];23289 -> 23270[label="",style="dashed", color="red", weight=0]; 23289[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2027)) ywz2028 ywz2029 ywz2030 ywz2031) (Pos Zero) ywz2032 ywz2033 ywz2032 ywz2033 (Just ywz2035)",fontsize=16,color="magenta"];23290[label="ywz2033 ywz2035 ywz2032",fontsize=16,color="green",shape="box"];23290 -> 23322[label="",style="dashed", color="green", weight=3]; 23290 -> 23323[label="",style="dashed", color="green", weight=3]; 22799 -> 22757[label="",style="dashed", color="red", weight=0]; 22799[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1942)) ywz1943 ywz1944 ywz1945 ywz1946) (Pos Zero) ywz1947 ywz1948 ywz1947 ywz1948 (Just ywz1950)",fontsize=16,color="magenta"];22800[label="ywz1948 ywz1950 ywz1947",fontsize=16,color="green",shape="box"];22800 -> 22840[label="",style="dashed", color="green", weight=3]; 22800 -> 22841[label="",style="dashed", color="green", weight=3]; 23238[label="ywz21030",fontsize=16,color="green",shape="box"];23239[label="ywz21040",fontsize=16,color="green",shape="box"];23240[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) True)",fontsize=16,color="black",shape="box"];23240 -> 23272[label="",style="solid", color="black", weight=3]; 23241[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) False)",fontsize=16,color="black",shape="triangle"];23241 -> 23273[label="",style="solid", color="black", weight=3]; 23242 -> 23241[label="",style="dashed", color="red", weight=0]; 23242[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM1 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) False)",fontsize=16,color="magenta"];18253[label="ywz1479 ywz1481 ywz1478",fontsize=16,color="green",shape="box"];18253 -> 18281[label="",style="dashed", color="green", weight=3]; 18253 -> 18282[label="",style="dashed", color="green", weight=3]; 25167[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (primCmpNat (Succ ywz24340) (Succ ywz24350) == GT))",fontsize=16,color="black",shape="box"];25167 -> 25185[label="",style="solid", color="black", weight=3]; 25168[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (primCmpNat (Succ ywz24340) Zero == GT))",fontsize=16,color="black",shape="box"];25168 -> 25186[label="",style="solid", color="black", weight=3]; 25169[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (primCmpNat Zero (Succ ywz24350) == GT))",fontsize=16,color="black",shape="box"];25169 -> 25187[label="",style="solid", color="black", weight=3]; 25170[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];25170 -> 25188[label="",style="solid", color="black", weight=3]; 18258[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (FiniteMap.lookupFM0 (Neg Zero) ywz1481 ywz1482 ywz1483 ywz1484 (Neg (Succ ywz1477)) True)",fontsize=16,color="black",shape="box"];18258 -> 18288[label="",style="solid", color="black", weight=3]; 21664[label="ywz1788 ywz1790 ywz1787",fontsize=16,color="green",shape="box"];21664 -> 21691[label="",style="dashed", color="green", weight=3]; 21664 -> 21692[label="",style="dashed", color="green", weight=3]; 25181[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (primCmpNat (Succ ywz24490) (Succ ywz24500) == GT))",fontsize=16,color="black",shape="box"];25181 -> 25215[label="",style="solid", color="black", weight=3]; 25182[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (primCmpNat (Succ ywz24490) Zero == GT))",fontsize=16,color="black",shape="box"];25182 -> 25216[label="",style="solid", color="black", weight=3]; 25183[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (primCmpNat Zero (Succ ywz24500) == GT))",fontsize=16,color="black",shape="box"];25183 -> 25217[label="",style="solid", color="black", weight=3]; 25184[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (primCmpNat Zero Zero == GT))",fontsize=16,color="black",shape="box"];25184 -> 25218[label="",style="solid", color="black", weight=3]; 21669[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (FiniteMap.lookupFM0 (Neg Zero) ywz1790 ywz1791 ywz1792 ywz1793 (Neg (Succ ywz1786)) True)",fontsize=16,color="black",shape="box"];21669 -> 21698[label="",style="solid", color="black", weight=3]; 23204[label="ywz2004 ywz2006 ywz2003",fontsize=16,color="green",shape="box"];23204 -> 23243[label="",style="dashed", color="green", weight=3]; 23204 -> 23244[label="",style="dashed", color="green", weight=3]; 25312[label="ywz2382 ywz2384 ywz2381",fontsize=16,color="green",shape="box"];25312 -> 25313[label="",style="dashed", color="green", weight=3]; 25312 -> 25314[label="",style="dashed", color="green", weight=3]; 2491[label="primPlusNat (primPlusNat (Succ (primPlusNat (Succ ywz72000) (Succ ywz72000))) (Succ ywz72000)) ywz72000",fontsize=16,color="black",shape="box"];2491 -> 2687[label="",style="solid", color="black", weight=3]; 2492[label="primPlusNat (Succ (primPlusNat Zero Zero)) Zero",fontsize=16,color="black",shape="box"];2492 -> 2688[label="",style="solid", color="black", weight=3]; 15034[label="ywz10064",fontsize=16,color="green",shape="box"];15035[label="primMulInt (Pos (Succ (Succ Zero))) ywz1209",fontsize=16,color="burlywood",shape="box"];25775[label="ywz1209/Pos ywz12090",fontsize=10,color="white",style="solid",shape="box"];15035 -> 25775[label="",style="solid", color="burlywood", weight=9]; 25775 -> 15092[label="",style="solid", color="burlywood", weight=3]; 25776[label="ywz1209/Neg ywz12090",fontsize=10,color="white",style="solid",shape="box"];15035 -> 25776[label="",style="solid", color="burlywood", weight=9]; 25776 -> 15093[label="",style="solid", color="burlywood", weight=3]; 15078[label="FiniteMap.mkBalBranch6MkBalBranch00 ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064) ywz10060 ywz10061 ywz10062 ywz10063 ywz10064 True",fontsize=16,color="black",shape="box"];15078 -> 15129[label="",style="solid", color="black", weight=3]; 15079 -> 15392[label="",style="dashed", color="red", weight=0]; 15079[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ Zero)))) ywz10060 ywz10061 (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) ywz70 ywz71 ywz73 ywz10063) ywz10064",fontsize=16,color="magenta"];15079 -> 15408[label="",style="dashed", color="magenta", weight=3]; 15079 -> 15409[label="",style="dashed", color="magenta", weight=3]; 15079 -> 15410[label="",style="dashed", color="magenta", weight=3]; 15079 -> 15411[label="",style="dashed", color="magenta", weight=3]; 15079 -> 15412[label="",style="dashed", color="magenta", weight=3]; 15080[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz118400) ywz11830 == GT)",fontsize=16,color="burlywood",shape="triangle"];25777[label="ywz11830/Succ ywz118300",fontsize=10,color="white",style="solid",shape="box"];15080 -> 25777[label="",style="solid", color="burlywood", weight=9]; 25777 -> 15131[label="",style="solid", color="burlywood", weight=3]; 25778[label="ywz11830/Zero",fontsize=10,color="white",style="solid",shape="box"];15080 -> 25778[label="",style="solid", color="burlywood", weight=9]; 25778 -> 15132[label="",style="solid", color="burlywood", weight=3]; 15081[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (GT == GT)",fontsize=16,color="black",shape="triangle"];15081 -> 15133[label="",style="solid", color="black", weight=3]; 15082[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Pos (Succ ywz118300)) == GT)",fontsize=16,color="black",shape="box"];15082 -> 15134[label="",style="solid", color="black", weight=3]; 15083[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];15083 -> 15135[label="",style="solid", color="black", weight=3]; 15084[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Neg (Succ ywz118300)) == GT)",fontsize=16,color="black",shape="box"];15084 -> 15136[label="",style="solid", color="black", weight=3]; 15085[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Pos Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];15085 -> 15137[label="",style="solid", color="black", weight=3]; 15086[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (LT == GT)",fontsize=16,color="black",shape="triangle"];15086 -> 15138[label="",style="solid", color="black", weight=3]; 15087[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat ywz11830 (Succ ywz118400) == GT)",fontsize=16,color="burlywood",shape="triangle"];25779[label="ywz11830/Succ ywz118300",fontsize=10,color="white",style="solid",shape="box"];15087 -> 25779[label="",style="solid", color="burlywood", weight=9]; 25779 -> 15139[label="",style="solid", color="burlywood", weight=3]; 25780[label="ywz11830/Zero",fontsize=10,color="white",style="solid",shape="box"];15087 -> 25780[label="",style="solid", color="burlywood", weight=9]; 25780 -> 15140[label="",style="solid", color="burlywood", weight=3]; 15088[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Pos (Succ ywz118300)) == GT)",fontsize=16,color="black",shape="box"];15088 -> 15141[label="",style="solid", color="black", weight=3]; 15089[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Pos Zero) == GT)",fontsize=16,color="black",shape="box"];15089 -> 15142[label="",style="solid", color="black", weight=3]; 15090[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Neg (Succ ywz118300)) == GT)",fontsize=16,color="black",shape="box"];15090 -> 15143[label="",style="solid", color="black", weight=3]; 15091[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpInt (Neg Zero) (Neg Zero) == GT)",fontsize=16,color="black",shape="box"];15091 -> 15144[label="",style="solid", color="black", weight=3]; 17689 -> 13476[label="",style="dashed", color="red", weight=0]; 17689[label="FiniteMap.mkBalBranch6Size_l ywz1434 ywz1415 (Pos (Succ ywz1412)) ywz1413",fontsize=16,color="magenta"];17689 -> 17706[label="",style="dashed", color="magenta", weight=3]; 17689 -> 17707[label="",style="dashed", color="magenta", weight=3]; 17689 -> 17708[label="",style="dashed", color="magenta", weight=3]; 17689 -> 17709[label="",style="dashed", color="magenta", weight=3]; 17690 -> 13515[label="",style="dashed", color="red", weight=0]; 17690[label="FiniteMap.mkBalBranch6Size_r ywz1434 ywz1415 (Pos (Succ ywz1412)) ywz1413",fontsize=16,color="magenta"];17690 -> 17710[label="",style="dashed", color="magenta", weight=3]; 17690 -> 17711[label="",style="dashed", color="magenta", weight=3]; 17690 -> 17712[label="",style="dashed", color="magenta", weight=3]; 17690 -> 17713[label="",style="dashed", color="magenta", weight=3]; 24849 -> 24501[label="",style="dashed", color="red", weight=0]; 24849[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (primCmpNat ywz24020 ywz24030 == GT))",fontsize=16,color="magenta"];24849 -> 25014[label="",style="dashed", color="magenta", weight=3]; 24849 -> 25015[label="",style="dashed", color="magenta", weight=3]; 24850[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (GT == GT))",fontsize=16,color="black",shape="box"];24850 -> 25016[label="",style="solid", color="black", weight=3]; 24851[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (LT == GT))",fontsize=16,color="black",shape="box"];24851 -> 25017[label="",style="solid", color="black", weight=3]; 24852[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) (EQ == GT))",fontsize=16,color="black",shape="box"];24852 -> 25018[label="",style="solid", color="black", weight=3]; 25171 -> 24704[label="",style="dashed", color="red", weight=0]; 25171[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (primCmpNat ywz24180 ywz24190 == GT))",fontsize=16,color="magenta"];25171 -> 25189[label="",style="dashed", color="magenta", weight=3]; 25171 -> 25190[label="",style="dashed", color="magenta", weight=3]; 25172[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (GT == GT))",fontsize=16,color="black",shape="box"];25172 -> 25191[label="",style="solid", color="black", weight=3]; 25173[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (LT == GT))",fontsize=16,color="black",shape="box"];25173 -> 25192[label="",style="solid", color="black", weight=3]; 25174[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM1 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) (EQ == GT))",fontsize=16,color="black",shape="box"];25174 -> 25193[label="",style="solid", color="black", weight=3]; 24335 -> 21687[label="",style="dashed", color="red", weight=0]; 24335[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM ywz2318 (Pos (Succ ywz2311)))",fontsize=16,color="magenta"];24335 -> 24491[label="",style="dashed", color="magenta", weight=3]; 24335 -> 24492[label="",style="dashed", color="magenta", weight=3]; 24335 -> 24493[label="",style="dashed", color="magenta", weight=3]; 24335 -> 24494[label="",style="dashed", color="magenta", weight=3]; 24335 -> 24495[label="",style="dashed", color="magenta", weight=3]; 24335 -> 24496[label="",style="dashed", color="magenta", weight=3]; 24335 -> 24497[label="",style="dashed", color="magenta", weight=3]; 24335 -> 24498[label="",style="dashed", color="magenta", weight=3]; 24335 -> 24499[label="",style="dashed", color="magenta", weight=3]; 24336[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (FiniteMap.lookupFM0 (Pos (Succ ywz2314)) ywz2315 ywz2316 ywz2317 ywz2318 (Pos (Succ ywz2311)) otherwise)",fontsize=16,color="black",shape="box"];24336 -> 24500[label="",style="solid", color="black", weight=3]; 23322[label="ywz2035",fontsize=16,color="green",shape="box"];23323[label="ywz2032",fontsize=16,color="green",shape="box"];22840[label="ywz1950",fontsize=16,color="green",shape="box"];22841[label="ywz1947",fontsize=16,color="green",shape="box"];23272 -> 19861[label="",style="dashed", color="red", weight=0]; 23272[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM ywz2102 (Neg (Succ ywz2095)))",fontsize=16,color="magenta"];23272 -> 23291[label="",style="dashed", color="magenta", weight=3]; 23272 -> 23292[label="",style="dashed", color="magenta", weight=3]; 23272 -> 23293[label="",style="dashed", color="magenta", weight=3]; 23272 -> 23294[label="",style="dashed", color="magenta", weight=3]; 23272 -> 23295[label="",style="dashed", color="magenta", weight=3]; 23272 -> 23296[label="",style="dashed", color="magenta", weight=3]; 23272 -> 23297[label="",style="dashed", color="magenta", weight=3]; 23272 -> 23298[label="",style="dashed", color="magenta", weight=3]; 23272 -> 23299[label="",style="dashed", color="magenta", weight=3]; 23273[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (FiniteMap.lookupFM0 (Neg (Succ ywz2098)) ywz2099 ywz2100 ywz2101 ywz2102 (Neg (Succ ywz2095)) otherwise)",fontsize=16,color="black",shape="box"];23273 -> 23300[label="",style="solid", color="black", weight=3]; 18281[label="ywz1481",fontsize=16,color="green",shape="box"];18282[label="ywz1478",fontsize=16,color="green",shape="box"];25185 -> 24854[label="",style="dashed", color="red", weight=0]; 25185[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (primCmpNat ywz24340 ywz24350 == GT))",fontsize=16,color="magenta"];25185 -> 25219[label="",style="dashed", color="magenta", weight=3]; 25185 -> 25220[label="",style="dashed", color="magenta", weight=3]; 25186[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (GT == GT))",fontsize=16,color="black",shape="box"];25186 -> 25221[label="",style="solid", color="black", weight=3]; 25187[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (LT == GT))",fontsize=16,color="black",shape="box"];25187 -> 25222[label="",style="solid", color="black", weight=3]; 25188[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) (EQ == GT))",fontsize=16,color="black",shape="box"];25188 -> 25223[label="",style="solid", color="black", weight=3]; 18288 -> 18195[label="",style="dashed", color="red", weight=0]; 18288[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz1472)) ywz1473 ywz1474 ywz1475 ywz1476) (Neg (Succ ywz1477)) ywz1478 ywz1479 ywz1478 ywz1479 (Just ywz1481)",fontsize=16,color="magenta"];21691[label="ywz1790",fontsize=16,color="green",shape="box"];21692[label="ywz1787",fontsize=16,color="green",shape="box"];25215 -> 25021[label="",style="dashed", color="red", weight=0]; 25215[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (primCmpNat ywz24490 ywz24500 == GT))",fontsize=16,color="magenta"];25215 -> 25233[label="",style="dashed", color="magenta", weight=3]; 25215 -> 25234[label="",style="dashed", color="magenta", weight=3]; 25216[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (GT == GT))",fontsize=16,color="black",shape="box"];25216 -> 25235[label="",style="solid", color="black", weight=3]; 25217[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (LT == GT))",fontsize=16,color="black",shape="box"];25217 -> 25236[label="",style="solid", color="black", weight=3]; 25218[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM1 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) (EQ == GT))",fontsize=16,color="black",shape="box"];25218 -> 25237[label="",style="solid", color="black", weight=3]; 21698 -> 21591[label="",style="dashed", color="red", weight=0]; 21698[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz1782 ywz1783 ywz1784 ywz1785) (Neg (Succ ywz1786)) ywz1787 ywz1788 ywz1787 ywz1788 (Just ywz1790)",fontsize=16,color="magenta"];23243[label="ywz2006",fontsize=16,color="green",shape="box"];23244[label="ywz2003",fontsize=16,color="green",shape="box"];25313[label="ywz2384",fontsize=16,color="green",shape="box"];25314[label="ywz2381",fontsize=16,color="green",shape="box"];2687[label="primPlusNat (Succ (Succ (primPlusNat (primPlusNat (Succ ywz72000) (Succ ywz72000)) ywz72000))) ywz72000",fontsize=16,color="burlywood",shape="box"];25781[label="ywz72000/Succ ywz720000",fontsize=10,color="white",style="solid",shape="box"];2687 -> 25781[label="",style="solid", color="burlywood", weight=9]; 25781 -> 2951[label="",style="solid", color="burlywood", weight=3]; 25782[label="ywz72000/Zero",fontsize=10,color="white",style="solid",shape="box"];2687 -> 25782[label="",style="solid", color="burlywood", weight=9]; 25782 -> 2952[label="",style="solid", color="burlywood", weight=3]; 2688[label="Succ (primPlusNat Zero Zero)",fontsize=16,color="green",shape="box"];2688 -> 2953[label="",style="dashed", color="green", weight=3]; 15092[label="primMulInt (Pos (Succ (Succ Zero))) (Pos ywz12090)",fontsize=16,color="black",shape="box"];15092 -> 15145[label="",style="solid", color="black", weight=3]; 15093[label="primMulInt (Pos (Succ (Succ Zero))) (Neg ywz12090)",fontsize=16,color="black",shape="box"];15093 -> 15146[label="",style="solid", color="black", weight=3]; 15129[label="FiniteMap.mkBalBranch6Double_L ywz1007 ywz73 ywz70 ywz71 ywz73 (FiniteMap.Branch ywz10060 ywz10061 ywz10062 ywz10063 ywz10064)",fontsize=16,color="burlywood",shape="box"];25783[label="ywz10063/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];15129 -> 25783[label="",style="solid", color="burlywood", weight=9]; 25783 -> 15173[label="",style="solid", color="burlywood", weight=3]; 25784[label="ywz10063/FiniteMap.Branch ywz100630 ywz100631 ywz100632 ywz100633 ywz100634",fontsize=10,color="white",style="solid",shape="box"];15129 -> 25784[label="",style="solid", color="burlywood", weight=9]; 25784 -> 15174[label="",style="solid", color="burlywood", weight=3]; 15408[label="ywz10060",fontsize=16,color="green",shape="box"];15409[label="ywz10061",fontsize=16,color="green",shape="box"];15410[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];15411 -> 15392[label="",style="dashed", color="red", weight=0]; 15411[label="FiniteMap.mkBranch (Pos (Succ 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color="red", weight=0]; 15141[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (LT == GT)",fontsize=16,color="magenta"];15142 -> 15135[label="",style="dashed", color="red", weight=0]; 15142[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (EQ == GT)",fontsize=16,color="magenta"];15143 -> 15080[label="",style="dashed", color="red", weight=0]; 15143[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz118300) Zero == GT)",fontsize=16,color="magenta"];15143 -> 15188[label="",style="dashed", color="magenta", weight=3]; 15143 -> 15189[label="",style="dashed", color="magenta", weight=3]; 15144 -> 15135[label="",style="dashed", color="red", weight=0]; 15144[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (EQ == 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25175[label="",style="solid", color="black", weight=3]; 25017[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) False)",fontsize=16,color="black",shape="triangle"];25017 -> 25176[label="",style="solid", color="black", weight=3]; 25018 -> 25017[label="",style="dashed", color="red", weight=0]; 25018[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM1 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) False)",fontsize=16,color="magenta"];25189[label="ywz24180",fontsize=16,color="green",shape="box"];25190[label="ywz24190",fontsize=16,color="green",shape="box"];25191[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 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25219[label="ywz24350",fontsize=16,color="green",shape="box"];25220[label="ywz24340",fontsize=16,color="green",shape="box"];25221[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) True)",fontsize=16,color="black",shape="box"];25221 -> 25238[label="",style="solid", color="black", weight=3]; 25222[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 ywz2425) (Neg (Succ ywz2426)) ywz2427 ywz2428 ywz2427 ywz2428 (FiniteMap.lookupFM1 (Neg (Succ ywz2429)) ywz2430 ywz2431 ywz2432 ywz2433 (Neg (Succ ywz2426)) False)",fontsize=16,color="black",shape="triangle"];25222 -> 25239[label="",style="solid", color="black", weight=3]; 25223 -> 25222[label="",style="dashed", color="red", weight=0]; 25223[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg 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15455[label="ywz70",fontsize=16,color="green",shape="box"];15456[label="ywz71",fontsize=16,color="green",shape="box"];15457[label="Succ (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];15458[label="ywz73",fontsize=16,color="green",shape="box"];15459[label="ywz10063",fontsize=16,color="green",shape="box"];15179[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat ywz118400 ywz118300 == GT)",fontsize=16,color="burlywood",shape="triangle"];25785[label="ywz118400/Succ ywz1184000",fontsize=10,color="white",style="solid",shape="box"];15179 -> 25785[label="",style="solid", color="burlywood", weight=9]; 25785 -> 15215[label="",style="solid", color="burlywood", weight=3]; 25786[label="ywz118400/Zero",fontsize=10,color="white",style="solid",shape="box"];15179 -> 25786[label="",style="solid", color="burlywood", weight=9]; 25786 -> 15216[label="",style="solid", color="burlywood", weight=3]; 15180 -> 15081[label="",style="dashed", color="red", weight=0]; 15180[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (GT == GT)",fontsize=16,color="magenta"];15181[label="FiniteMap.mkBalBranch6MkBalBranch1 ywz1007 ywz73 ywz70 ywz71 ywz73 ywz1006 ywz73",fontsize=16,color="burlywood",shape="box"];25787[label="ywz73/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];15181 -> 25787[label="",style="solid", color="burlywood", weight=9]; 25787 -> 15217[label="",style="solid", color="burlywood", weight=3]; 25788[label="ywz73/FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734",fontsize=10,color="white",style="solid",shape="box"];15181 -> 25788[label="",style="solid", color="burlywood", weight=9]; 25788 -> 15218[label="",style="solid", color="burlywood", weight=3]; 15182[label="ywz118300",fontsize=16,color="green",shape="box"];15183[label="Zero",fontsize=16,color="green",shape="box"];15184 -> 15138[label="",style="dashed", color="red", weight=0]; 15184[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 False",fontsize=16,color="magenta"];15185[label="FiniteMap.mkBalBranch6MkBalBranch2 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 otherwise",fontsize=16,color="black",shape="box"];15185 -> 15219[label="",style="solid", color="black", weight=3]; 15186 -> 15179[label="",style="dashed", color="red", weight=0]; 15186[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat ywz118300 ywz118400 == GT)",fontsize=16,color="magenta"];15186 -> 15220[label="",style="dashed", color="magenta", weight=3]; 15186 -> 15221[label="",style="dashed", color="magenta", weight=3]; 15187 -> 15086[label="",style="dashed", color="red", weight=0]; 15187[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (LT == 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weight=3]; 25175 -> 25202[label="",style="dashed", color="magenta", weight=3]; 25176[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM0 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) otherwise)",fontsize=16,color="black",shape="box"];25176 -> 25203[label="",style="solid", color="black", weight=3]; 25224 -> 21663[label="",style="dashed", color="red", weight=0]; 25224[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM ywz2417 (Pos (Succ ywz2410)))",fontsize=16,color="magenta"];25224 -> 25240[label="",style="dashed", color="magenta", weight=3]; 25224 -> 25241[label="",style="dashed", color="magenta", weight=3]; 25224 -> 25242[label="",style="dashed", color="magenta", weight=3]; 25224 -> 25243[label="",style="dashed", color="magenta", weight=3]; 25224 -> 25244[label="",style="dashed", color="magenta", weight=3]; 25224 -> 25245[label="",style="dashed", color="magenta", weight=3]; 25224 -> 25246[label="",style="dashed", color="magenta", weight=3]; 25224 -> 25247[label="",style="dashed", color="magenta", weight=3]; 25225[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM0 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) otherwise)",fontsize=16,color="black",shape="box"];25225 -> 25248[label="",style="solid", color="black", weight=3]; 24703[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg ywz2306) ywz2307 ywz2308 ywz2309 ywz2310) (Pos (Succ ywz2311)) ywz2312 ywz2313 ywz2312 ywz2313 (Just ywz2315)",fontsize=16,color="black",shape="box"];24703 -> 24853[label="",style="solid", color="black", weight=3]; 23324 -> 20052[label="",style="dashed", color="red", weight=0]; 23324[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos ywz2090) ywz2091 ywz2092 ywz2093 ywz2094) (Neg (Succ ywz2095)) ywz2096 ywz2097 ywz2096 ywz2097 (Just ywz2099)",fontsize=16,color="magenta"];23324 -> 23351[label="",style="dashed", color="magenta", weight=3]; 23324 -> 23352[label="",style="dashed", color="magenta", weight=3]; 23324 -> 23353[label="",style="dashed", color="magenta", weight=3]; 23324 -> 23354[label="",style="dashed", color="magenta", weight=3]; 23324 -> 23355[label="",style="dashed", color="magenta", weight=3]; 23324 -> 23356[label="",style="dashed", color="magenta", weight=3]; 23324 -> 23357[label="",style="dashed", color="magenta", weight=3]; 23324 -> 23358[label="",style="dashed", color="magenta", weight=3]; 23324 -> 23359[label="",style="dashed", color="magenta", weight=3]; 25238 -> 18059[label="",style="dashed", color="red", weight=0]; 25238[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg (Succ ywz2421)) ywz2422 ywz2423 ywz2424 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25255[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (FiniteMap.lookupFM0 (Neg (Succ ywz2444)) ywz2445 ywz2446 ywz2447 ywz2448 (Neg (Succ ywz2441)) otherwise)",fontsize=16,color="black",shape="box"];25255 -> 25281[label="",style="solid", color="black", weight=3]; 3374[label="Succ (Succ (primPlusNat (Succ (primPlusNat (primPlusNat (Succ (Succ ywz720000)) (Succ (Succ ywz720000))) (Succ ywz720000))) ywz720000))",fontsize=16,color="green",shape="box"];3374 -> 3771[label="",style="dashed", color="green", weight=3]; 3375[label="Succ (Succ (primPlusNat (primPlusNat (Succ Zero) (Succ Zero)) Zero))",fontsize=16,color="green",shape="box"];3375 -> 3772[label="",style="dashed", color="green", weight=3]; 3376[label="Zero",fontsize=16,color="green",shape="box"];15190[label="primMulNat (Succ (Succ Zero)) ywz12090",fontsize=16,color="burlywood",shape="triangle"];25789[label="ywz12090/Succ 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color="burlywood", weight=9]; 25792 -> 15274[label="",style="solid", color="burlywood", weight=3]; 15216[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat Zero ywz118300 == GT)",fontsize=16,color="burlywood",shape="box"];25793[label="ywz118300/Succ ywz1183000",fontsize=10,color="white",style="solid",shape="box"];15216 -> 25793[label="",style="solid", color="burlywood", weight=9]; 25793 -> 15275[label="",style="solid", color="burlywood", weight=3]; 25794[label="ywz118300/Zero",fontsize=10,color="white",style="solid",shape="box"];15216 -> 25794[label="",style="solid", color="burlywood", weight=9]; 25794 -> 15276[label="",style="solid", color="burlywood", weight=3]; 15217[label="FiniteMap.mkBalBranch6MkBalBranch1 ywz1007 FiniteMap.EmptyFM ywz70 ywz71 FiniteMap.EmptyFM ywz1006 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];15217 -> 15277[label="",style="solid", color="black", weight=3]; 15218[label="FiniteMap.mkBalBranch6MkBalBranch1 ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz1006 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734)",fontsize=16,color="black",shape="box"];15218 -> 15278[label="",style="solid", color="black", weight=3]; 15219[label="FiniteMap.mkBalBranch6MkBalBranch2 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 True",fontsize=16,color="black",shape="box"];15219 -> 15279[label="",style="solid", color="black", weight=3]; 15220[label="ywz118300",fontsize=16,color="green",shape="box"];15221[label="ywz118400",fontsize=16,color="green",shape="box"];25194[label="ywz2401",fontsize=16,color="green",shape="box"];25195[label="ywz2391",fontsize=16,color="green",shape="box"];25196[label="ywz2393",fontsize=16,color="green",shape="box"];25197[label="ywz2392",fontsize=16,color="green",shape="box"];25198[label="ywz2390",fontsize=16,color="green",shape="box"];25199[label="ywz2394",fontsize=16,color="green",shape="box"];25200[label="ywz2395",fontsize=16,color="green",shape="box"];25201[label="ywz2396",fontsize=16,color="green",shape="box"];25202[label="ywz2389",fontsize=16,color="green",shape="box"];25203[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (FiniteMap.lookupFM0 (Pos (Succ ywz2397)) ywz2398 ywz2399 ywz2400 ywz2401 (Pos (Succ ywz2394)) True)",fontsize=16,color="black",shape="box"];25203 -> 25226[label="",style="solid", color="black", weight=3]; 25240[label="ywz2407",fontsize=16,color="green",shape="box"];25241[label="ywz2417",fontsize=16,color="green",shape="box"];25242[label="ywz2409",fontsize=16,color="green",shape="box"];25243[label="ywz2411",fontsize=16,color="green",shape="box"];25244[label="ywz2406",fontsize=16,color="green",shape="box"];25245[label="ywz2410",fontsize=16,color="green",shape="box"];25246[label="ywz2412",fontsize=16,color="green",shape="box"];25247[label="ywz2408",fontsize=16,color="green",shape="box"];25248[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 ywz2408 ywz2409) (Pos (Succ ywz2410)) ywz2411 ywz2412 ywz2411 ywz2412 (FiniteMap.lookupFM0 (Pos (Succ ywz2413)) ywz2414 ywz2415 ywz2416 ywz2417 (Pos (Succ ywz2410)) True)",fontsize=16,color="black",shape="box"];25248 -> 25266[label="",style="solid", color="black", weight=3]; 24853[label="ywz2313 ywz2315 ywz2312",fontsize=16,color="green",shape="box"];24853 -> 25019[label="",style="dashed", color="green", weight=3]; 24853 -> 25020[label="",style="dashed", color="green", weight=3]; 23351[label="ywz2091",fontsize=16,color="green",shape="box"];23352[label="ywz2090",fontsize=16,color="green",shape="box"];23353[label="ywz2097",fontsize=16,color="green",shape="box"];23354[label="ywz2096",fontsize=16,color="green",shape="box"];23355[label="ywz2099",fontsize=16,color="green",shape="box"];23356[label="ywz2092",fontsize=16,color="green",shape="box"];23357[label="ywz2094",fontsize=16,color="green",shape="box"];23358[label="ywz2093",fontsize=16,color="green",shape="box"];23359[label="ywz2095",fontsize=16,color="green",shape="box"];25256[label="ywz2423",fontsize=16,color="green",shape="box"];25257[label="ywz2421",fontsize=16,color="green",shape="box"];25258[label="ywz2425",fontsize=16,color="green",shape="box"];25259[label="ywz2428",fontsize=16,color="green",shape="box"];25260[label="ywz2424",fontsize=16,color="green",shape="box"];25261[label="ywz2427",fontsize=16,color="green",shape="box"];25262[label="ywz2433",fontsize=16,color="green",shape="box"];25263[label="ywz2426",fontsize=16,color="green",shape="box"];25264[label="ywz2422",fontsize=16,color="green",shape="box"];25265[label="FiniteMap.plusFM_CNew_elt0 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15463[label="",style="dashed", color="magenta", weight=3]; 15421 -> 15464[label="",style="dashed", color="magenta", weight=3]; 15422 -> 15392[label="",style="dashed", color="red", weight=0]; 15422[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ywz10060 ywz10061 ywz100634 ywz10064",fontsize=16,color="magenta"];15422 -> 15465[label="",style="dashed", color="magenta", weight=3]; 15422 -> 15466[label="",style="dashed", color="magenta", weight=3]; 15422 -> 15467[label="",style="dashed", color="magenta", weight=3]; 15422 -> 15468[label="",style="dashed", color="magenta", weight=3]; 15422 -> 15469[label="",style="dashed", color="magenta", weight=3]; 15273[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat (Succ ywz1184000) (Succ ywz1183000) == GT)",fontsize=16,color="black",shape="box"];15273 -> 15321[label="",style="solid", color="black", weight=3]; 15274[label="FiniteMap.mkBalBranch6MkBalBranch3 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ywz734)",fontsize=16,color="black",shape="box"];15278 -> 15325[label="",style="solid", color="black", weight=3]; 15279 -> 15392[label="",style="dashed", color="red", weight=0]; 15279[label="FiniteMap.mkBranch (Pos (Succ (Succ Zero))) ywz70 ywz71 ywz73 ywz1006",fontsize=16,color="magenta"];15279 -> 15423[label="",style="dashed", color="magenta", weight=3]; 15279 -> 15424[label="",style="dashed", color="magenta", weight=3]; 15279 -> 15425[label="",style="dashed", color="magenta", weight=3]; 15279 -> 15426[label="",style="dashed", color="magenta", weight=3]; 15279 -> 15427[label="",style="dashed", color="magenta", weight=3]; 25226[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos (Succ ywz2389)) ywz2390 ywz2391 ywz2392 ywz2393) (Pos (Succ ywz2394)) ywz2395 ywz2396 ywz2395 ywz2396 (Just ywz2398)",fontsize=16,color="black",shape="box"];25226 -> 25249[label="",style="solid", color="black", weight=3]; 25266[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Pos Zero) ywz2406 ywz2407 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-> 25295[label="",style="dashed", color="magenta", weight=3]; 25282 -> 25296[label="",style="dashed", color="magenta", weight=3]; 25282 -> 25297[label="",style="dashed", color="magenta", weight=3]; 25288 -> 21591[label="",style="dashed", color="red", weight=0]; 25288[label="FiniteMap.plusFM_CNew_elt0 (FiniteMap.Branch (Neg Zero) ywz2437 ywz2438 ywz2439 ywz2440) (Neg (Succ ywz2441)) ywz2442 ywz2443 ywz2442 ywz2443 (Just ywz2445)",fontsize=16,color="magenta"];25288 -> 25304[label="",style="dashed", color="magenta", weight=3]; 25288 -> 25305[label="",style="dashed", color="magenta", weight=3]; 25288 -> 25306[label="",style="dashed", color="magenta", weight=3]; 25288 -> 25307[label="",style="dashed", color="magenta", weight=3]; 25288 -> 25308[label="",style="dashed", color="magenta", weight=3]; 25288 -> 25309[label="",style="dashed", color="magenta", weight=3]; 25288 -> 25310[label="",style="dashed", color="magenta", weight=3]; 25288 -> 25311[label="",style="dashed", color="magenta", weight=3]; 4182[label="primPlusNat (Succ (primPlusNat (primPlusNat (Succ (Succ (Succ ywz7200000))) (Succ (Succ (Succ ywz7200000)))) (Succ (Succ ywz7200000)))) (Succ ywz7200000)",fontsize=16,color="black",shape="box"];4182 -> 4714[label="",style="solid", color="black", weight=3]; 4183[label="primPlusNat (Succ (primPlusNat (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero))) (Succ Zero))) Zero",fontsize=16,color="black",shape="box"];4183 -> 4715[label="",style="solid", color="black", weight=3]; 4184 -> 4716[label="",style="dashed", color="red", weight=0]; 4184[label="primPlusNat (Succ (Succ (primPlusNat Zero Zero))) Zero",fontsize=16,color="magenta"];4184 -> 4717[label="",style="dashed", color="magenta", weight=3]; 15280 -> 5537[label="",style="dashed", color="red", weight=0]; 15280[label="primPlusNat (primMulNat (Succ Zero) (Succ ywz120900)) (Succ ywz120900)",fontsize=16,color="magenta"];15280 -> 15327[label="",style="dashed", color="magenta", weight=3]; 15280 -> 15328[label="",style="dashed", color="magenta", weight=3]; 15281[label="Zero",fontsize=16,color="green",shape="box"];15460[label="ywz70",fontsize=16,color="green",shape="box"];15461[label="ywz71",fontsize=16,color="green",shape="box"];15462[label="Succ (Succ (Succ (Succ (Succ Zero))))",fontsize=16,color="green",shape="box"];15463[label="ywz73",fontsize=16,color="green",shape="box"];15464[label="ywz100633",fontsize=16,color="green",shape="box"];15465[label="ywz10060",fontsize=16,color="green",shape="box"];15466[label="ywz10061",fontsize=16,color="green",shape="box"];15467[label="Succ (Succ (Succ (Succ (Succ (Succ Zero)))))",fontsize=16,color="green",shape="box"];15468[label="ywz100634",fontsize=16,color="green",shape="box"];15469[label="ywz10064",fontsize=16,color="green",shape="box"];15321 -> 15179[label="",style="dashed", color="red", weight=0]; 15321[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (primCmpNat ywz1184000 ywz1183000 == GT)",fontsize=16,color="magenta"];15321 -> 15470[label="",style="dashed", color="magenta", weight=3]; 15321 -> 15471[label="",style="dashed", color="magenta", weight=3]; 15322 -> 15081[label="",style="dashed", color="red", weight=0]; 15322[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (GT == GT)",fontsize=16,color="magenta"];15323 -> 15086[label="",style="dashed", color="red", weight=0]; 15323[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (LT == GT)",fontsize=16,color="magenta"];15324 -> 15135[label="",style="dashed", color="red", weight=0]; 15324[label="FiniteMap.mkBalBranch6MkBalBranch3 ywz1007 ywz73 ywz70 ywz71 ywz70 ywz71 ywz73 ywz1006 (EQ == GT)",fontsize=16,color="magenta"];15325 -> 15472[label="",style="dashed", color="red", weight=0]; 15325[label="FiniteMap.mkBalBranch6MkBalBranch11 ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz1006 ywz730 ywz731 ywz732 ywz733 ywz734 (FiniteMap.sizeFM ywz734 < Pos (Succ (Succ Zero)) * FiniteMap.sizeFM ywz733)",fontsize=16,color="magenta"];15325 -> 15473[label="",style="dashed", color="magenta", weight=3]; 15423[label="ywz70",fontsize=16,color="green",shape="box"];15424[label="ywz71",fontsize=16,color="green",shape="box"];15425[label="Succ Zero",fontsize=16,color="green",shape="box"];15426[label="ywz73",fontsize=16,color="green",shape="box"];15427[label="ywz1006",fontsize=16,color="green",shape="box"];25249[label="ywz2396 ywz2398 ywz2395",fontsize=16,color="green",shape="box"];25249 -> 25267[label="",style="dashed", color="green", weight=3]; 25249 -> 25268[label="",style="dashed", color="green", weight=3]; 25283[label="ywz2412 ywz2414 ywz2411",fontsize=16,color="green",shape="box"];25283 -> 25298[label="",style="dashed", color="green", weight=3]; 25283 -> 25299[label="",style="dashed", color="green", weight=3]; 25289[label="ywz2423",fontsize=16,color="green",shape="box"];25290[label="ywz2421",fontsize=16,color="green",shape="box"];25291[label="ywz2425",fontsize=16,color="green",shape="box"];25292[label="ywz2428",fontsize=16,color="green",shape="box"];25293[label="ywz2424",fontsize=16,color="green",shape="box"];25294[label="ywz2427",fontsize=16,color="green",shape="box"];25295[label="ywz2430",fontsize=16,color="green",shape="box"];25296[label="ywz2426",fontsize=16,color="green",shape="box"];25297[label="ywz2422",fontsize=16,color="green",shape="box"];25304[label="ywz2438",fontsize=16,color="green",shape="box"];25305[label="ywz2443",fontsize=16,color="green",shape="box"];25306[label="ywz2441",fontsize=16,color="green",shape="box"];25307[label="ywz2437",fontsize=16,color="green",shape="box"];25308[label="ywz2440",fontsize=16,color="green",shape="box"];25309[label="ywz2442",fontsize=16,color="green",shape="box"];25310[label="ywz2439",fontsize=16,color="green",shape="box"];25311[label="ywz2445",fontsize=16,color="green",shape="box"];4714[label="Succ (Succ (primPlusNat (primPlusNat (primPlusNat (Succ (Succ (Succ ywz7200000))) (Succ (Succ (Succ ywz7200000)))) (Succ (Succ ywz7200000))) ywz7200000))",fontsize=16,color="green",shape="box"];4714 -> 5150[label="",style="dashed", color="green", weight=3]; 4715[label="Succ (primPlusNat (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero))) (Succ Zero))",fontsize=16,color="green",shape="box"];4715 -> 5151[label="",style="dashed", color="green", weight=3]; 4717 -> 2953[label="",style="dashed", color="red", weight=0]; 4717[label="primPlusNat Zero Zero",fontsize=16,color="magenta"];4716[label="primPlusNat (Succ (Succ ywz302)) Zero",fontsize=16,color="black",shape="triangle"];4716 -> 5152[label="",style="solid", color="black", weight=3]; 15327[label="primMulNat (Succ Zero) (Succ ywz120900)",fontsize=16,color="black",shape="box"];15327 -> 15501[label="",style="solid", color="black", weight=3]; 15328[label="Succ ywz120900",fontsize=16,color="green",shape="box"];15470[label="ywz1184000",fontsize=16,color="green",shape="box"];15471[label="ywz1183000",fontsize=16,color="green",shape="box"];15473 -> 10999[label="",style="dashed", color="red", weight=0]; 15473[label="FiniteMap.sizeFM ywz734 < Pos (Succ (Succ Zero)) * FiniteMap.sizeFM ywz733",fontsize=16,color="magenta"];15473 -> 15502[label="",style="dashed", color="magenta", weight=3]; 15473 -> 15503[label="",style="dashed", color="magenta", weight=3]; 15472[label="FiniteMap.mkBalBranch6MkBalBranch11 ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz1006 ywz730 ywz731 ywz732 ywz733 ywz734 ywz1239",fontsize=16,color="burlywood",shape="triangle"];25797[label="ywz1239/False",fontsize=10,color="white",style="solid",shape="box"];15472 -> 25797[label="",style="solid", color="burlywood", weight=9]; 25797 -> 15504[label="",style="solid", color="burlywood", weight=3]; 25798[label="ywz1239/True",fontsize=10,color="white",style="solid",shape="box"];15472 -> 25798[label="",style="solid", color="burlywood", weight=9]; 25798 -> 15505[label="",style="solid", color="burlywood", weight=3]; 25267[label="ywz2398",fontsize=16,color="green",shape="box"];25268[label="ywz2395",fontsize=16,color="green",shape="box"];25298[label="ywz2414",fontsize=16,color="green",shape="box"];25299[label="ywz2411",fontsize=16,color="green",shape="box"];5150 -> 5537[label="",style="dashed", color="red", weight=0]; 5150[label="primPlusNat (primPlusNat (primPlusNat (Succ (Succ (Succ ywz7200000))) (Succ (Succ (Succ ywz7200000)))) (Succ (Succ ywz7200000))) ywz7200000",fontsize=16,color="magenta"];5150 -> 5839[label="",style="dashed", color="magenta", weight=3]; 5150 -> 5840[label="",style="dashed", color="magenta", weight=3]; 5151 -> 5537[label="",style="dashed", color="red", weight=0]; 5151[label="primPlusNat (primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero))) (Succ Zero)",fontsize=16,color="magenta"];5151 -> 5841[label="",style="dashed", color="magenta", weight=3]; 5151 -> 5842[label="",style="dashed", color="magenta", weight=3]; 5152[label="Succ (Succ ywz302)",fontsize=16,color="green",shape="box"];15501 -> 5537[label="",style="dashed", color="red", weight=0]; 15501[label="primPlusNat (primMulNat Zero (Succ ywz120900)) (Succ ywz120900)",fontsize=16,color="magenta"];15501 -> 15562[label="",style="dashed", color="magenta", weight=3]; 15501 -> 15563[label="",style="dashed", color="magenta", weight=3]; 15502 -> 3313[label="",style="dashed", color="red", weight=0]; 15502[label="FiniteMap.sizeFM ywz734",fontsize=16,color="magenta"];15502 -> 15564[label="",style="dashed", color="magenta", weight=3]; 15503 -> 15017[label="",style="dashed", color="red", weight=0]; 15503[label="Pos (Succ (Succ Zero)) * FiniteMap.sizeFM ywz733",fontsize=16,color="magenta"];15503 -> 15565[label="",style="dashed", color="magenta", weight=3]; 15504[label="FiniteMap.mkBalBranch6MkBalBranch11 ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz1006 ywz730 ywz731 ywz732 ywz733 ywz734 False",fontsize=16,color="black",shape="box"];15504 -> 15566[label="",style="solid", color="black", weight=3]; 15505[label="FiniteMap.mkBalBranch6MkBalBranch11 ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz1006 ywz730 ywz731 ywz732 ywz733 ywz734 True",fontsize=16,color="black",shape="box"];15505 -> 15567[label="",style="solid", color="black", weight=3]; 5839 -> 5537[label="",style="dashed", color="red", weight=0]; 5839[label="primPlusNat (primPlusNat (Succ (Succ (Succ ywz7200000))) (Succ (Succ (Succ ywz7200000)))) (Succ (Succ ywz7200000))",fontsize=16,color="magenta"];5839 -> 6765[label="",style="dashed", color="magenta", weight=3]; 5839 -> 6766[label="",style="dashed", color="magenta", weight=3]; 5840[label="ywz7200000",fontsize=16,color="green",shape="box"];5841 -> 5537[label="",style="dashed", color="red", weight=0]; 5841[label="primPlusNat (Succ (Succ Zero)) (Succ (Succ Zero))",fontsize=16,color="magenta"];5841 -> 6767[label="",style="dashed", color="magenta", weight=3]; 5841 -> 6768[label="",style="dashed", color="magenta", weight=3]; 5842[label="Succ Zero",fontsize=16,color="green",shape="box"];15562[label="primMulNat Zero (Succ ywz120900)",fontsize=16,color="black",shape="box"];15562 -> 15602[label="",style="solid", color="black", weight=3]; 15563[label="Succ ywz120900",fontsize=16,color="green",shape="box"];15564[label="ywz734",fontsize=16,color="green",shape="box"];15565 -> 3313[label="",style="dashed", color="red", weight=0]; 15565[label="FiniteMap.sizeFM ywz733",fontsize=16,color="magenta"];15565 -> 15603[label="",style="dashed", color="magenta", weight=3]; 15566[label="FiniteMap.mkBalBranch6MkBalBranch10 ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz1006 ywz730 ywz731 ywz732 ywz733 ywz734 otherwise",fontsize=16,color="black",shape="box"];15566 -> 15604[label="",style="solid", color="black", weight=3]; 15567[label="FiniteMap.mkBalBranch6Single_R ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz1006",fontsize=16,color="black",shape="box"];15567 -> 15605[label="",style="solid", color="black", weight=3]; 6765 -> 5537[label="",style="dashed", color="red", weight=0]; 6765[label="primPlusNat (Succ (Succ (Succ ywz7200000))) (Succ (Succ (Succ ywz7200000)))",fontsize=16,color="magenta"];6765 -> 7398[label="",style="dashed", color="magenta", weight=3]; 6765 -> 7399[label="",style="dashed", color="magenta", weight=3]; 6766[label="Succ (Succ ywz7200000)",fontsize=16,color="green",shape="box"];6767[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];6768[label="Succ (Succ Zero)",fontsize=16,color="green",shape="box"];15602[label="Zero",fontsize=16,color="green",shape="box"];15603[label="ywz733",fontsize=16,color="green",shape="box"];15604[label="FiniteMap.mkBalBranch6MkBalBranch10 ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz1006 ywz730 ywz731 ywz732 ywz733 ywz734 True",fontsize=16,color="black",shape="box"];15604 -> 15654[label="",style="solid", color="black", weight=3]; 15605 -> 15392[label="",style="dashed", color="red", weight=0]; 15605[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) ywz730 ywz731 ywz733 (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) ywz70 ywz71 ywz734 ywz1006)",fontsize=16,color="magenta"];15605 -> 15655[label="",style="dashed", color="magenta", weight=3]; 15605 -> 15656[label="",style="dashed", color="magenta", weight=3]; 15605 -> 15657[label="",style="dashed", color="magenta", weight=3]; 15605 -> 15658[label="",style="dashed", color="magenta", weight=3]; 15605 -> 15659[label="",style="dashed", color="magenta", weight=3]; 7398[label="Succ (Succ (Succ ywz7200000))",fontsize=16,color="green",shape="box"];7399[label="Succ (Succ (Succ ywz7200000))",fontsize=16,color="green",shape="box"];15654[label="FiniteMap.mkBalBranch6Double_R ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 ywz734) ywz1006",fontsize=16,color="burlywood",shape="box"];25799[label="ywz734/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];15654 -> 25799[label="",style="solid", color="burlywood", weight=9]; 25799 -> 15691[label="",style="solid", color="burlywood", weight=3]; 25800[label="ywz734/FiniteMap.Branch ywz7340 ywz7341 ywz7342 ywz7343 ywz7344",fontsize=10,color="white",style="solid",shape="box"];15654 -> 25800[label="",style="solid", color="burlywood", weight=9]; 25800 -> 15692[label="",style="solid", color="burlywood", weight=3]; 15655[label="ywz730",fontsize=16,color="green",shape="box"];15656[label="ywz731",fontsize=16,color="green",shape="box"];15657[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))",fontsize=16,color="green",shape="box"];15658[label="ywz733",fontsize=16,color="green",shape="box"];15659 -> 15392[label="",style="dashed", color="red", weight=0]; 15659[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) ywz70 ywz71 ywz734 ywz1006",fontsize=16,color="magenta"];15659 -> 15693[label="",style="dashed", color="magenta", weight=3]; 15659 -> 15694[label="",style="dashed", color="magenta", weight=3]; 15659 -> 15695[label="",style="dashed", color="magenta", weight=3]; 15659 -> 15696[label="",style="dashed", color="magenta", weight=3]; 15659 -> 15697[label="",style="dashed", color="magenta", weight=3]; 15691[label="FiniteMap.mkBalBranch6Double_R ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 FiniteMap.EmptyFM) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 FiniteMap.EmptyFM) ywz1006",fontsize=16,color="black",shape="box"];15691 -> 15751[label="",style="solid", color="black", weight=3]; 15692[label="FiniteMap.mkBalBranch6Double_R ywz1007 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 (FiniteMap.Branch ywz7340 ywz7341 ywz7342 ywz7343 ywz7344)) ywz70 ywz71 (FiniteMap.Branch ywz730 ywz731 ywz732 ywz733 (FiniteMap.Branch ywz7340 ywz7341 ywz7342 ywz7343 ywz7344)) ywz1006",fontsize=16,color="black",shape="box"];15692 -> 15752[label="",style="solid", color="black", weight=3]; 15693[label="ywz70",fontsize=16,color="green",shape="box"];15694[label="ywz71",fontsize=16,color="green",shape="box"];15695[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))",fontsize=16,color="green",shape="box"];15696[label="ywz734",fontsize=16,color="green",shape="box"];15697[label="ywz1006",fontsize=16,color="green",shape="box"];15751[label="error []",fontsize=16,color="red",shape="box"];15752 -> 15392[label="",style="dashed", color="red", weight=0]; 15752[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ywz7340 ywz7341 (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) ywz730 ywz731 ywz733 ywz7343) (FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) ywz70 ywz71 ywz7344 ywz1006)",fontsize=16,color="magenta"];15752 -> 15777[label="",style="dashed", color="magenta", weight=3]; 15752 -> 15778[label="",style="dashed", color="magenta", weight=3]; 15752 -> 15779[label="",style="dashed", color="magenta", weight=3]; 15752 -> 15780[label="",style="dashed", color="magenta", weight=3]; 15752 -> 15781[label="",style="dashed", color="magenta", weight=3]; 15777[label="ywz7340",fontsize=16,color="green",shape="box"];15778[label="ywz7341",fontsize=16,color="green",shape="box"];15779[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];15780 -> 15392[label="",style="dashed", color="red", weight=0]; 15780[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) ywz730 ywz731 ywz733 ywz7343",fontsize=16,color="magenta"];15780 -> 16953[label="",style="dashed", color="magenta", weight=3]; 15780 -> 16954[label="",style="dashed", color="magenta", weight=3]; 15780 -> 16955[label="",style="dashed", color="magenta", weight=3]; 15780 -> 16956[label="",style="dashed", color="magenta", weight=3]; 15780 -> 16957[label="",style="dashed", color="magenta", weight=3]; 15781 -> 15392[label="",style="dashed", color="red", weight=0]; 15781[label="FiniteMap.mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) ywz70 ywz71 ywz7344 ywz1006",fontsize=16,color="magenta"];15781 -> 16958[label="",style="dashed", color="magenta", weight=3]; 15781 -> 16959[label="",style="dashed", color="magenta", weight=3]; 15781 -> 16960[label="",style="dashed", color="magenta", weight=3]; 15781 -> 16961[label="",style="dashed", color="magenta", weight=3]; 15781 -> 16962[label="",style="dashed", color="magenta", weight=3]; 16953[label="ywz730",fontsize=16,color="green",shape="box"];16954[label="ywz731",fontsize=16,color="green",shape="box"];16955[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))",fontsize=16,color="green",shape="box"];16956[label="ywz733",fontsize=16,color="green",shape="box"];16957[label="ywz7343",fontsize=16,color="green",shape="box"];16958[label="ywz70",fontsize=16,color="green",shape="box"];16959[label="ywz71",fontsize=16,color="green",shape="box"];16960[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="green",shape="box"];16961[label="ywz7344",fontsize=16,color="green",shape="box"];16962[label="ywz1006",fontsize=16,color="green",shape="box"];} ---------------------------------------- (16) Complex Obligation (AND) ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT4(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Neg(Zero), h) new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Zero), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Zero), h) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_lt(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> new_splitGT0(ywz43, h) new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_lt(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT0(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Zero), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Neg(Zero), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Neg(Zero), h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_lt(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_lt(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> new_splitGT4(ywz43, h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs. ---------------------------------------- (19) Complex Obligation (AND) ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> new_splitGT0(ywz43, h) new_splitGT0(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Zero), h) new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Zero), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Zero), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) 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_splitGT0(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Zero), h) The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 7 *new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Zero), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Zero), h) The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7 *new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> new_splitGT0(ywz43, h) The graph contains the following edges 4 >= 1, 7 >= 2 ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Neg(Zero), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Neg(Zero), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> new_splitGT4(ywz43, h) new_splitGT4(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Neg(Zero), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) 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_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Neg(Zero), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Neg(Zero), h) The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7 *new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> new_splitGT4(ywz43, h) The graph contains the following edges 4 >= 1, 7 >= 2 *new_splitGT4(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Neg(Zero), h) The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 7 ---------------------------------------- (25) YES ---------------------------------------- (26) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_lt(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_lt(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (27) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_lt(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc),new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc)) ---------------------------------------- (28) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_lt(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (29) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_lt(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc),new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc)) ---------------------------------------- (30) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (31) 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. ---------------------------------------- (32) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (33) 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_lt(x0, x1) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) ---------------------------------------- (34) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (35) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc),new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc)) ---------------------------------------- (36) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (37) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs0(Neg(Succ(ywz459)), Neg(Succ(ywz454))), bc) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc),new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc)) ---------------------------------------- (38) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (39) 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. ---------------------------------------- (40) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) The TRS R consists of the following rules: new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (41) 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_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) ---------------------------------------- (42) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) The TRS R consists of the following rules: new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (43) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc),new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc)) ---------------------------------------- (44) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc) The TRS R consists of the following rules: new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (45) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs3(Succ(ywz454), ywz459), bc) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc),new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc)) ---------------------------------------- (46) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc) The TRS R consists of the following rules: new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (47) 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. ---------------------------------------- (48) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc) The TRS R consists of the following rules: new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (49) 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_esEs3(Zero, x0) new_esEs3(Succ(x0), x1) ---------------------------------------- (50) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc) new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc) The TRS R consists of the following rules: new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (51) 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_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), bc) -> new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 *new_splitGT1(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 3 >= 7 *new_splitGT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7 *new_splitGT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 1 > 7, 6 > 8, 7 >= 9 *new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, bc) -> new_splitGT1(ywz458, ywz459, bc) The graph contains the following edges 5 >= 1, 6 >= 2, 9 >= 3 *new_splitGT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT1(ywz43, ywz5000, h) The graph contains the following edges 4 >= 1, 6 > 2, 7 >= 3 *new_splitGT11(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, bd) -> new_splitGT1(ywz1840, ywz1842, bd) The graph contains the following edges 4 >= 1, 6 >= 2, 8 >= 3 *new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 8 *new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), bc) -> new_splitGT11(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_esEs6(ywz454, ywz459), bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 8 *new_splitGT20(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, bc) -> new_splitGT22(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7 ---------------------------------------- (52) YES ---------------------------------------- (53) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_lt(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_lt(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (54) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_lt(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba),new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba)) ---------------------------------------- (55) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_lt(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (56) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_lt(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba),new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba)) ---------------------------------------- (57) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (58) 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. ---------------------------------------- (59) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (60) 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_lt(x0, x1) new_esEs3(Zero, x0) new_esEs3(Succ(x0), x1) ---------------------------------------- (61) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (62) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba),new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba)) ---------------------------------------- (63) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (64) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs0(Pos(Succ(ywz450)), Pos(Succ(ywz445))), ba) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba),new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba)) ---------------------------------------- (65) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (66) 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. ---------------------------------------- (67) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) The TRS R consists of the following rules: new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (68) 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_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) ---------------------------------------- (69) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) The TRS R consists of the following rules: new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (70) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba),new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba)) ---------------------------------------- (71) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba) The TRS R consists of the following rules: new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (72) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs1(ywz450, Succ(ywz445)), ba) at position [6] we obtained the following new rules [LPAR04]: (new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba),new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba)) ---------------------------------------- (73) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba) The TRS R consists of the following rules: new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (74) 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. ---------------------------------------- (75) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba) The TRS R consists of the following rules: new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (76) 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_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) ---------------------------------------- (77) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) new_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba) new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba) The TRS R consists of the following rules: new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs2 new_esEs4 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (78) 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_splitGT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 3 >= 7 *new_splitGT3(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT(ywz44, ywz5000, h) The graph contains the following edges 5 >= 1, 6 > 2, 7 >= 3 *new_splitGT3(Neg(ywz400), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_splitGT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7 *new_splitGT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 6 > 7, 1 > 8, 7 >= 9 *new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 8 *new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) -> new_splitGT10(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_esEs6(ywz450, ywz445), ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 8 *new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, ba) -> new_splitGT(ywz449, ywz450, ba) The graph contains the following edges 5 >= 1, 6 >= 2, 9 >= 3 *new_splitGT10(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bb) -> new_splitGT(ywz1830, ywz1832, bb) The graph contains the following edges 4 >= 1, 6 >= 2, 8 >= 3 *new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), ba) -> new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 *new_splitGT2(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, ba) -> new_splitGT21(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7 ---------------------------------------- (79) YES ---------------------------------------- (80) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Zero, ba) -> new_plusFM_CNew_elt021(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2417, ba) new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_lt(Pos(Succ(ywz1877)), ywz18830), h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Zero), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Neg(ywz18800), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Succ(ywz24190), ba) -> new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, ywz24180, ywz24190, ba) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Succ(ywz188000)), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt020(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz188000, ywz1881, ywz1882, ywz1883, ywz1884, ywz1877, ywz188000, h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1880, ywz1881, ywz1882, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), ywz1884, True, h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_lt(Pos(Succ(ywz1877)), ywz18830), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (81) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_lt(Pos(Succ(ywz1877)), ywz18830), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h),new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h)) ---------------------------------------- (82) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Zero, ba) -> new_plusFM_CNew_elt021(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2417, ba) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Zero), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Neg(ywz18800), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Succ(ywz24190), ba) -> new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, ywz24180, ywz24190, ba) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Succ(ywz188000)), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt020(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz188000, ywz1881, ywz1882, ywz1883, ywz1884, ywz1877, ywz188000, h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1880, ywz1881, ywz1882, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), ywz1884, True, h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_lt(Pos(Succ(ywz1877)), ywz18830), h) new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (83) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1880, ywz1881, ywz1882, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), ywz1884, True, h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_lt(Pos(Succ(ywz1877)), ywz18830), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1880, ywz1881, ywz1882, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), ywz1884, True, h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h),new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1880, ywz1881, ywz1882, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), ywz1884, True, h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h)) ---------------------------------------- (84) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Zero, ba) -> new_plusFM_CNew_elt021(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2417, ba) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Zero), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Neg(ywz18800), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Succ(ywz24190), ba) -> new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, ywz24180, ywz24190, ba) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Succ(ywz188000)), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt020(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz188000, ywz1881, ywz1882, ywz1883, ywz1884, ywz1877, ywz188000, h) new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1880, ywz1881, ywz1882, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), ywz1884, True, h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (85) 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. ---------------------------------------- (86) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Zero, ba) -> new_plusFM_CNew_elt021(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2417, ba) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Zero), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Neg(ywz18800), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Succ(ywz24190), ba) -> new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, ywz24180, ywz24190, ba) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Succ(ywz188000)), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt020(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz188000, ywz1881, ywz1882, ywz1883, ywz1884, ywz1877, ywz188000, h) new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1880, ywz1881, ywz1882, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), ywz1884, True, h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (87) 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_lt(x0, x1) new_esEs3(Zero, x0) new_esEs3(Succ(x0), x1) ---------------------------------------- (88) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Zero, ba) -> new_plusFM_CNew_elt021(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2417, ba) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Zero), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Neg(ywz18800), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Succ(ywz24190), ba) -> new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, ywz24180, ywz24190, ba) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Succ(ywz188000)), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt020(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz188000, ywz1881, ywz1882, ywz1883, ywz1884, ywz1877, ywz188000, h) new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h) new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1880, ywz1881, ywz1882, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), ywz1884, True, h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (89) 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_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 *new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1880, ywz1881, ywz1882, Branch(ywz18830, ywz18831, ywz18832, ywz18833, ywz18834), ywz1884, True, h) -> new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz18830, ywz18831, ywz18832, ywz18833, ywz18834, new_esEs0(Pos(Succ(ywz1877)), ywz18830), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 14 >= 14 *new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Succ(ywz24190), ba) -> new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, ywz24180, ywz24190, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 *new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Succ(ywz188000)), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt020(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz188000, ywz1881, ywz1882, ywz1883, ywz1884, ywz1877, ywz188000, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 5 >= 13, 8 > 14, 14 >= 15 *new_plusFM_CNew_elt020(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2413, ywz2414, ywz2415, ywz2416, ywz2417, Succ(ywz24180), Zero, ba) -> new_plusFM_CNew_elt021(ywz2406, ywz2407, ywz2408, ywz2409, ywz2410, ywz2411, ywz2412, ywz2417, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 12 >= 8, 15 >= 9 *new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Pos(Zero), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 12 >= 8, 14 >= 9 *new_plusFM_CNew_elt019(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, Neg(ywz18800), ywz1881, ywz1882, ywz1883, ywz1884, False, h) -> new_plusFM_CNew_elt021(ywz1873, ywz1874, ywz1875, ywz1876, ywz1877, ywz1878, ywz1879, ywz1884, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 12 >= 8, 14 >= 9 ---------------------------------------- (90) YES ---------------------------------------- (91) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Zero, ba) -> new_plusFM_CNew_elt08(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2433, ba) new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Succ(ywz24350), ba) -> new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, ywz24340, ywz24350, ba) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Neg(Succ(ywz148000)), ywz1481, ywz1482, ywz1483, ywz1484, False, h) -> new_plusFM_CNew_elt07(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz148000, ywz1481, ywz1482, ywz1483, ywz1484, ywz148000, ywz1477, h) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz1480, ywz1481, ywz1482, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), ywz1484, True, h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_lt(Neg(Succ(ywz1477)), ywz14830), h) new_plusFM_CNew_elt08(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_lt(Neg(Succ(ywz1477)), ywz14830), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (92) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz1480, ywz1481, ywz1482, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), ywz1484, True, h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_lt(Neg(Succ(ywz1477)), ywz14830), h) at position [13] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz1480, ywz1481, ywz1482, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), ywz1484, True, h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h),new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz1480, ywz1481, ywz1482, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), ywz1484, True, h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h)) ---------------------------------------- (93) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Zero, ba) -> new_plusFM_CNew_elt08(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2433, ba) new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Succ(ywz24350), ba) -> new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, ywz24340, ywz24350, ba) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Neg(Succ(ywz148000)), ywz1481, ywz1482, ywz1483, ywz1484, False, h) -> new_plusFM_CNew_elt07(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz148000, ywz1481, ywz1482, ywz1483, ywz1484, ywz148000, ywz1477, h) new_plusFM_CNew_elt08(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_lt(Neg(Succ(ywz1477)), ywz14830), h) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz1480, ywz1481, ywz1482, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), ywz1484, True, h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (94) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt08(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_lt(Neg(Succ(ywz1477)), ywz14830), h) at position [13] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt08(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h),new_plusFM_CNew_elt08(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h)) ---------------------------------------- (95) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Zero, ba) -> new_plusFM_CNew_elt08(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2433, ba) new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Succ(ywz24350), ba) -> new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, ywz24340, ywz24350, ba) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Neg(Succ(ywz148000)), ywz1481, ywz1482, ywz1483, ywz1484, False, h) -> new_plusFM_CNew_elt07(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz148000, ywz1481, ywz1482, ywz1483, ywz1484, ywz148000, ywz1477, h) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz1480, ywz1481, ywz1482, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), ywz1484, True, h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h) new_plusFM_CNew_elt08(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (96) 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. ---------------------------------------- (97) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Zero, ba) -> new_plusFM_CNew_elt08(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2433, ba) new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Succ(ywz24350), ba) -> new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, ywz24340, ywz24350, ba) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Neg(Succ(ywz148000)), ywz1481, ywz1482, ywz1483, ywz1484, False, h) -> new_plusFM_CNew_elt07(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz148000, ywz1481, ywz1482, ywz1483, ywz1484, ywz148000, ywz1477, h) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz1480, ywz1481, ywz1482, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), ywz1484, True, h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h) new_plusFM_CNew_elt08(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs5 -> True new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (98) 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_lt(x0, x1) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) ---------------------------------------- (99) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Zero, ba) -> new_plusFM_CNew_elt08(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2433, ba) new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Succ(ywz24350), ba) -> new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, ywz24340, ywz24350, ba) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Neg(Succ(ywz148000)), ywz1481, ywz1482, ywz1483, ywz1484, False, h) -> new_plusFM_CNew_elt07(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz148000, ywz1481, ywz1482, ywz1483, ywz1484, ywz148000, ywz1477, h) new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz1480, ywz1481, ywz1482, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), ywz1484, True, h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h) new_plusFM_CNew_elt08(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs5 -> True new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (100) 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_plusFM_CNew_elt08(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 9 > 10, 9 > 11, 9 > 12, 9 > 13, 10 >= 15 *new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Succ(ywz24350), ba) -> new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, ywz24340, ywz24350, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 > 14, 15 > 15, 16 >= 16 *new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, Neg(Succ(ywz148000)), ywz1481, ywz1482, ywz1483, ywz1484, False, h) -> new_plusFM_CNew_elt07(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz148000, ywz1481, ywz1482, ywz1483, ywz1484, ywz148000, ywz1477, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 9 > 14, 6 >= 15, 15 >= 16 *new_plusFM_CNew_elt07(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2429, ywz2430, ywz2431, ywz2432, ywz2433, Succ(ywz24340), Zero, ba) -> new_plusFM_CNew_elt08(ywz2421, ywz2422, ywz2423, ywz2424, ywz2425, ywz2426, ywz2427, ywz2428, ywz2433, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 13 >= 9, 16 >= 10 *new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz1480, ywz1481, ywz1482, Branch(ywz14830, ywz14831, ywz14832, ywz14833, ywz14834), ywz1484, True, h) -> new_plusFM_CNew_elt06(ywz1472, ywz1473, ywz1474, ywz1475, ywz1476, ywz1477, ywz1478, ywz1479, ywz14830, ywz14831, ywz14832, ywz14833, ywz14834, new_esEs0(Neg(Succ(ywz1477)), ywz14830), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 12 > 9, 12 > 10, 12 > 11, 12 > 12, 12 > 13, 15 >= 15 ---------------------------------------- (101) YES ---------------------------------------- (102) Obligation: Q DP problem: The TRS P consists of the following rules: new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C10(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz74000, ywz5000, ba) new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Neg(Zero), ywz9, ba) new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Succ(ywz13690), bb) -> new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, ywz13680, ywz13690, bb) new_addToFM_C2(ywz740, ywz741, ywz742, Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Zero, bb) -> new_addToFM_C(ywz1365, Neg(Succ(ywz1366)), ywz1367, bb) new_addToFM_C2(Neg(ywz7400), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) new_addToFM_C2(Pos(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C1(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz5000, ywz74000, ba) new_addToFM_C3(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, ba) -> new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, new_lt(ywz50, ywz740), ba) new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Succ(ywz14200), h) -> new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, ywz14190, ywz14200, h) new_addToFM_C2(Pos(Zero), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C(ywz743, ywz50, ywz9, ba) new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Zero, h) -> new_addToFM_C(ywz1416, Pos(Succ(ywz1417)), ywz1418, h) new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Zero), ywz9, ba) new_addToFM_C(Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz50, ywz9, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (103) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_addToFM_C3(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, ba) -> new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, new_lt(ywz50, ywz740), ba) at position [7] we obtained the following new rules [LPAR04]: (new_addToFM_C3(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, ba) -> new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, new_esEs0(ywz50, ywz740), ba),new_addToFM_C3(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, ba) -> new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, new_esEs0(ywz50, ywz740), ba)) ---------------------------------------- (104) Obligation: Q DP problem: The TRS P consists of the following rules: new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C10(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz74000, ywz5000, ba) new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Neg(Zero), ywz9, ba) new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Succ(ywz13690), bb) -> new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, ywz13680, ywz13690, bb) new_addToFM_C2(ywz740, ywz741, ywz742, Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Zero, bb) -> new_addToFM_C(ywz1365, Neg(Succ(ywz1366)), ywz1367, bb) new_addToFM_C2(Neg(ywz7400), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) new_addToFM_C2(Pos(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C1(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz5000, ywz74000, ba) new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Succ(ywz14200), h) -> new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, ywz14190, ywz14200, h) new_addToFM_C2(Pos(Zero), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C(ywz743, ywz50, ywz9, ba) new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Zero, h) -> new_addToFM_C(ywz1416, Pos(Succ(ywz1417)), ywz1418, h) new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Zero), ywz9, ba) new_addToFM_C(Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz50, ywz9, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) new_addToFM_C3(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, ba) -> new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, new_esEs0(ywz50, ywz740), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (105) 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. ---------------------------------------- (106) Obligation: Q DP problem: The TRS P consists of the following rules: new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C10(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz74000, ywz5000, ba) new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Neg(Zero), ywz9, ba) new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Succ(ywz13690), bb) -> new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, ywz13680, ywz13690, bb) new_addToFM_C2(ywz740, ywz741, ywz742, Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Zero, bb) -> new_addToFM_C(ywz1365, Neg(Succ(ywz1366)), ywz1367, bb) new_addToFM_C2(Neg(ywz7400), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) new_addToFM_C2(Pos(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C1(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz5000, ywz74000, ba) new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Succ(ywz14200), h) -> new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, ywz14190, ywz14200, h) new_addToFM_C2(Pos(Zero), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C(ywz743, ywz50, ywz9, ba) new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Zero, h) -> new_addToFM_C(ywz1416, Pos(Succ(ywz1417)), ywz1418, h) new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Zero), ywz9, ba) new_addToFM_C(Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz50, ywz9, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) new_addToFM_C3(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, ba) -> new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, new_esEs0(ywz50, ywz740), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs4 -> False new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (107) 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_lt(x0, x1) ---------------------------------------- (108) Obligation: Q DP problem: The TRS P consists of the following rules: new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C10(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz74000, ywz5000, ba) new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Neg(Zero), ywz9, ba) new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Succ(ywz13690), bb) -> new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, ywz13680, ywz13690, bb) new_addToFM_C2(ywz740, ywz741, ywz742, Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Zero, bb) -> new_addToFM_C(ywz1365, Neg(Succ(ywz1366)), ywz1367, bb) new_addToFM_C2(Neg(ywz7400), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) new_addToFM_C2(Pos(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C1(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz5000, ywz74000, ba) new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Succ(ywz14200), h) -> new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, ywz14190, ywz14200, h) new_addToFM_C2(Pos(Zero), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C(ywz743, ywz50, ywz9, ba) new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Zero, h) -> new_addToFM_C(ywz1416, Pos(Succ(ywz1417)), ywz1418, h) new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Zero), ywz9, ba) new_addToFM_C(Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz50, ywz9, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) new_addToFM_C3(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, ba) -> new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, new_esEs0(ywz50, ywz740), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs4 -> False new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (109) 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_addToFM_C3(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, ba) -> new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, new_esEs0(ywz50, ywz740), ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 9 *new_addToFM_C(Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz50, ywz9, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 6, 3 >= 7, 4 >= 8 *new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Succ(ywz13690), bb) -> new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, ywz13680, ywz13690, bb) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 *new_addToFM_C10(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Zero, bb) -> new_addToFM_C(ywz1365, Neg(Succ(ywz1366)), ywz1367, bb) The graph contains the following edges 5 >= 1, 7 >= 3, 10 >= 4 *new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C10(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz74000, ywz5000, ba) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 >= 7, 1 > 8, 6 > 9, 9 >= 10 *new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Succ(ywz14200), h) -> new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, ywz14190, ywz14200, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 > 9, 10 >= 10 *new_addToFM_C1(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Zero, h) -> new_addToFM_C(ywz1416, Pos(Succ(ywz1417)), ywz1418, h) The graph contains the following edges 5 >= 1, 7 >= 3, 10 >= 4 *new_addToFM_C2(Pos(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C1(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz5000, ywz74000, ba) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 >= 7, 6 > 8, 1 > 9, 9 >= 10 *new_addToFM_C2(ywz740, ywz741, ywz742, Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C3(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, ba) The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7, 9 >= 8 *new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Neg(Zero), ywz9, ba) The graph contains the following edges 5 >= 1, 6 >= 2, 7 >= 3, 9 >= 4 *new_addToFM_C2(Neg(ywz7400), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) The graph contains the following edges 5 >= 1, 6 >= 2, 7 >= 3, 9 >= 4 *new_addToFM_C2(Pos(Zero), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Succ(ywz5000)), ywz9, ba) The graph contains the following edges 5 >= 1, 6 >= 2, 7 >= 3, 9 >= 4 *new_addToFM_C2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, True, ba) -> new_addToFM_C(ywz743, ywz50, ywz9, ba) The graph contains the following edges 4 >= 1, 6 >= 2, 7 >= 3, 9 >= 4 *new_addToFM_C2(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Zero), ywz9, False, ba) -> new_addToFM_C(ywz744, Pos(Zero), ywz9, ba) The graph contains the following edges 5 >= 1, 6 >= 2, 7 >= 3, 9 >= 4 ---------------------------------------- (110) YES ---------------------------------------- (111) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2034, ywz2035, ywz2036, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), ywz2038, True, h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_lt(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_lt(Pos(Zero), ywz20370), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (112) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2034, ywz2035, ywz2036, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), ywz2038, True, h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_lt(Pos(Zero), ywz20370), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2034, ywz2035, ywz2036, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), ywz2038, True, h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h),new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2034, ywz2035, ywz2036, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), ywz2038, True, h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h)) ---------------------------------------- (113) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_lt(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2034, ywz2035, ywz2036, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), ywz2038, True, h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (114) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_lt(Pos(Zero), ywz20370), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h),new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h)) ---------------------------------------- (115) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2034, ywz2035, ywz2036, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), ywz2038, True, h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (116) 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. ---------------------------------------- (117) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2034, ywz2035, ywz2036, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), ywz2038, True, h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (118) 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_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) ---------------------------------------- (119) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2034, ywz2035, ywz2036, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), ywz2038, True, h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (120) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2034, ywz2035, ywz2036, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), ywz2038, True, h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16),new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16)) (new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16),new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16)) (new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16),new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16)) (new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16),new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16)) ---------------------------------------- (121) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (122) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (123) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (124) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16),new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16)) ---------------------------------------- (125) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (126) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16),new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16)) ---------------------------------------- (127) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (128) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16),new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16)) ---------------------------------------- (129) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (130) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Branch(ywz20370, ywz20371, ywz20372, ywz20373, ywz20374), h) -> new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz20370, ywz20371, ywz20372, ywz20373, ywz20374, new_esEs0(Pos(Zero), ywz20370), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12),new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12)) (new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12),new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12)) (new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12),new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12)) (new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12),new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12)) ---------------------------------------- (131) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (132) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (133) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) 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_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) 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_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) ---------------------------------------- (137) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs2 -> False The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (138) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12),new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12)) ---------------------------------------- (139) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs2 -> False The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (140) 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. ---------------------------------------- (141) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (142) 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_esEs2 ---------------------------------------- (143) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (144) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12),new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12)) ---------------------------------------- (145) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (146) 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. ---------------------------------------- (147) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) The TRS R consists of the following rules: new_esEs5 -> True The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (148) 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_esEs3(Zero, x0) new_esEs3(Succ(x0), x1) ---------------------------------------- (149) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) The TRS R consists of the following rules: new_esEs5 -> True The set Q consists of the following terms: new_esEs5 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (150) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12),new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12)) ---------------------------------------- (151) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The TRS R consists of the following rules: new_esEs5 -> True The set Q consists of the following terms: new_esEs5 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (152) 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. ---------------------------------------- (153) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) R is empty. The set Q consists of the following terms: new_esEs5 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (154) 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_esEs5 ---------------------------------------- (155) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (156) 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_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 *new_plusFM_CNew_elt015(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 *new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 14 >= 14 *new_plusFM_CNew_elt014(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, Neg(Succ(ywz203400)), ywz2035, ywz2036, ywz2037, ywz2038, False, h) -> new_plusFM_CNew_elt015(ywz2027, ywz2028, ywz2029, ywz2030, ywz2031, ywz2032, ywz2033, ywz2038, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 12 >= 8, 14 >= 9 *new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt014(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 13 >= 13, 14 >= 14 ---------------------------------------- (157) YES ---------------------------------------- (158) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Neg(Succ(ywz178900)), ywz1790, ywz1791, ywz1792, ywz1793, False, h) -> new_plusFM_CNew_elt04(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz178900, ywz1790, ywz1791, ywz1792, ywz1793, ywz178900, ywz1786, h) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Zero, ba) -> new_plusFM_CNew_elt05(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2448, ba) new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz1789, ywz1790, ywz1791, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), ywz1793, True, h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_lt(Neg(Succ(ywz1786)), ywz17920), h) new_plusFM_CNew_elt05(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_lt(Neg(Succ(ywz1786)), ywz17920), h) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Succ(ywz24500), ba) -> new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, ywz24490, ywz24500, ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (159) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz1789, ywz1790, ywz1791, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), ywz1793, True, h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_lt(Neg(Succ(ywz1786)), ywz17920), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz1789, ywz1790, ywz1791, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), ywz1793, True, h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h),new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz1789, ywz1790, ywz1791, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), ywz1793, True, h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h)) ---------------------------------------- (160) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Neg(Succ(ywz178900)), ywz1790, ywz1791, ywz1792, ywz1793, False, h) -> new_plusFM_CNew_elt04(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz178900, ywz1790, ywz1791, ywz1792, ywz1793, ywz178900, ywz1786, h) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Zero, ba) -> new_plusFM_CNew_elt05(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2448, ba) new_plusFM_CNew_elt05(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_lt(Neg(Succ(ywz1786)), ywz17920), h) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Succ(ywz24500), ba) -> new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, ywz24490, ywz24500, ba) new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz1789, ywz1790, ywz1791, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), ywz1793, True, h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (161) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt05(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_lt(Neg(Succ(ywz1786)), ywz17920), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt05(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h),new_plusFM_CNew_elt05(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h)) ---------------------------------------- (162) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Neg(Succ(ywz178900)), ywz1790, ywz1791, ywz1792, ywz1793, False, h) -> new_plusFM_CNew_elt04(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz178900, ywz1790, ywz1791, ywz1792, ywz1793, ywz178900, ywz1786, h) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Zero, ba) -> new_plusFM_CNew_elt05(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2448, ba) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Succ(ywz24500), ba) -> new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, ywz24490, ywz24500, ba) new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz1789, ywz1790, ywz1791, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), ywz1793, True, h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h) new_plusFM_CNew_elt05(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (163) 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. ---------------------------------------- (164) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Neg(Succ(ywz178900)), ywz1790, ywz1791, ywz1792, ywz1793, False, h) -> new_plusFM_CNew_elt04(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz178900, ywz1790, ywz1791, ywz1792, ywz1793, ywz178900, ywz1786, h) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Zero, ba) -> new_plusFM_CNew_elt05(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2448, ba) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Succ(ywz24500), ba) -> new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, ywz24490, ywz24500, ba) new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz1789, ywz1790, ywz1791, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), ywz1793, True, h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h) new_plusFM_CNew_elt05(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs5 -> True new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (165) 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_lt(x0, x1) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) ---------------------------------------- (166) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Neg(Succ(ywz178900)), ywz1790, ywz1791, ywz1792, ywz1793, False, h) -> new_plusFM_CNew_elt04(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz178900, ywz1790, ywz1791, ywz1792, ywz1793, ywz178900, ywz1786, h) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Zero, ba) -> new_plusFM_CNew_elt05(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2448, ba) new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Succ(ywz24500), ba) -> new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, ywz24490, ywz24500, ba) new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz1789, ywz1790, ywz1791, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), ywz1793, True, h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h) new_plusFM_CNew_elt05(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs5 -> True new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (167) 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_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Neg(Succ(ywz178900)), ywz1790, ywz1791, ywz1792, ywz1793, False, h) -> new_plusFM_CNew_elt04(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz178900, ywz1790, ywz1791, ywz1792, ywz1793, ywz178900, ywz1786, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 8 > 13, 5 >= 14, 14 >= 15 *new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Succ(ywz24500), ba) -> new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, ywz24490, ywz24500, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 > 13, 14 > 14, 15 >= 15 *new_plusFM_CNew_elt04(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2444, ywz2445, ywz2446, ywz2447, ywz2448, Succ(ywz24490), Zero, ba) -> new_plusFM_CNew_elt05(ywz2437, ywz2438, ywz2439, ywz2440, ywz2441, ywz2442, ywz2443, ywz2448, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 12 >= 8, 15 >= 9 *new_plusFM_CNew_elt05(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 *new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz1789, ywz1790, ywz1791, Branch(ywz17920, ywz17921, ywz17922, ywz17923, ywz17924), ywz1793, True, h) -> new_plusFM_CNew_elt03(ywz1782, ywz1783, ywz1784, ywz1785, ywz1786, ywz1787, ywz1788, ywz17920, ywz17921, ywz17922, ywz17923, ywz17924, new_esEs0(Neg(Succ(ywz1786)), ywz17920), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 14 >= 14 ---------------------------------------- (168) YES ---------------------------------------- (169) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Succ(ywz144400)), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt022(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz144400, ywz1445, ywz1446, ywz1447, ywz1448, ywz1441, ywz144400, ba) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Succ(ywz24030), h) -> new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, ywz24020, ywz24030, h) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Zero, h) -> new_plusFM_CNew_elt023(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2401, h) new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_lt(Pos(Succ(ywz1441)), ywz14470), ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Zero), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1444, ywz1445, ywz1446, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ywz1448, True, ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_lt(Pos(Succ(ywz1441)), ywz14470), ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Neg(ywz14440), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (170) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_lt(Pos(Succ(ywz1441)), ywz14470), ba) at position [13] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba),new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba)) ---------------------------------------- (171) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Succ(ywz144400)), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt022(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz144400, ywz1445, ywz1446, ywz1447, ywz1448, ywz1441, ywz144400, ba) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Succ(ywz24030), h) -> new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, ywz24020, ywz24030, h) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Zero, h) -> new_plusFM_CNew_elt023(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2401, h) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Zero), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1444, ywz1445, ywz1446, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ywz1448, True, ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_lt(Pos(Succ(ywz1441)), ywz14470), ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Neg(ywz14440), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (172) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1444, ywz1445, ywz1446, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ywz1448, True, ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_lt(Pos(Succ(ywz1441)), ywz14470), ba) at position [13] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1444, ywz1445, ywz1446, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ywz1448, True, ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba),new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1444, ywz1445, ywz1446, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ywz1448, True, ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba)) ---------------------------------------- (173) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Succ(ywz144400)), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt022(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz144400, ywz1445, ywz1446, ywz1447, ywz1448, ywz1441, ywz144400, ba) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Succ(ywz24030), h) -> new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, ywz24020, ywz24030, h) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Zero, h) -> new_plusFM_CNew_elt023(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2401, h) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Zero), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Neg(ywz14440), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1444, ywz1445, ywz1446, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ywz1448, True, ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (174) 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. ---------------------------------------- (175) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Succ(ywz144400)), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt022(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz144400, ywz1445, ywz1446, ywz1447, ywz1448, ywz1441, ywz144400, ba) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Succ(ywz24030), h) -> new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, ywz24020, ywz24030, h) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Zero, h) -> new_plusFM_CNew_elt023(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2401, h) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Zero), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Neg(ywz14440), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1444, ywz1445, ywz1446, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ywz1448, True, ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (176) 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_lt(x0, x1) new_esEs3(Zero, x0) new_esEs3(Succ(x0), x1) ---------------------------------------- (177) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Succ(ywz144400)), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt022(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz144400, ywz1445, ywz1446, ywz1447, ywz1448, ywz1441, ywz144400, ba) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Succ(ywz24030), h) -> new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, ywz24020, ywz24030, h) new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Zero, h) -> new_plusFM_CNew_elt023(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2401, h) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Zero), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Neg(ywz14440), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba) new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1444, ywz1445, ywz1446, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ywz1448, True, ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (178) 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_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Succ(ywz24030), h) -> new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, ywz24020, ywz24030, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 > 14, 15 > 15, 16 >= 16 *new_plusFM_CNew_elt022(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2397, ywz2398, ywz2399, ywz2400, ywz2401, Succ(ywz24020), Zero, h) -> new_plusFM_CNew_elt023(ywz2389, ywz2390, ywz2391, ywz2392, ywz2393, ywz2394, ywz2395, ywz2396, ywz2401, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 13 >= 9, 16 >= 10 *new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Succ(ywz144400)), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt022(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz144400, ywz1445, ywz1446, ywz1447, ywz1448, ywz1441, ywz144400, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 6 >= 14, 9 > 15, 15 >= 16 *new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 9 > 10, 9 > 11, 9 > 12, 9 > 13, 10 >= 15 *new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1444, ywz1445, ywz1446, Branch(ywz14470, ywz14471, ywz14472, ywz14473, ywz14474), ywz1448, True, ba) -> new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz14470, ywz14471, ywz14472, ywz14473, ywz14474, new_esEs0(Pos(Succ(ywz1441)), ywz14470), ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 12 > 9, 12 > 10, 12 > 11, 12 > 12, 12 > 13, 15 >= 15 *new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Pos(Zero), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 13 >= 9, 15 >= 10 *new_plusFM_CNew_elt024(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, Neg(ywz14440), ywz1445, ywz1446, ywz1447, ywz1448, False, ba) -> new_plusFM_CNew_elt023(ywz1436, ywz1437, ywz1438, ywz1439, ywz1440, ywz1441, ywz1442, ywz1443, ywz1448, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 13 >= 9, 15 >= 10 ---------------------------------------- (179) YES ---------------------------------------- (180) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Succ(ywz189400)), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt017(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz189400, ywz1895, ywz1896, ywz1897, ywz1898, ywz1891, ywz189400, h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1894, ywz1895, ywz1896, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), ywz1898, True, h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_lt(Pos(Succ(ywz1891)), ywz18970), h) new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_lt(Pos(Succ(ywz1891)), ywz18970), h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Zero), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Succ(ywz23200), ba) -> new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, ywz23190, ywz23200, ba) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Zero, ba) -> new_plusFM_CNew_elt018(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2318, ba) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Neg(ywz18940), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (181) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1894, ywz1895, ywz1896, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), ywz1898, True, h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_lt(Pos(Succ(ywz1891)), ywz18970), h) at position [13] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1894, ywz1895, ywz1896, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), ywz1898, True, h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h),new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1894, ywz1895, ywz1896, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), ywz1898, True, h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h)) ---------------------------------------- (182) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Succ(ywz189400)), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt017(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz189400, ywz1895, ywz1896, ywz1897, ywz1898, ywz1891, ywz189400, h) new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_lt(Pos(Succ(ywz1891)), ywz18970), h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Zero), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Succ(ywz23200), ba) -> new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, ywz23190, ywz23200, ba) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Zero, ba) -> new_plusFM_CNew_elt018(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2318, ba) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Neg(ywz18940), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1894, ywz1895, ywz1896, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), ywz1898, True, h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (183) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_lt(Pos(Succ(ywz1891)), ywz18970), h) at position [13] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h),new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h)) ---------------------------------------- (184) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Succ(ywz189400)), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt017(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz189400, ywz1895, ywz1896, ywz1897, ywz1898, ywz1891, ywz189400, h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Zero), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Succ(ywz23200), ba) -> new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, ywz23190, ywz23200, ba) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Zero, ba) -> new_plusFM_CNew_elt018(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2318, ba) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Neg(ywz18940), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1894, ywz1895, ywz1896, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), ywz1898, True, h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h) new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (185) 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. ---------------------------------------- (186) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Succ(ywz189400)), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt017(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz189400, ywz1895, ywz1896, ywz1897, ywz1898, ywz1891, ywz189400, h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Zero), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Succ(ywz23200), ba) -> new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, ywz23190, ywz23200, ba) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Zero, ba) -> new_plusFM_CNew_elt018(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2318, ba) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Neg(ywz18940), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1894, ywz1895, ywz1896, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), ywz1898, True, h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h) new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (187) 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_lt(x0, x1) new_esEs3(Zero, x0) new_esEs3(Succ(x0), x1) ---------------------------------------- (188) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Succ(ywz189400)), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt017(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz189400, ywz1895, ywz1896, ywz1897, ywz1898, ywz1891, ywz189400, h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Zero), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Succ(ywz23200), ba) -> new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, ywz23190, ywz23200, ba) new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Zero, ba) -> new_plusFM_CNew_elt018(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2318, ba) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Neg(ywz18940), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1894, ywz1895, ywz1896, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), ywz1898, True, h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h) new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (189) 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_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 9 > 10, 9 > 11, 9 > 12, 9 > 13, 10 >= 15 *new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1894, ywz1895, ywz1896, Branch(ywz18970, ywz18971, ywz18972, ywz18973, ywz18974), ywz1898, True, h) -> new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz18970, ywz18971, ywz18972, ywz18973, ywz18974, new_esEs0(Pos(Succ(ywz1891)), ywz18970), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 12 > 9, 12 > 10, 12 > 11, 12 > 12, 12 > 13, 15 >= 15 *new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Succ(ywz23200), ba) -> new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, ywz23190, ywz23200, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 > 14, 15 > 15, 16 >= 16 *new_plusFM_CNew_elt017(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2314, ywz2315, ywz2316, ywz2317, ywz2318, Succ(ywz23190), Zero, ba) -> new_plusFM_CNew_elt018(ywz2306, ywz2307, ywz2308, ywz2309, ywz2310, ywz2311, ywz2312, ywz2313, ywz2318, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 13 >= 9, 16 >= 10 *new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Succ(ywz189400)), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt017(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz189400, ywz1895, ywz1896, ywz1897, ywz1898, ywz1891, ywz189400, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 6 >= 14, 9 > 15, 15 >= 16 *new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Pos(Zero), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 13 >= 9, 15 >= 10 *new_plusFM_CNew_elt016(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, Neg(ywz18940), ywz1895, ywz1896, ywz1897, ywz1898, False, h) -> new_plusFM_CNew_elt018(ywz1886, ywz1887, ywz1888, ywz1889, ywz1890, ywz1891, ywz1892, ywz1893, ywz1898, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 13 >= 9, 15 >= 10 ---------------------------------------- (190) YES ---------------------------------------- (191) Obligation: Q DP problem: The TRS P consists of the following rules: new_mkBalBranch6MkBalBranch3(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz1184000), Succ(ywz1183000), h) -> new_mkBalBranch6MkBalBranch3(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz1184000, ywz1183000, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (192) 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_mkBalBranch6MkBalBranch3(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz1184000), Succ(ywz1183000), h) -> new_mkBalBranch6MkBalBranch3(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz1184000, ywz1183000, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7, 8 >= 8 ---------------------------------------- (193) YES ---------------------------------------- (194) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitLT1(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Succ(ywz18150), Succ(ywz18160), h) -> new_splitLT1(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, ywz18150, ywz18160, h) new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz4330), Zero, bb) -> new_splitLT1(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz432), Succ(ywz427), bb) new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Zero, Zero, bc) -> new_splitLT22(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, bc) new_splitLT10(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Succ(ywz18240), Succ(ywz18250), bd) -> new_splitLT10(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, ywz18240, ywz18250, bd) new_splitLT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), ba) new_splitLT10(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Succ(ywz18240), Zero, bd) -> new_splitLT4(ywz1822, ywz1823, bd) new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz4420), Zero, bc) -> new_splitLT10(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz436), Succ(ywz441), bc) new_splitLT3(Pos(Succ(ywz4000)), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Pos(Zero), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Pos(Zero), ba) new_splitLT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), ba) -> new_splitLT5(ywz44, ba) new_splitLT3(Neg(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), ba) -> new_splitLT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), ba) new_splitLT22(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, bc) -> new_splitLT10(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz436), Succ(ywz441), bc) new_splitLT3(Neg(ywz400), ywz41, ywz42, EmptyFM, ywz44, Pos(Succ(ywz5000)), ba) -> new_splitLT(ywz44, ywz5000, ba) new_splitLT21(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, bb) -> new_splitLT1(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz432), Succ(ywz427), bb) new_splitLT1(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Succ(ywz18150), Zero, h) -> new_splitLT(ywz1813, ywz1814, h) new_splitLT4(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), ba) new_splitLT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), ba) -> new_splitLT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, ba) new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Zero, Succ(ywz4430), bc) -> new_splitLT4(ywz439, ywz441, bc) new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Zero, Zero, bb) -> new_splitLT21(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, bb) new_splitLT0(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Pos(Zero), ba) new_splitLT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), ba) -> new_splitLT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, ba) new_splitLT3(Pos(Zero), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), ba) -> new_splitLT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), ba) new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz4330), Succ(ywz4340), bb) -> new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, ywz4330, ywz4340, bb) new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Zero, Succ(ywz4340), bb) -> new_splitLT(ywz430, ywz432, bb) new_splitLT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, ba) -> new_splitLT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), ba) new_splitLT5(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Zero), ba) new_splitLT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), ba) -> new_splitLT4(ywz43, ywz5000, ba) new_splitLT3(Pos(Succ(ywz4000)), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Zero), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Zero), ba) new_splitLT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), ba) -> new_splitLT0(ywz44, ba) new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz4420), Succ(ywz4430), bc) -> new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, ywz4420, ywz4430, bc) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (195) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs. ---------------------------------------- (196) Complex Obligation (AND) ---------------------------------------- (197) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitLT5(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Zero), ba) new_splitLT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), ba) -> new_splitLT5(ywz44, ba) new_splitLT3(Pos(Succ(ywz4000)), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Zero), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Zero), ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (198) 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_splitLT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), ba) -> new_splitLT5(ywz44, ba) The graph contains the following edges 5 >= 1, 7 >= 2 *new_splitLT3(Pos(Succ(ywz4000)), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Zero), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Zero), ba) The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7 *new_splitLT5(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Zero), ba) The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 7 ---------------------------------------- (199) YES ---------------------------------------- (200) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitLT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), ba) -> new_splitLT0(ywz44, ba) new_splitLT0(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Pos(Zero), ba) new_splitLT3(Pos(Succ(ywz4000)), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Pos(Zero), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Pos(Zero), ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (201) 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_splitLT0(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Pos(Zero), ba) The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 2 >= 7 *new_splitLT3(Pos(Succ(ywz4000)), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Pos(Zero), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Pos(Zero), ba) The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7 *new_splitLT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), ba) -> new_splitLT0(ywz44, ba) The graph contains the following edges 5 >= 1, 7 >= 2 ---------------------------------------- (202) YES ---------------------------------------- (203) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitLT22(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, bc) -> new_splitLT10(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz436), Succ(ywz441), bc) new_splitLT10(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Succ(ywz18240), Succ(ywz18250), bd) -> new_splitLT10(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, ywz18240, ywz18250, bd) new_splitLT10(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Succ(ywz18240), Zero, bd) -> new_splitLT4(ywz1822, ywz1823, bd) new_splitLT4(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), ba) new_splitLT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), ba) new_splitLT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), ba) -> new_splitLT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, ba) new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Zero, Zero, bc) -> new_splitLT22(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, bc) new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz4420), Zero, bc) -> new_splitLT10(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz436), Succ(ywz441), bc) new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Zero, Succ(ywz4430), bc) -> new_splitLT4(ywz439, ywz441, bc) new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz4420), Succ(ywz4430), bc) -> new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, ywz4420, ywz4430, bc) new_splitLT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), ba) -> new_splitLT4(ywz43, ywz5000, ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (204) 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_splitLT10(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Succ(ywz18240), Succ(ywz18250), bd) -> new_splitLT10(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, ywz18240, ywz18250, bd) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 *new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Zero, Zero, bc) -> new_splitLT22(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7 *new_splitLT10(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Succ(ywz18240), Zero, bd) -> new_splitLT4(ywz1822, ywz1823, bd) The graph contains the following edges 5 >= 1, 6 >= 2, 9 >= 3 *new_splitLT4(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), ba) The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 3 >= 7 *new_splitLT3(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), ba) -> new_splitLT4(ywz43, ywz5000, ba) The graph contains the following edges 4 >= 1, 6 > 2, 7 >= 3 *new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Zero, Succ(ywz4430), bc) -> new_splitLT4(ywz439, ywz441, bc) The graph contains the following edges 4 >= 1, 6 >= 2, 9 >= 3 *new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz4420), Succ(ywz4430), bc) -> new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, ywz4420, ywz4430, bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 *new_splitLT3(Pos(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz44, Neg(Succ(ywz5000)), ba) -> new_splitLT3(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), ba) The graph contains the following edges 4 > 1, 4 > 2, 4 > 3, 4 > 4, 4 > 5, 6 >= 6, 7 >= 7 *new_splitLT3(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), ba) -> new_splitLT20(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, ba) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 1 > 7, 6 > 8, 7 >= 9 *new_splitLT20(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz4420), Zero, bc) -> new_splitLT10(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz436), Succ(ywz441), bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9 *new_splitLT22(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, bc) -> new_splitLT10(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz436), Succ(ywz441), bc) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9 ---------------------------------------- (205) YES ---------------------------------------- (206) Obligation: Q DP problem: The TRS P consists of the following rules: new_splitLT1(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Succ(ywz18150), Zero, h) -> new_splitLT(ywz1813, ywz1814, h) new_splitLT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, ba) -> new_splitLT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), ba) new_splitLT3(Neg(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), ba) -> new_splitLT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), ba) new_splitLT3(Neg(ywz400), ywz41, ywz42, EmptyFM, ywz44, Pos(Succ(ywz5000)), ba) -> new_splitLT(ywz44, ywz5000, ba) new_splitLT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), ba) -> new_splitLT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, ba) new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz4330), Zero, bb) -> new_splitLT1(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz432), Succ(ywz427), bb) new_splitLT1(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Succ(ywz18150), Succ(ywz18160), h) -> new_splitLT1(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, ywz18150, ywz18160, h) new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Zero, Zero, bb) -> new_splitLT21(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, bb) new_splitLT21(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, bb) -> new_splitLT1(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz432), Succ(ywz427), bb) new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz4330), Succ(ywz4340), bb) -> new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, ywz4330, ywz4340, bb) new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Zero, Succ(ywz4340), bb) -> new_splitLT(ywz430, ywz432, bb) new_splitLT3(Pos(Zero), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), ba) -> new_splitLT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (207) 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_splitLT(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, ba) -> new_splitLT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), ba) The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5, 3 >= 7 *new_splitLT1(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Succ(ywz18150), Succ(ywz18160), h) -> new_splitLT1(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, ywz18150, ywz18160, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 *new_splitLT3(Neg(ywz400), ywz41, ywz42, EmptyFM, ywz44, Pos(Succ(ywz5000)), ba) -> new_splitLT(ywz44, ywz5000, ba) The graph contains the following edges 5 >= 1, 6 > 2, 7 >= 3 *new_splitLT3(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), ba) -> new_splitLT2(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, ba) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 6 > 7, 1 > 8, 7 >= 9 *new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Zero, Succ(ywz4340), bb) -> new_splitLT(ywz430, ywz432, bb) The graph contains the following edges 4 >= 1, 6 >= 2, 9 >= 3 *new_splitLT1(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Succ(ywz18150), Zero, h) -> new_splitLT(ywz1813, ywz1814, h) The graph contains the following edges 5 >= 1, 6 >= 2, 9 >= 3 *new_splitLT21(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, bb) -> new_splitLT1(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz432), Succ(ywz427), bb) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 9 *new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz4330), Succ(ywz4340), bb) -> new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, ywz4330, ywz4340, bb) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 > 7, 8 > 8, 9 >= 9 *new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz4330), Zero, bb) -> new_splitLT1(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz432), Succ(ywz427), bb) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 9 *new_splitLT2(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Zero, Zero, bb) -> new_splitLT21(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, bb) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 9 >= 7 *new_splitLT3(Neg(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), ba) -> new_splitLT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), ba) The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7 *new_splitLT3(Pos(Zero), ywz41, ywz42, ywz43, Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), ba) -> new_splitLT3(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), ba) The graph contains the following edges 5 > 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 6 >= 6, 7 >= 7 ---------------------------------------- (208) YES ---------------------------------------- (209) Obligation: Q DP problem: The TRS P consists of the following rules: new_primMinusNat(Succ(ywz104900), Succ(ywz104800)) -> new_primMinusNat(ywz104900, ywz104800) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (210) 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_primMinusNat(Succ(ywz104900), Succ(ywz104800)) -> new_primMinusNat(ywz104900, ywz104800) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (211) YES ---------------------------------------- (212) Obligation: Q DP problem: The TRS P consists of the following rules: new_primPlusNat(Succ(ywz250000), Succ(ywz372000)) -> new_primPlusNat(ywz250000, ywz372000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (213) 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(ywz250000), Succ(ywz372000)) -> new_primPlusNat(ywz250000, ywz372000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (214) YES ---------------------------------------- (215) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_C(ywz3, Branch(ywz40, ywz41, ywz42, ywz43, ywz44), Branch(ywz50, ywz51, ywz52, ywz53, ywz54), h) -> new_plusFM_C(ywz3, new_splitLT30(ywz40, ywz41, ywz42, ywz43, ywz44, ywz50, h), ywz53, h) new_plusFM_C(ywz3, Branch(ywz40, ywz41, ywz42, ywz43, ywz44), Branch(ywz50, ywz51, ywz52, ywz53, ywz54), h) -> new_plusFM_C(ywz3, new_splitGT30(ywz40, ywz41, ywz42, ywz43, ywz44, ywz50, h), ywz54, h) The TRS R consists of the following rules: new_sizeFM(Branch(ywz630, ywz631, ywz632, ywz633, ywz634), h) -> ywz632 new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Succ(ywz115700)), Pos(ywz11540), h) -> new_mkBalBranch6MkBalBranch46(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz115700, ywz11540, h) new_splitGT6(EmptyFM, ywz5000, h) -> new_emptyFM(h) new_mkBalBranch6MkBalBranch5(ywz1007, ywz73, ywz70, ywz71, ywz1006, False, h) -> new_mkBalBranch6MkBalBranch40(ywz1007, ywz73, ywz70, ywz71, ywz1006, new_sr(new_mkBalBranch6Size_l(ywz1007, ywz73, ywz70, ywz71, h)), h) new_primPlusNat0(Zero, Zero) -> Zero new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_mkVBalBranch5(ywz41, EmptyFM, ywz44, h) -> new_addToFM_C4(ywz44, Zero, ywz41, h) new_sizeFM(EmptyFM, h) -> Pos(Zero) new_splitLT30(Neg(ywz400), ywz41, ywz42, EmptyFM, ywz44, Pos(Succ(ywz5000)), h) -> new_addToFM_C4(new_splitLT7(ywz44, ywz5000, h), ywz400, ywz41, h) new_mkVBalBranch3MkVBalBranch20(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, False, h) -> new_mkVBalBranch3MkVBalBranch10(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h)), new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h)), h) new_splitLT26(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz4330), Succ(ywz4340), bg) -> new_splitLT26(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, ywz4330, ywz4340, bg) new_mkBalBranch6MkBalBranch41(ywz1007, ywz73, ywz70, ywz71, ywz1006, Zero, Succ(ywz1154000), h) -> new_mkBalBranch6MkBalBranch43(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_primPlusNat1(Zero) -> Succ(Succ(new_primPlusNat3)) new_splitLT9(EmptyFM, h) -> new_emptyFM(h) new_splitGT30(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> new_splitGT8(ywz44, h) new_splitLT13(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Zero, Zero, cc) -> new_splitLT14(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, cc) new_mkBalBranch6Size_r(ywz634, ywz1156, ywz630, ywz631, h) -> new_sizeFM(ywz634, h) new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Succ(ywz115700)), Neg(ywz11540), h) -> new_mkBalBranch6MkBalBranch45(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz11540, ywz115700, h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Zero), Pos(Succ(ywz118300)), h) -> new_mkBalBranch6MkBalBranch30(ywz1007, ywz73, ywz70, ywz71, ywz1006, Zero, ywz118300, h) new_mkVBalBranch3MkVBalBranch10(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, False, h) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), ywz50, ywz9, Branch(ywz740, ywz741, ywz742, ywz743, ywz744), Branch(ywz630, ywz631, ywz632, ywz633, ywz634), ty_Int, h) new_mkBalBranch6MkBalBranch36(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz118400, Succ(ywz118300), h) -> new_mkBalBranch6MkBalBranch31(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz118400, ywz118300, h) new_splitLT30(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> ywz43 new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Zero), Pos(Succ(ywz115400)), h) -> new_mkBalBranch6MkBalBranch43(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_splitGT12(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, False, ba) -> ywz1841 new_addToFM_C20(Pos(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Zero), ywz9, False, h) -> Branch(Neg(Zero), new_addToFM0(ywz741, ywz9, h), ywz742, ywz743, ywz744) new_addToFM_C20(Pos(ywz7400), ywz741, ywz742, ywz743, ywz744, Neg(Succ(ywz5000)), ywz9, False, h) -> Branch(Neg(Succ(ywz5000)), new_addToFM0(ywz741, ywz9, h), ywz742, ywz743, ywz744) new_addToFM_C13(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Zero, Succ(ywz13690), cb) -> new_addToFM_C14(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, cb) new_mkVBalBranch6(ywz50, ywz9, Branch(ywz7440, ywz7441, ywz7442, ywz7443, ywz7444), ywz630, ywz631, ywz632, ywz633, ywz634, h) -> new_mkVBalBranch31(ywz50, ywz9, ywz7440, ywz7441, ywz7442, ywz7443, ywz7444, ywz630, ywz631, ywz632, ywz633, ywz634, h) new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_mkBalBranch6MkBalBranch41(ywz1007, ywz73, ywz70, ywz71, ywz1006, Zero, Zero, h) -> new_mkBalBranch6MkBalBranch44(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_splitGT30(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> ywz44 new_splitGT30(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> ywz44 new_splitGT5(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitGT30(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_splitGT30(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> new_mkVBalBranch2(Succ(ywz4000), ywz41, new_splitGT7(ywz43, h), ywz44, h) new_addToFM_C11(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Succ(ywz14200), bb) -> new_addToFM_C11(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, ywz14190, ywz14200, bb) new_mkBalBranch6MkBalBranch5(ywz1007, ywz73, ywz70, ywz71, ywz1006, True, h) -> new_mkBranch(Zero, ywz70, ywz71, ywz73, ywz1006, ty_Int, h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Succ(ywz118400)), Pos(ywz11830), h) -> new_mkBalBranch6MkBalBranch36(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz118400, ywz11830, h) new_sr0(Pos(ywz12090)) -> Pos(new_primMulNat1(ywz12090)) new_mkVBalBranch3Size_l(ywz70, ywz71, ywz72, ywz73, ywz74, ywz60, ywz61, ywz62, ywz63, ywz64, h) -> new_sizeFM(Branch(ywz70, ywz71, ywz72, ywz73, ywz74), h) new_splitGT26(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, cd) -> new_splitGT13(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, new_lt(Pos(Succ(ywz450)), Pos(Succ(ywz445))), cd) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_primMulNat(Succ(ywz103700)) -> new_primPlusNat0(new_primMulNat0(ywz103700), Succ(ywz103700)) new_primMinusNat0(Zero, Zero) -> Pos(Zero) new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Zero), Neg(Zero), h) -> new_mkBalBranch6MkBalBranch44(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Zero), Pos(Zero), h) -> new_mkBalBranch6MkBalBranch44(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_splitLT30(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> new_splitLT8(ywz43, h) new_mkBalBranch6MkBalBranch37(ywz1007, Branch(ywz730, ywz731, ywz732, ywz733, ywz734), ywz70, ywz71, ywz1006, h) -> new_mkBalBranch6MkBalBranch11(ywz1007, ywz730, ywz731, ywz732, ywz733, ywz734, ywz70, ywz71, ywz1006, new_lt(new_sizeFM(ywz734, h), new_sr0(new_sizeFM(ywz733, h))), h) new_addToFM_C20(Pos(Zero), ywz741, ywz742, ywz743, ywz744, Pos(Zero), ywz9, False, h) -> Branch(Pos(Zero), new_addToFM0(ywz741, ywz9, h), ywz742, ywz743, ywz744) new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_splitLT6(EmptyFM, ywz5000, h) -> new_emptyFM(h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Zero), Neg(Succ(ywz118300)), h) -> new_mkBalBranch6MkBalBranch37(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_splitLT26(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Zero, Zero, bg) -> new_splitLT25(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, bg) new_splitGT13(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, True, bc) -> new_mkVBalBranch2(Succ(ywz1827), ywz1828, new_splitGT6(ywz1830, ywz1832, bc), ywz1831, bc) new_mkBalBranch6MkBalBranch31(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz1184000), Zero, h) -> new_mkBalBranch6MkBalBranch37(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_addToFM_C5(EmptyFM, ywz400, ywz41, h) -> Branch(Pos(ywz400), ywz41, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h)) new_mkBalBranch6MkBalBranch33(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) -> new_mkBalBranch6MkBalBranch34(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_addToFM_C4(EmptyFM, ywz400, ywz41, h) -> Branch(Neg(ywz400), ywz41, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h)) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Zero), Neg(Succ(ywz118300)), h) -> new_mkBalBranch6MkBalBranch36(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz118300, Zero, h) new_sr(Pos(ywz10370)) -> Pos(new_primMulNat(ywz10370)) new_splitGT25(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Succ(ywz4520), cd) -> new_splitGT26(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, cd) new_splitLT30(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitLT23(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_addToFM_C20(Neg(Zero), ywz741, ywz742, ywz743, ywz744, Neg(Zero), ywz9, False, h) -> Branch(Neg(Zero), new_addToFM0(ywz741, ywz9, h), ywz742, ywz743, ywz744) new_splitGT23(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Succ(ywz4610), ca) -> new_splitGT23(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ywz4600, ywz4610, ca) new_addToFM_C12(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, bb) -> Branch(Pos(Succ(ywz1417)), new_addToFM0(ywz1413, ywz1418, bb), ywz1414, ywz1415, ywz1416) new_splitLT13(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Zero, Succ(ywz18250), cc) -> new_splitLT14(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, cc) new_splitGT30(Pos(ywz400), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_mkVBalBranch2(ywz400, ywz41, new_splitGT5(ywz43, ywz5000, h), ywz44, h) new_mkBalBranch6MkBalBranch31(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz1184000), Succ(ywz1183000), h) -> new_mkBalBranch6MkBalBranch31(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz1184000, ywz1183000, h) new_addToFM_C20(Neg(Zero), ywz741, ywz742, ywz743, ywz744, Pos(Zero), ywz9, False, h) -> Branch(Pos(Zero), new_addToFM0(ywz741, ywz9, h), ywz742, ywz743, ywz744) new_splitGT6(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitGT30(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Zero), Neg(Succ(ywz115400)), h) -> new_mkBalBranch6MkBalBranch42(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_addToFM_C5(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz400, ywz41, h) -> new_addToFM_C20(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(ywz400), ywz41, new_lt(Pos(ywz400), ywz440), h) new_splitLT30(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitLT26(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_splitGT30(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> ywz44 new_splitLT13(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Succ(ywz18240), Succ(ywz18250), cc) -> new_splitLT13(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, ywz18240, ywz18250, cc) new_splitLT30(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> new_splitLT9(ywz43, h) new_splitLT11(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Succ(ywz18150), Succ(ywz18160), bh) -> new_splitLT11(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, ywz18150, ywz18160, bh) new_mkBalBranch6MkBalBranch42(ywz1007, ywz73, ywz70, ywz71, Branch(ywz10060, ywz10061, ywz10062, ywz10063, ywz10064), h) -> new_mkBalBranch6MkBalBranch01(ywz1007, ywz73, ywz70, ywz71, ywz10060, ywz10061, ywz10062, ywz10063, ywz10064, new_lt(new_sizeFM(ywz10063, h), new_sr0(new_sizeFM(ywz10064, h))), h) new_mkVBalBranch3Size_r(ywz70, ywz71, ywz72, ywz73, ywz74, ywz60, ywz61, ywz62, ywz63, ywz64, h) -> new_sizeFM(Branch(ywz60, ywz61, ywz62, ywz63, ywz64), h) new_esEs4 -> False new_addToFM1(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, h) -> new_addToFM_C30(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, h) new_splitGT30(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_mkVBalBranch5(ywz41, new_splitGT5(ywz43, ywz5000, h), ywz44, h) new_splitGT30(Neg(ywz400), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT6(ywz44, ywz5000, h) new_splitLT23(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Zero, Zero, bf) -> new_splitLT24(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, bf) new_primMinusNat0(Succ(ywz104900), Zero) -> Pos(Succ(ywz104900)) new_splitGT30(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> new_mkVBalBranch2(Succ(ywz4000), ywz41, new_splitGT8(ywz43, h), ywz44, h) new_mkBalBranch0(ywz741, ywz743, ywz1247, h) -> new_mkBalBranch6MkBalBranch5(ywz1247, ywz743, Pos(Zero), ywz741, ywz1247, new_lt(new_ps(new_mkBalBranch6Size_l(ywz1247, ywz743, Pos(Zero), ywz741, h), new_mkBalBranch6Size_r(ywz1247, ywz743, Pos(Zero), ywz741, h)), Pos(Succ(Succ(Zero)))), h) new_ps(Pos(ywz10490), Pos(ywz10480)) -> Pos(new_primPlusNat0(ywz10490, ywz10480)) new_splitGT23(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Succ(ywz4610), ca) -> new_splitGT24(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ca) new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Zero), Pos(Succ(ywz115400)), h) -> new_mkBalBranch6MkBalBranch45(ywz1007, ywz73, ywz70, ywz71, ywz1006, Zero, ywz115400, h) new_splitGT25(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Succ(ywz4520), cd) -> new_splitGT25(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, ywz4510, ywz4520, cd) new_splitLT25(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, bg) -> new_splitLT11(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz432), Succ(ywz427), bg) new_ps(Neg(ywz10490), Neg(ywz10480)) -> Neg(new_primPlusNat0(ywz10490, ywz10480)) new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Succ(ywz118400)), Pos(ywz11830), h) -> new_mkBalBranch6MkBalBranch32(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_splitLT23(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Zero, Succ(ywz4430), bf) -> new_splitLT6(ywz439, ywz441, bf) new_addToFM_C0(EmptyFM, ywz50, ywz9, h) -> Branch(ywz50, ywz9, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h)) new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_splitLT8(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), h) -> new_splitLT30(ywz430, ywz431, ywz432, ywz433, ywz434, Pos(Zero), h) new_mkBalBranch6MkBalBranch30(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz118300), ywz118400, h) -> new_mkBalBranch6MkBalBranch31(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz118300, ywz118400, h) new_addToFM_C20(Pos(Zero), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, h) -> new_mkBalBranch0(ywz741, ywz743, new_addToFM_C0(ywz744, Pos(Succ(ywz5000)), ywz9, h), h) new_splitLT6(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz5000, h) -> new_splitLT30(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Succ(ywz5000)), h) new_mkBalBranch6MkBalBranch36(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz118400, Zero, h) -> new_mkBalBranch6MkBalBranch37(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkVBalBranch2(ywz400, ywz41, EmptyFM, ywz44, h) -> new_addToFM2(ywz44, ywz400, ywz41, h) new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_splitLT30(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> ywz43 new_addToFM_C20(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, True, h) -> new_mkBalBranch6MkBalBranch5(ywz744, new_addToFM_C0(ywz743, ywz50, ywz9, h), ywz740, ywz741, ywz744, new_lt(new_ps(new_mkBalBranch6Size_l(ywz744, new_addToFM_C0(ywz743, ywz50, ywz9, h), ywz740, ywz741, h), new_mkBalBranch6Size_r(ywz744, new_addToFM_C0(ywz743, ywz50, ywz9, h), ywz740, ywz741, h)), Pos(Succ(Succ(Zero)))), h) new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_splitLT7(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), ywz5000, h) -> new_splitLT30(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h) new_mkVBalBranch5(ywz41, Branch(ywz140, ywz141, ywz142, ywz143, ywz144), Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_mkVBalBranch30(Zero, ywz41, ywz140, ywz141, ywz142, ywz143, ywz144, ywz440, ywz441, ywz442, ywz443, ywz444, h) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_addToFM_C20(Pos(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, h) -> new_addToFM_C11(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz5000, ywz74000, h) new_mkBalBranch6MkBalBranch40(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz1154, h) -> new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, new_mkBalBranch6Size_r(ywz1007, ywz73, ywz70, ywz71, h), ywz1154, h) new_mkBalBranch6MkBalBranch45(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz115400), ywz115700, h) -> new_mkBalBranch6MkBalBranch41(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz115400, ywz115700, h) new_splitGT30(Pos(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT25(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz5000, ywz4000, h) new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Zero), Pos(Zero), h) -> new_mkBalBranch6MkBalBranch44(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_mkBalBranch6MkBalBranch31(ywz1007, ywz73, ywz70, ywz71, ywz1006, Zero, Zero, h) -> new_mkBalBranch6MkBalBranch33(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_addToFM_C13(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Succ(ywz13690), cb) -> new_addToFM_C13(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, ywz13680, ywz13690, cb) new_splitGT25(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Zero, Zero, cd) -> new_splitGT26(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, cd) new_addToFM_C20(Neg(Zero), ywz741, ywz742, ywz743, ywz744, Neg(Succ(ywz5000)), ywz9, False, h) -> Branch(Neg(Succ(ywz5000)), new_addToFM0(ywz741, ywz9, h), ywz742, ywz743, ywz744) new_splitGT30(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> ywz44 new_splitLT7(EmptyFM, ywz5000, h) -> new_splitLT40(ywz5000, h) new_mkVBalBranch6(ywz50, ywz9, EmptyFM, ywz630, ywz631, ywz632, ywz633, ywz634, h) -> new_addToFM1(ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, h) new_mkBalBranch6MkBalBranch31(ywz1007, ywz73, ywz70, ywz71, ywz1006, Zero, Succ(ywz1183000), h) -> new_mkBalBranch6MkBalBranch32(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_sr0(Neg(ywz12090)) -> Neg(new_primMulNat1(ywz12090)) new_splitLT8(EmptyFM, h) -> new_emptyFM(h) new_sizeFM0(Branch(ywz12380, ywz12381, ywz12382, ywz12383, ywz12384), bd, be) -> ywz12382 new_addToFM_C11(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Succ(ywz14190), Zero, bb) -> new_mkBalBranch(ywz1412, ywz1413, ywz1415, new_addToFM_C0(ywz1416, Pos(Succ(ywz1417)), ywz1418, bb), bb) new_addToFM_C11(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Zero, Succ(ywz14200), bb) -> new_addToFM_C12(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, bb) new_splitGT8(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_splitGT30(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Zero), h) new_splitLT30(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> new_mkVBalBranch1(ywz4000, ywz41, ywz43, new_splitLT9(ywz44, h), h) new_primPlusNat3 -> Zero new_mkVBalBranch2(ywz400, ywz41, Branch(ywz120, ywz121, ywz122, ywz123, ywz124), Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_mkVBalBranch3MkVBalBranch20(ywz120, ywz121, ywz122, ywz123, ywz124, ywz440, ywz441, ywz442, ywz443, ywz444, Pos(ywz400), ywz41, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz120, ywz121, ywz122, ywz123, ywz124, ywz440, ywz441, ywz442, ywz443, ywz444, h)), new_mkVBalBranch3Size_r(ywz120, ywz121, ywz122, ywz123, ywz124, ywz440, ywz441, ywz442, ywz443, ywz444, h)), h) new_esEs3(Zero, ywz82100) -> new_esEs5 new_primMinusNat0(Succ(ywz104900), Succ(ywz104800)) -> new_primMinusNat0(ywz104900, ywz104800) new_splitGT12(ywz1837, ywz1838, ywz1839, ywz1840, ywz1841, ywz1842, True, ba) -> new_mkVBalBranch1(ywz1837, ywz1838, new_splitGT5(ywz1840, ywz1842, ba), ywz1841, ba) new_primPlusNat2(Succ(ywz720000)) -> Succ(Succ(new_primPlusNat4(ywz720000))) new_mkBalBranch6MkBalBranch11(ywz1007, ywz730, ywz731, ywz732, ywz733, ywz734, ywz70, ywz71, ywz1006, True, h) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ywz730, ywz731, ywz733, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ywz70, ywz71, ywz734, ywz1006, ty_Int, h), ty_Int, h) new_splitLT14(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, cc) -> ywz1821 new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Zero), Neg(Zero), h) -> new_mkBalBranch6MkBalBranch44(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_addToFM0(ywz741, ywz9, h) -> ywz9 new_splitLT13(ywz1818, ywz1819, ywz1820, ywz1821, ywz1822, ywz1823, Succ(ywz18240), Zero, cc) -> new_mkVBalBranch1(ywz1818, ywz1819, ywz1821, new_splitLT6(ywz1822, ywz1823, cc), cc) new_splitGT30(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitGT23(ywz4000, ywz41, ywz42, ywz43, ywz44, ywz5000, ywz4000, ywz5000, h) new_splitLT11(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Succ(ywz18150), Zero, bh) -> new_mkVBalBranch2(Succ(ywz1809), ywz1810, ywz1812, new_splitLT7(ywz1813, ywz1814, bh), bh) new_mkVBalBranch3MkVBalBranch10(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, True, h) -> new_mkBalBranch6MkBalBranch5(new_mkVBalBranch6(ywz50, ywz9, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h), ywz743, ywz740, ywz741, new_mkVBalBranch6(ywz50, ywz9, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h), new_lt(new_ps(new_mkBalBranch6Size_l(new_mkVBalBranch6(ywz50, ywz9, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h), ywz743, ywz740, ywz741, h), new_mkBalBranch6Size_r(new_mkVBalBranch6(ywz50, ywz9, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h), ywz743, ywz740, ywz741, h)), Pos(Succ(Succ(Zero)))), h) new_splitLT30(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_mkVBalBranch2(Zero, ywz41, ywz43, new_splitLT7(ywz44, ywz5000, h), h) new_primPlusNat0(Succ(ywz250000), Succ(ywz372000)) -> Succ(Succ(new_primPlusNat0(ywz250000, ywz372000))) new_addToFM_C4(Branch(ywz150, ywz151, ywz152, ywz153, ywz154), ywz400, ywz41, h) -> new_addToFM_C20(ywz150, ywz151, ywz152, ywz153, ywz154, Neg(ywz400), ywz41, new_lt(Neg(ywz400), ywz150), h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Zero), Neg(Zero), h) -> new_mkBalBranch6MkBalBranch33(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_splitLT11(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Zero, Succ(ywz18160), bh) -> new_splitLT12(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, bh) new_primPlusNat4(Succ(ywz7200000)) -> Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(ywz7200000))), Succ(Succ(Succ(ywz7200000)))), Succ(Succ(ywz7200000))), ywz7200000))) new_mkVBalBranch5(ywz41, Branch(ywz140, ywz141, ywz142, ywz143, ywz144), EmptyFM, h) -> new_mkVBalBranch40(Zero, ywz41, ywz140, ywz141, ywz142, ywz143, ywz144, h) new_splitGT13(ywz1827, ywz1828, ywz1829, ywz1830, ywz1831, ywz1832, False, bc) -> ywz1831 new_mkVBalBranch1(ywz4000, ywz41, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), Branch(ywz100, ywz101, ywz102, ywz103, ywz104), h) -> new_mkVBalBranch3MkVBalBranch20(ywz430, ywz431, ywz432, ywz433, ywz434, ywz100, ywz101, ywz102, ywz103, ywz104, Neg(Succ(ywz4000)), ywz41, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz430, ywz431, ywz432, ywz433, ywz434, ywz100, ywz101, ywz102, ywz103, ywz104, h)), new_mkVBalBranch3Size_r(ywz430, ywz431, ywz432, ywz433, ywz434, ywz100, ywz101, ywz102, ywz103, ywz104, h)), h) new_mkVBalBranch40(ywz400, ywz41, ywz430, ywz431, ywz432, ywz433, ywz434, h) -> new_addToFM_C4(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz400, ywz41, h) new_mkBalBranch6MkBalBranch01(ywz1007, ywz73, ywz70, ywz71, ywz10060, ywz10061, ywz10062, EmptyFM, ywz10064, False, h) -> error([]) new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Zero), Neg(Succ(ywz115400)), h) -> new_mkBalBranch6MkBalBranch46(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz115400, Zero, h) new_splitLT26(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Succ(ywz4330), Zero, bg) -> new_splitLT25(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, bg) new_mkBalBranch6MkBalBranch46(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz115700, Zero, h) -> new_mkBalBranch6MkBalBranch42(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch47(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) -> new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, new_mkBalBranch6Size_l(ywz1007, ywz73, ywz70, ywz71, h), new_sr(new_mkBalBranch6Size_r(ywz1007, ywz73, ywz70, ywz71, h)), h) new_addToFM_C20(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Succ(ywz5000)), ywz9, False, h) -> new_addToFM_C13(ywz74000, ywz741, ywz742, ywz743, ywz744, ywz5000, ywz9, ywz74000, ywz5000, h) new_addToFM_C30(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, h) -> new_addToFM_C20(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, new_lt(ywz50, ywz740), h) new_primMulNat(Zero) -> Zero new_mkVBalBranch30(ywz400, ywz41, ywz430, ywz431, ywz432, ywz433, ywz434, ywz130, ywz131, ywz132, ywz133, ywz134, h) -> new_mkVBalBranch3MkVBalBranch20(ywz430, ywz431, ywz432, ywz433, ywz434, ywz130, ywz131, ywz132, ywz133, ywz134, Neg(ywz400), ywz41, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz430, ywz431, ywz432, ywz433, ywz434, ywz130, ywz131, ywz132, ywz133, ywz134, h)), new_mkVBalBranch3Size_r(ywz430, ywz431, ywz432, ywz433, ywz434, ywz130, ywz131, ywz132, ywz133, ywz134, h)), h) new_splitLT30(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> ywz43 new_splitLT30(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> ywz43 new_primPlusNat1(Succ(ywz72000)) -> Succ(Succ(new_primPlusNat2(ywz72000))) new_esEs6(Zero, Zero) -> new_esEs4 new_splitLT12(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, bh) -> ywz1812 new_splitLT30(Neg(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), Branch(ywz440, ywz441, ywz442, ywz443, ywz444), Pos(Succ(ywz5000)), h) -> new_mkVBalBranch4(ywz400, ywz41, ywz430, ywz431, ywz432, ywz433, ywz434, new_splitLT30(ywz440, ywz441, ywz442, ywz443, ywz444, Pos(Succ(ywz5000)), h), h) new_splitGT5(EmptyFM, ywz5000, h) -> new_emptyFM(h) new_mkBranch(ywz1234, ywz1235, ywz1236, ywz1237, ywz1238, bd, be) -> Branch(ywz1235, ywz1236, new_mkBranchUnbox(ywz1238, ywz1235, ywz1237, new_ps(new_ps(Pos(Succ(Zero)), new_sizeFM0(ywz1237, bd, be)), new_sizeFM0(ywz1238, bd, be)), bd, be), ywz1237, ywz1238) new_esEs1(ywz82100, Zero) -> new_esEs2 new_primPlusNat2(Zero) -> Succ(Succ(new_primPlusNat5(new_primPlusNat3))) new_addToFM_C20(Pos(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Zero), ywz9, False, h) -> Branch(Pos(Zero), new_addToFM0(ywz741, ywz9, h), ywz742, ywz743, ywz744) new_ps(Pos(ywz10490), Neg(ywz10480)) -> new_primMinusNat0(ywz10490, ywz10480) new_ps(Neg(ywz10490), Pos(ywz10480)) -> new_primMinusNat0(ywz10480, ywz10490) new_sr(Neg(ywz10370)) -> Neg(new_primMulNat(ywz10370)) new_mkVBalBranch1(ywz4000, ywz41, EmptyFM, ywz10, h) -> new_addToFM(ywz10, ywz4000, ywz41, h) new_splitLT23(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz4420), Succ(ywz4430), bf) -> new_splitLT23(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, ywz4420, ywz4430, bf) new_mkBalBranch6MkBalBranch37(ywz1007, EmptyFM, ywz70, ywz71, ywz1006, h) -> error([]) new_primMulNat0(ywz7200) -> Succ(Succ(new_primPlusNat1(ywz7200))) new_esEs5 -> True new_splitGT30(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Neg(Zero), h) -> new_splitGT7(ywz44, h) new_addToFM_C20(Pos(Zero), ywz741, ywz742, ywz743, ywz744, Neg(Zero), ywz9, False, h) -> Branch(Neg(Zero), new_addToFM0(ywz741, ywz9, h), ywz742, ywz743, ywz744) new_mkVBalBranch4(ywz400, ywz41, ywz430, ywz431, ywz432, ywz433, ywz434, Branch(ywz130, ywz131, ywz132, ywz133, ywz134), h) -> new_mkVBalBranch30(ywz400, ywz41, ywz430, ywz431, ywz432, ywz433, ywz434, ywz130, ywz131, ywz132, ywz133, ywz134, h) new_splitLT11(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, Zero, Zero, bh) -> new_splitLT12(ywz1809, ywz1810, ywz1811, ywz1812, ywz1813, ywz1814, bh) new_splitGT25(ywz445, ywz446, ywz447, ywz448, ywz449, ywz450, Succ(ywz4510), Zero, cd) -> new_splitGT6(ywz449, ywz450, cd) new_splitLT30(Neg(ywz400), ywz41, ywz42, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), EmptyFM, Pos(Succ(ywz5000)), h) -> new_mkVBalBranch4(ywz400, ywz41, ywz430, ywz431, ywz432, ywz433, ywz434, new_splitLT40(ywz5000, h), h) new_splitGT8(EmptyFM, h) -> new_emptyFM(h) new_mkBalBranch6MkBalBranch41(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz1157000), Succ(ywz1154000), h) -> new_mkBalBranch6MkBalBranch41(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz1157000, ywz1154000, h) new_splitLT23(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz4420), Zero, bf) -> new_splitLT24(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, bf) new_splitLT30(Neg(Zero), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitLT6(ywz43, ywz5000, h) new_addToFM_C0(Branch(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434), ywz50, ywz9, h) -> new_addToFM_C30(ywz7430, ywz7431, ywz7432, ywz7433, ywz7434, ywz50, ywz9, h) new_mkBalBranch(ywz1412, ywz1413, ywz1415, ywz1434, bb) -> new_mkBalBranch6MkBalBranch5(ywz1434, ywz1415, Pos(Succ(ywz1412)), ywz1413, ywz1434, new_lt(new_ps(new_mkBalBranch6Size_l(ywz1434, ywz1415, Pos(Succ(ywz1412)), ywz1413, bb), new_mkBalBranch6Size_r(ywz1434, ywz1415, Pos(Succ(ywz1412)), ywz1413, bb)), Pos(Succ(Succ(Zero)))), bb) new_addToFM_C20(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Pos(Zero), ywz9, False, h) -> new_mkBalBranch1(Succ(ywz74000), ywz741, ywz743, new_addToFM_C0(ywz744, Pos(Zero), ywz9, h), h) new_addToFM_C20(Neg(ywz7400), ywz741, ywz742, ywz743, ywz744, Pos(Succ(ywz5000)), ywz9, False, h) -> new_mkBalBranch1(ywz7400, ywz741, ywz743, new_addToFM_C0(ywz744, Pos(Succ(ywz5000)), ywz9, h), h) new_mkVBalBranch2(ywz400, ywz41, Branch(ywz120, ywz121, ywz122, ywz123, ywz124), EmptyFM, h) -> new_addToFM2(Branch(ywz120, ywz121, ywz122, ywz123, ywz124), ywz400, ywz41, h) new_primPlusNat0(Succ(ywz250000), Zero) -> Succ(ywz250000) new_primPlusNat0(Zero, Succ(ywz372000)) -> Succ(ywz372000) new_splitLT26(ywz427, ywz428, ywz429, ywz430, ywz431, ywz432, Zero, Succ(ywz4340), bg) -> new_splitLT7(ywz430, ywz432, bg) new_esEs2 -> False new_mkBalBranch6MkBalBranch43(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) -> new_mkBalBranch6MkBalBranch47(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Succ(ywz115700)), Neg(ywz11540), h) -> new_mkBalBranch6MkBalBranch42(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch41(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz1157000), Zero, h) -> new_mkBalBranch6MkBalBranch42(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkVBalBranch1(ywz4000, ywz41, Branch(ywz430, ywz431, ywz432, ywz433, ywz434), EmptyFM, h) -> new_addToFM(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), ywz4000, ywz41, h) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_addToFM_C11(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, Zero, Zero, bb) -> new_addToFM_C12(ywz1412, ywz1413, ywz1414, ywz1415, ywz1416, ywz1417, ywz1418, bb) new_mkBalBranch6MkBalBranch32(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) -> new_mkBalBranch6MkBalBranch34(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch11(ywz1007, ywz730, ywz731, ywz732, ywz733, Branch(ywz7340, ywz7341, ywz7342, ywz7343, ywz7344), ywz70, ywz71, ywz1006, False, h) -> new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), ywz7340, ywz7341, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), ywz730, ywz731, ywz733, ywz7343, ty_Int, h), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), ywz70, ywz71, ywz7344, ywz1006, ty_Int, h), ty_Int, h) new_primMulNat1(Zero) -> Zero new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_mkBranchUnbox(ywz1238, ywz1235, ywz1237, ywz1245, bd, be) -> ywz1245 new_splitLT30(Neg(Succ(ywz4000)), ywz41, ywz42, ywz43, ywz44, Pos(Zero), h) -> new_mkVBalBranch1(ywz4000, ywz41, ywz43, new_splitLT8(ywz44, h), h) new_mkBalBranch6MkBalBranch01(ywz1007, ywz73, ywz70, ywz71, ywz10060, ywz10061, ywz10062, ywz10063, ywz10064, True, h) -> new_mkBranch(Succ(Succ(Zero)), ywz10060, ywz10061, new_mkBranch(Succ(Succ(Succ(Zero))), ywz70, ywz71, ywz73, ywz10063, ty_Int, h), ywz10064, ty_Int, h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Succ(ywz118400)), Neg(ywz11830), h) -> new_mkBalBranch6MkBalBranch37(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Succ(ywz118400)), Neg(ywz11830), h) -> new_mkBalBranch6MkBalBranch30(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz11830, ywz118400, h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Zero), Neg(Zero), h) -> new_mkBalBranch6MkBalBranch33(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Zero), Pos(Zero), h) -> new_mkBalBranch6MkBalBranch33(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_primMinusNat0(Zero, Succ(ywz104800)) -> Neg(Succ(ywz104800)) new_mkVBalBranch7(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, Branch(ywz6330, ywz6331, ywz6332, ywz6333, ywz6334), h) -> new_mkVBalBranch31(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h) new_mkVBalBranch3MkVBalBranch20(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, True, h) -> new_mkBalBranch6MkBalBranch5(ywz634, new_mkVBalBranch7(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, ywz633, h), ywz630, ywz631, ywz634, new_lt(new_ps(new_mkBalBranch6Size_l(ywz634, new_mkVBalBranch7(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, ywz633, h), ywz630, ywz631, h), new_mkBalBranch6Size_r(ywz634, new_mkVBalBranch7(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, ywz633, h), ywz630, ywz631, h)), Pos(Succ(Succ(Zero)))), h) new_splitGT24(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ca) -> new_splitGT12(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, new_lt(Neg(Succ(ywz459)), Neg(Succ(ywz454))), ca) new_addToFM(ywz10, ywz4000, ywz41, h) -> new_addToFM_C4(ywz10, Succ(ywz4000), ywz41, h) new_mkBalBranch6Size_l(ywz634, ywz1155, ywz630, ywz631, h) -> new_sizeFM(ywz1155, h) new_splitLT9(Branch(ywz430, ywz431, ywz432, ywz433, ywz434), h) -> new_splitLT30(ywz430, ywz431, ywz432, ywz433, ywz434, Neg(Zero), h) new_primPlusNat5(ywz302) -> Succ(Succ(ywz302)) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_mkBalBranch6MkBalBranch30(ywz1007, ywz73, ywz70, ywz71, ywz1006, Zero, ywz118400, h) -> new_mkBalBranch6MkBalBranch32(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_splitGT23(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Zero, Zero, ca) -> new_splitGT24(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, ca) new_splitGT7(EmptyFM, h) -> new_emptyFM(h) new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_splitLT24(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, bf) -> new_splitLT13(ywz436, ywz437, ywz438, ywz439, ywz440, ywz441, Succ(ywz436), Succ(ywz441), bf) new_splitGT7(Branch(ywz440, ywz441, ywz442, ywz443, ywz444), h) -> new_splitGT30(ywz440, ywz441, ywz442, ywz443, ywz444, Neg(Zero), h) new_splitGT30(Pos(Zero), ywz41, ywz42, ywz43, ywz44, Pos(Succ(ywz5000)), h) -> new_splitGT6(ywz44, ywz5000, h) new_primMulNat1(Succ(ywz120900)) -> new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywz120900)), Succ(ywz120900)) new_mkVBalBranch31(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h) -> new_mkVBalBranch3MkVBalBranch20(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), h) new_splitLT40(ywz5000, h) -> new_emptyFM(h) new_splitLT30(Pos(ywz400), ywz41, ywz42, ywz43, ywz44, Neg(Succ(ywz5000)), h) -> new_splitLT6(ywz43, ywz5000, h) new_addToFM2(ywz44, ywz400, ywz41, h) -> new_addToFM_C5(ywz44, ywz400, ywz41, h) new_mkBalBranch6MkBalBranch01(ywz1007, ywz73, ywz70, ywz71, ywz10060, ywz10061, ywz10062, Branch(ywz100630, ywz100631, ywz100632, ywz100633, ywz100634), ywz10064, False, h) -> new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), ywz100630, ywz100631, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), ywz70, ywz71, ywz73, ywz100633, ty_Int, h), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), ywz10060, ywz10061, ywz100634, ywz10064, ty_Int, h), ty_Int, h) new_emptyFM(h) -> EmptyFM new_mkVBalBranch7(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, EmptyFM, h) -> new_addToFM1(ywz740, ywz741, ywz742, ywz743, ywz744, ywz50, ywz9, h) new_mkBalBranch6MkBalBranch34(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) -> new_mkBranch(Succ(Zero), ywz70, ywz71, ywz73, ywz1006, ty_Int, h) new_mkBalBranch1(ywz7400, ywz741, ywz743, ywz1243, h) -> new_mkBalBranch6MkBalBranch5(ywz1243, ywz743, Neg(ywz7400), ywz741, ywz1243, new_lt(new_ps(new_mkBalBranch6Size_l(ywz1243, ywz743, Neg(ywz7400), ywz741, h), new_mkBalBranch6Size_r(ywz1243, ywz743, Neg(ywz7400), ywz741, h)), Pos(Succ(Succ(Zero)))), h) new_splitGT23(ywz454, ywz455, ywz456, ywz457, ywz458, ywz459, Succ(ywz4600), Zero, ca) -> new_splitGT5(ywz458, ywz459, ca) new_primPlusNat4(Zero) -> Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Zero))) new_mkBalBranch6MkBalBranch45(ywz1007, ywz73, ywz70, ywz71, ywz1006, Zero, ywz115700, h) -> new_mkBalBranch6MkBalBranch43(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Pos(Zero), Pos(Zero), h) -> new_mkBalBranch6MkBalBranch33(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch42(ywz1007, ywz73, ywz70, ywz71, EmptyFM, h) -> error([]) new_mkBalBranch6MkBalBranch48(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Succ(ywz115700)), Pos(ywz11540), h) -> new_mkBalBranch6MkBalBranch43(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch46(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz115700, Succ(ywz115400), h) -> new_mkBalBranch6MkBalBranch41(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz115700, ywz115400, h) new_addToFM_C13(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Succ(ywz13680), Zero, cb) -> new_mkBalBranch1(Succ(ywz1361), ywz1362, ywz1364, new_addToFM_C0(ywz1365, Neg(Succ(ywz1366)), ywz1367, cb), cb) new_mkBalBranch6MkBalBranch44(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) -> new_mkBalBranch6MkBalBranch47(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_mkBalBranch6MkBalBranch35(ywz1007, ywz73, ywz70, ywz71, ywz1006, Neg(Zero), Pos(Succ(ywz118300)), h) -> new_mkBalBranch6MkBalBranch32(ywz1007, ywz73, ywz70, ywz71, ywz1006, h) new_sizeFM0(EmptyFM, bd, be) -> Pos(Zero) new_mkBalBranch6MkBalBranch11(ywz1007, ywz730, ywz731, ywz732, ywz733, EmptyFM, ywz70, ywz71, ywz1006, False, h) -> error([]) new_addToFM_C20(Neg(Succ(ywz74000)), ywz741, ywz742, ywz743, ywz744, Neg(Zero), ywz9, False, h) -> new_mkBalBranch1(Succ(ywz74000), ywz741, ywz743, new_addToFM_C0(ywz744, Neg(Zero), ywz9, h), h) new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_addToFM_C13(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, Zero, Zero, cb) -> new_addToFM_C14(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, cb) new_mkVBalBranch4(ywz400, ywz41, ywz430, ywz431, ywz432, ywz433, ywz434, EmptyFM, h) -> new_mkVBalBranch40(ywz400, ywz41, ywz430, ywz431, ywz432, ywz433, ywz434, h) new_addToFM_C14(ywz1361, ywz1362, ywz1363, ywz1364, ywz1365, ywz1366, ywz1367, cb) -> Branch(Neg(Succ(ywz1366)), new_addToFM0(ywz1362, ywz1367, cb), ywz1363, ywz1364, ywz1365) The set Q consists of the following terms: new_sizeFM0(Branch(x0, x1, x2, x3, x4), x5, x6) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Neg(Succ(x5)), Neg(x6), x7) new_splitLT23(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Pos(Succ(x5)), Neg(x6), x7) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Neg(Succ(x5)), Pos(x6), x7) new_esEs3(Zero, x0) new_mkBalBranch6Size_r(x0, x1, x2, x3, x4) new_addToFM0(x0, x1, x2) new_splitLT30(Pos(x0), x1, x2, x3, x4, Neg(Succ(x5)), x6) new_splitGT24(x0, x1, x2, x3, x4, x5, x6) new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, x5) new_splitLT6(EmptyFM, x0, x1) new_splitLT12(x0, x1, x2, x3, x4, x5, x6) new_mkVBalBranch1(x0, x1, EmptyFM, x2, x3) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Neg(Succ(x5)), Pos(x6), x7) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Pos(Succ(x5)), Neg(x6), x7) new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, Zero, Zero, x5) new_addToFM_C20(Pos(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5, False, x6) new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5) new_addToFM_C20(Neg(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5, False, x6) new_primMulNat(Succ(x0)) new_splitLT11(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) new_emptyFM(x0) new_splitGT30(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Succ(x5)), x6) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Pos(Succ(x5)), Pos(x6), x7) new_mkVBalBranch3MkVBalBranch10(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12) new_addToFM_C20(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5, False, x6) new_splitLT13(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12, False, x13) new_splitLT30(Neg(x0), x1, x2, EmptyFM, x3, Pos(Succ(x4)), x5) new_addToFM_C0(Branch(x0, x1, x2, x3, x4), x5, x6, x7) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Neg(Succ(x5)), Neg(x6), x7) new_primMulNat1(Succ(x0)) new_splitLT11(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) new_splitGT30(Neg(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5) new_splitGT30(Pos(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5) new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, Branch(x4, x5, x6, x7, x8), x9) new_mkBalBranch0(x0, x1, x2, x3) new_addToFM2(x0, x1, x2, x3) new_primPlusNat0(Succ(x0), Zero) new_ps(Pos(x0), Pos(x1)) new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) new_esEs1(x0, Succ(x1)) new_primMinusNat0(Zero, Zero) new_splitGT30(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5) new_ps(Neg(x0), Neg(x1)) new_mkVBalBranch5(x0, EmptyFM, x1, x2) new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(x0))) new_splitGT30(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Succ(x5)), x6) new_splitGT25(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) new_esEs2 new_esEs0(Pos(Zero), Pos(Succ(x0))) new_splitGT13(x0, x1, x2, x3, x4, x5, False, x6) new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, EmptyFM, x4) new_esEs0(Neg(Zero), Neg(Zero)) new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, False, x5) new_splitGT12(x0, x1, x2, x3, x4, x5, False, x6) new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, Succ(x5), Zero, x6) new_addToFM_C14(x0, x1, x2, x3, x4, x5, x6, x7) new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5, x6) new_mkVBalBranch1(x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12) new_addToFM_C20(Neg(Zero), x0, x1, x2, x3, Neg(Zero), x4, False, x5) new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, x11, x12, False, x13) new_splitLT26(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) new_addToFM_C20(Neg(Zero), x0, x1, x2, x3, Neg(Succ(x4)), x5, False, x6) new_mkVBalBranch1(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7) new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, x5) new_splitGT23(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) new_primMinusNat0(Succ(x0), Zero) new_mkVBalBranch5(x0, Branch(x1, x2, x3, x4, x5), Branch(x6, x7, x8, x9, x10), x11) new_mkBranch(x0, x1, x2, x3, x4, x5, x6) new_primPlusNat0(Zero, Zero) new_addToFM(x0, x1, x2, x3) new_addToFM_C5(Branch(x0, x1, x2, x3, x4), x5, x6, x7) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Pos(Zero), Pos(Zero), x5) new_splitLT30(Pos(Zero), x0, x1, x2, x3, Pos(Zero), x4) new_mkVBalBranch3MkVBalBranch20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, True, x12) new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) new_esEs6(Succ(x0), Succ(x1)) new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) new_mkVBalBranch3MkVBalBranch20(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12) new_primPlusNat1(Zero) new_splitLT30(Neg(Zero), x0, x1, x2, x3, Neg(Succ(x4)), x5) new_primPlusNat2(Zero) new_primPlusNat4(Succ(x0)) new_splitGT25(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Pos(Zero), Neg(Zero), x5) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Neg(Zero), Pos(Zero), x5) new_splitGT25(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) new_splitLT14(x0, x1, x2, x3, x4, x5, x6) new_splitLT6(Branch(x0, x1, x2, x3, x4), x5, x6) new_mkVBalBranch4(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12) new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, x4, Zero, Succ(x5), x6) new_splitLT7(Branch(x0, x1, x2, x3, x4), x5, x6) new_lt(x0, x1) new_splitLT24(x0, x1, x2, x3, x4, x5, x6) new_splitGT5(EmptyFM, x0, x1) new_splitGT5(Branch(x0, x1, x2, x3, x4), x5, x6) new_addToFM_C20(x0, x1, x2, x3, x4, x5, x6, True, x7) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_splitLT13(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) new_splitLT30(Neg(Zero), x0, x1, x2, x3, Pos(Zero), x4) new_splitLT30(Pos(Zero), x0, x1, x2, x3, Neg(Zero), x4) new_esEs3(Succ(x0), x1) new_addToFM_C20(Pos(Zero), x0, x1, x2, x3, Pos(Zero), x4, False, x5) new_primPlusNat4(Zero) new_splitGT23(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) new_primPlusNat0(Zero, Succ(x0)) new_splitGT30(Pos(x0), x1, x2, x3, x4, Neg(Succ(x5)), x6) new_splitGT30(Neg(x0), x1, x2, x3, x4, Pos(Succ(x5)), x6) new_esEs6(Succ(x0), Zero) new_primPlusNat5(x0) new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, x7) new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, Zero, Succ(x5), x6) new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7) new_splitGT30(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5) new_mkVBalBranch2(x0, x1, EmptyFM, x2, x3) new_splitLT9(Branch(x0, x1, x2, x3, x4), x5) new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, True, x5) new_splitGT23(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) new_splitGT7(Branch(x0, x1, x2, x3, x4), x5) new_sizeFM0(EmptyFM, x0, x1) new_splitGT6(Branch(x0, x1, x2, x3, x4), x5, x6) new_mkVBalBranch6(x0, x1, EmptyFM, x2, x3, x4, x5, x6, x7) new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Succ(x5), x6, x7) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Neg(Zero), Pos(Succ(x5)), x6) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Pos(Zero), Neg(Succ(x5)), x6) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Pos(Succ(x5)), Pos(x6), x7) new_addToFM_C20(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Succ(x5)), x6, False, x7) new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, x7, x8, True, x9) new_splitLT30(Neg(x0), x1, x2, Branch(x3, x4, x5, x6, x7), EmptyFM, Pos(Succ(x8)), x9) new_sr0(Pos(x0)) new_splitLT30(Pos(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5) new_splitLT30(Neg(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Pos(Zero), Neg(Succ(x5)), x6) new_splitLT23(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Neg(Zero), Pos(Succ(x5)), x6) new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8) new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, Succ(x5), Succ(x6), x7) new_splitLT30(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5) new_esEs6(Zero, Zero) new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, x4, Succ(x5), Succ(x6), x7) new_splitLT9(EmptyFM, x0) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Neg(Zero), Neg(Zero), x5) new_mkVBalBranch3MkVBalBranch10(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, False, x12) new_esEs0(Pos(Succ(x0)), Pos(x1)) new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5, Zero, x6) new_splitLT30(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5) new_mkBalBranch6MkBalBranch37(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9) new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Zero, x5, x6) new_splitLT8(EmptyFM, x0) new_mkBalBranch6Size_l(x0, x1, x2, x3, x4) new_addToFM_C0(EmptyFM, x0, x1, x2) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Pos(Zero), Pos(Succ(x5)), x6) new_splitGT8(EmptyFM, x0) new_sizeFM(Branch(x0, x1, x2, x3, x4), x5) new_primMinusNat0(Succ(x0), Succ(x1)) new_mkVBalBranch7(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12) new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, Succ(x5), x6, x7) new_splitGT26(x0, x1, x2, x3, x4, x5, x6) new_splitLT30(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Succ(x5)), x6) new_splitLT13(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, x4, Succ(x5), Zero, x6) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Pos(Zero), Neg(Zero), x5) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Neg(Zero), Pos(Zero), x5) new_addToFM_C4(EmptyFM, x0, x1, x2) new_mkVBalBranch2(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7) new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5, Succ(x6), x7) new_addToFM1(x0, x1, x2, x3, x4, x5, x6, x7) new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, x5, x6, x7, x8, True, x9) new_mkVBalBranch5(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6) new_mkBranchUnbox(x0, x1, x2, x3, x4, x5) new_primPlusNat3 new_splitLT13(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) new_splitGT30(Pos(Zero), x0, x1, x2, x3, Pos(Zero), x4) new_splitLT11(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8) new_splitGT30(Pos(Zero), x0, x1, x2, x3, Pos(Succ(x4)), x5) new_esEs0(Neg(Succ(x0)), Neg(x1)) new_splitLT26(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5, Zero, x6) new_splitGT30(Neg(Zero), x0, x1, x2, x3, Neg(Succ(x4)), x5) new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, x4, x5) new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5, Succ(x6), x7) new_primPlusNat1(Succ(x0)) new_splitLT23(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) new_primMinusNat0(Zero, Succ(x0)) new_addToFM_C5(EmptyFM, x0, x1, x2) new_splitGT30(Neg(Zero), x0, x1, x2, x3, Neg(Zero), x4) new_sr(Neg(x0)) new_mkBalBranch6MkBalBranch01(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7, False, x8) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Neg(Zero), Neg(Succ(x5)), x6) new_splitGT23(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) new_mkBalBranch6MkBalBranch37(x0, EmptyFM, x1, x2, x3, x4) new_mkBalBranch1(x0, x1, x2, x3, x4) new_splitLT30(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Succ(x5)), x6) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Pos(Zero), Pos(Succ(x5)), x6) new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, x4, x5) new_mkVBalBranch30(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) new_sr0(Neg(x0)) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Neg(Zero), Neg(Zero), x5) new_addToFM_C20(Pos(Zero), x0, x1, x2, x3, Pos(Succ(x4)), x5, False, x6) new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) new_splitLT40(x0, x1) new_addToFM_C4(Branch(x0, x1, x2, x3, x4), x5, x6, x7) new_splitLT25(x0, x1, x2, x3, x4, x5, x6) new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, Neg(Zero), Neg(Succ(x5)), x6) new_splitGT25(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, Zero, x5, x6) new_splitLT30(Neg(Zero), x0, x1, x2, x3, Neg(Zero), x4) new_addToFM_C20(Neg(Zero), x0, x1, x2, x3, Pos(Zero), x4, False, x5) new_addToFM_C20(Pos(Zero), x0, x1, x2, x3, Neg(Zero), x4, False, x5) new_esEs6(Zero, Succ(x0)) new_splitGT8(Branch(x0, x1, x2, x3, x4), x5) new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5) new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, x4, Zero, Zero, x5) new_mkVBalBranch7(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7) new_splitLT30(Pos(Zero), x0, x1, x2, x3, Pos(Succ(x4)), x5) new_splitLT11(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) new_mkVBalBranch40(x0, x1, x2, x3, x4, x5, x6, x7) new_esEs0(Neg(Zero), Pos(Succ(x0))) new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_splitLT26(x0, x1, x2, x3, x4, x5, Zero, Zero, x6) new_mkBalBranch6MkBalBranch11(x0, x1, x2, x3, x4, EmptyFM, x5, x6, x7, False, x8) new_sizeFM(EmptyFM, x0) new_addToFM_C20(Pos(x0), x1, x2, x3, x4, Neg(Succ(x5)), x6, False, x7) new_addToFM_C20(Neg(x0), x1, x2, x3, x4, Pos(Succ(x5)), x6, False, x7) new_ps(Pos(x0), Neg(x1)) new_ps(Neg(x0), Pos(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_splitGT13(x0, x1, x2, x3, x4, x5, True, x6) new_splitLT8(Branch(x0, x1, x2, x3, x4), x5) new_mkVBalBranch31(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) new_addToFM_C20(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Succ(x5)), x6, False, x7) new_mkVBalBranch4(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7) new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, Pos(Zero), Pos(Zero), x5) new_primMulNat(Zero) new_mkVBalBranch2(x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), x12) new_primMulNat0(x0) new_splitGT7(EmptyFM, x0) new_splitGT6(EmptyFM, x0, x1) new_splitLT7(EmptyFM, x0, x1) new_primPlusNat2(Succ(x0)) new_addToFM_C20(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5, False, x6) new_esEs1(x0, Zero) new_mkBalBranch(x0, x1, x2, x3, x4) new_splitGT30(Neg(Zero), x0, x1, x2, x3, Pos(Zero), x4) new_splitGT30(Pos(Zero), x0, x1, x2, x3, Neg(Zero), x4) new_splitLT30(Neg(x0), x1, x2, Branch(x3, x4, x5, x6, x7), Branch(x8, x9, x10, x11, x12), Pos(Succ(x13)), x14) new_addToFM_C30(x0, x1, x2, x3, x4, x5, x6, x7) new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9) new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) new_sr(Pos(x0)) new_primPlusNat0(Succ(x0), Succ(x1)) new_mkVBalBranch6(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11, x12) new_splitLT23(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7) new_esEs4 new_primMulNat1(Zero) new_splitGT12(x0, x1, x2, x3, x4, x5, True, x6) new_splitLT26(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (216) 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_plusFM_C(ywz3, Branch(ywz40, ywz41, ywz42, ywz43, ywz44), Branch(ywz50, ywz51, ywz52, ywz53, ywz54), h) -> new_plusFM_C(ywz3, new_splitLT30(ywz40, ywz41, ywz42, ywz43, ywz44, ywz50, h), ywz53, h) The graph contains the following edges 1 >= 1, 3 > 3, 4 >= 4 *new_plusFM_C(ywz3, Branch(ywz40, ywz41, ywz42, ywz43, ywz44), Branch(ywz50, ywz51, ywz52, ywz53, ywz54), h) -> new_plusFM_C(ywz3, new_splitGT30(ywz40, ywz41, ywz42, ywz43, ywz44, ywz50, h), ywz54, h) The graph contains the following edges 1 >= 1, 3 > 3, 4 >= 4 ---------------------------------------- (217) YES ---------------------------------------- (218) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1949, ywz1950, ywz1951, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), ywz1953, True, h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_lt(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_lt(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (219) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1949, ywz1950, ywz1951, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), ywz1953, True, h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_lt(Pos(Zero), ywz19520), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1949, ywz1950, ywz1951, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), ywz1953, True, h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h),new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1949, ywz1950, ywz1951, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), ywz1953, True, h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h)) ---------------------------------------- (220) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_lt(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1949, ywz1950, ywz1951, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), ywz1953, True, h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (221) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_lt(Pos(Zero), ywz19520), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h),new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h)) ---------------------------------------- (222) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1949, ywz1950, ywz1951, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), ywz1953, True, h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (223) 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. ---------------------------------------- (224) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1949, ywz1950, ywz1951, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), ywz1953, True, h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (225) 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_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs6(Zero, Succ(x0)) ---------------------------------------- (226) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1949, ywz1950, ywz1951, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), ywz1953, True, h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (227) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1949, ywz1950, ywz1951, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), ywz1953, True, h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16),new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16)) (new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16),new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16)) (new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16),new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16)) (new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16),new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16)) ---------------------------------------- (228) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (229) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (230) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (231) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16),new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16)) ---------------------------------------- (232) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (233) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs3(Zero, x0), y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16),new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16)) ---------------------------------------- (234) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (235) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16),new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16)) ---------------------------------------- (236) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (237) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Branch(ywz19520, ywz19521, ywz19522, ywz19523, ywz19524), h) -> new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz19520, ywz19521, ywz19522, ywz19523, ywz19524, new_esEs0(Pos(Zero), ywz19520), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12),new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12)) (new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12),new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12)) (new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12),new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12)) (new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12),new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12)) ---------------------------------------- (238) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) 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 2 less nodes. ---------------------------------------- (240) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (241) 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. ---------------------------------------- (242) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs3(Zero, x0) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (243) 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_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) ---------------------------------------- (244) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs2 -> False The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (245) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12),new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12)) ---------------------------------------- (246) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True new_esEs2 -> False The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (247) 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. ---------------------------------------- (248) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs2 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (249) 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_esEs2 ---------------------------------------- (250) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (251) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs3(Zero, x0), y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12),new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12)) ---------------------------------------- (252) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) The TRS R consists of the following rules: new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs5 -> True The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (253) 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. ---------------------------------------- (254) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) The TRS R consists of the following rules: new_esEs5 -> True The set Q consists of the following terms: new_esEs3(Zero, x0) new_esEs5 new_esEs3(Succ(x0), x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (255) 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_esEs3(Zero, x0) new_esEs3(Succ(x0), x1) ---------------------------------------- (256) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) The TRS R consists of the following rules: new_esEs5 -> True The set Q consists of the following terms: new_esEs5 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (257) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12),new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12)) ---------------------------------------- (258) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The TRS R consists of the following rules: new_esEs5 -> True The set Q consists of the following terms: new_esEs5 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (259) 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. ---------------------------------------- (260) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) R is empty. The set Q consists of the following terms: new_esEs5 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (261) 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_esEs5 ---------------------------------------- (262) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (263) 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_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 *new_plusFM_CNew_elt013(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 *new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 14 >= 14 *new_plusFM_CNew_elt012(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, Neg(Succ(ywz194900)), ywz1950, ywz1951, ywz1952, ywz1953, False, h) -> new_plusFM_CNew_elt013(ywz1942, ywz1943, ywz1944, ywz1945, ywz1946, ywz1947, ywz1948, ywz1953, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 12 >= 8, 14 >= 9 *new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt012(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 13 >= 13, 14 >= 14 ---------------------------------------- (264) YES ---------------------------------------- (265) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz1702, ywz1703, ywz1704, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), ywz1706, True, h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_lt(Neg(Succ(ywz1699)), ywz17050), h) new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Neg(Succ(ywz170200)), ywz1703, ywz1704, ywz1705, ywz1706, False, h) -> new_plusFM_CNew_elt010(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz170200, ywz1703, ywz1704, ywz1705, ywz1706, ywz170200, ywz1699, h) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Succ(ywz21040), ba) -> new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, ywz21030, ywz21040, ba) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Zero, ba) -> new_plusFM_CNew_elt011(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2102, ba) new_plusFM_CNew_elt011(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_lt(Neg(Succ(ywz1699)), ywz17050), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (266) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz1702, ywz1703, ywz1704, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), ywz1706, True, h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_lt(Neg(Succ(ywz1699)), ywz17050), h) at position [13] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz1702, ywz1703, ywz1704, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), ywz1706, True, h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h),new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz1702, ywz1703, ywz1704, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), ywz1706, True, h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h)) ---------------------------------------- (267) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Neg(Succ(ywz170200)), ywz1703, ywz1704, ywz1705, ywz1706, False, h) -> new_plusFM_CNew_elt010(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz170200, ywz1703, ywz1704, ywz1705, ywz1706, ywz170200, ywz1699, h) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Succ(ywz21040), ba) -> new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, ywz21030, ywz21040, ba) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Zero, ba) -> new_plusFM_CNew_elt011(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2102, ba) new_plusFM_CNew_elt011(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_lt(Neg(Succ(ywz1699)), ywz17050), h) new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz1702, ywz1703, ywz1704, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), ywz1706, True, h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (268) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt011(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_lt(Neg(Succ(ywz1699)), ywz17050), h) at position [13] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt011(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h),new_plusFM_CNew_elt011(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h)) ---------------------------------------- (269) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Neg(Succ(ywz170200)), ywz1703, ywz1704, ywz1705, ywz1706, False, h) -> new_plusFM_CNew_elt010(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz170200, ywz1703, ywz1704, ywz1705, ywz1706, ywz170200, ywz1699, h) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Succ(ywz21040), ba) -> new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, ywz21030, ywz21040, ba) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Zero, ba) -> new_plusFM_CNew_elt011(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2102, ba) new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz1702, ywz1703, ywz1704, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), ywz1706, True, h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h) new_plusFM_CNew_elt011(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (270) 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. ---------------------------------------- (271) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Neg(Succ(ywz170200)), ywz1703, ywz1704, ywz1705, ywz1706, False, h) -> new_plusFM_CNew_elt010(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz170200, ywz1703, ywz1704, ywz1705, ywz1706, ywz170200, ywz1699, h) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Succ(ywz21040), ba) -> new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, ywz21030, ywz21040, ba) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Zero, ba) -> new_plusFM_CNew_elt011(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2102, ba) new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz1702, ywz1703, ywz1704, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), ywz1706, True, h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h) new_plusFM_CNew_elt011(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs5 -> True new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (272) 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_lt(x0, x1) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) ---------------------------------------- (273) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Neg(Succ(ywz170200)), ywz1703, ywz1704, ywz1705, ywz1706, False, h) -> new_plusFM_CNew_elt010(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz170200, ywz1703, ywz1704, ywz1705, ywz1706, ywz170200, ywz1699, h) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Succ(ywz21040), ba) -> new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, ywz21030, ywz21040, ba) new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Zero, ba) -> new_plusFM_CNew_elt011(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2102, ba) new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz1702, ywz1703, ywz1704, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), ywz1706, True, h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h) new_plusFM_CNew_elt011(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h) The TRS R consists of the following rules: new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs5 -> True new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs4 -> False new_esEs2 -> False The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (274) 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_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Neg(Succ(ywz170200)), ywz1703, ywz1704, ywz1705, ywz1706, False, h) -> new_plusFM_CNew_elt010(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz170200, ywz1703, ywz1704, ywz1705, ywz1706, ywz170200, ywz1699, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 9 > 14, 6 >= 15, 15 >= 16 *new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Succ(ywz21040), ba) -> new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, ywz21030, ywz21040, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 13 >= 13, 14 > 14, 15 > 15, 16 >= 16 *new_plusFM_CNew_elt010(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2098, ywz2099, ywz2100, ywz2101, ywz2102, Succ(ywz21030), Zero, ba) -> new_plusFM_CNew_elt011(ywz2090, ywz2091, ywz2092, ywz2093, ywz2094, ywz2095, ywz2096, ywz2097, ywz2102, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 13 >= 9, 16 >= 10 *new_plusFM_CNew_elt011(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 > 9, 9 > 10, 9 > 11, 9 > 12, 9 > 13, 10 >= 15 *new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz1702, ywz1703, ywz1704, Branch(ywz17050, ywz17051, ywz17052, ywz17053, ywz17054), ywz1706, True, h) -> new_plusFM_CNew_elt09(ywz1694, ywz1695, ywz1696, ywz1697, ywz1698, ywz1699, ywz1700, ywz1701, ywz17050, ywz17051, ywz17052, ywz17053, ywz17054, new_esEs0(Neg(Succ(ywz1699)), ywz17050), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 12 > 9, 12 > 10, 12 > 11, 12 > 12, 12 > 13, 15 >= 15 ---------------------------------------- (275) YES ---------------------------------------- (276) Obligation: Q DP problem: The TRS P consists of the following rules: new_mkBalBranch6MkBalBranch4(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz1157000), Succ(ywz1154000), h) -> new_mkBalBranch6MkBalBranch4(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz1157000, ywz1154000, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (277) 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_mkBalBranch6MkBalBranch4(ywz1007, ywz73, ywz70, ywz71, ywz1006, Succ(ywz1157000), Succ(ywz1154000), h) -> new_mkBalBranch6MkBalBranch4(ywz1007, ywz73, ywz70, ywz71, ywz1006, ywz1157000, ywz1154000, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 > 7, 8 >= 8 ---------------------------------------- (278) YES ---------------------------------------- (279) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2383, ywz2384, ywz2385, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), ywz2387, True, h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_lt(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_lt(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (280) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2383, ywz2384, ywz2385, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), ywz2387, True, h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_lt(Neg(Zero), ywz23860), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2383, ywz2384, ywz2385, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), ywz2387, True, h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h),new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2383, ywz2384, ywz2385, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), ywz2387, True, h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h)) ---------------------------------------- (281) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_lt(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2383, ywz2384, ywz2385, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), ywz2387, True, h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (282) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_lt(Neg(Zero), ywz23860), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h),new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h)) ---------------------------------------- (283) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2383, ywz2384, ywz2385, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), ywz2387, True, h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (284) 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. ---------------------------------------- (285) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2383, ywz2384, ywz2385, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), ywz2387, True, h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (286) 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_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs3(Succ(x0), x1) ---------------------------------------- (287) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2383, ywz2384, ywz2385, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), ywz2387, True, h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (288) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2383, ywz2384, ywz2385, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), ywz2387, True, h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16),new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16)) (new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16),new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16)) (new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16),new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16)) (new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16),new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16)) ---------------------------------------- (289) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (290) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (291) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (292) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16),new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16)) ---------------------------------------- (293) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (294) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16),new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16)) ---------------------------------------- (295) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (296) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16),new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16)) ---------------------------------------- (297) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (298) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Branch(ywz23860, ywz23861, ywz23862, ywz23863, ywz23864), h) -> new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz23860, ywz23861, ywz23862, ywz23863, ywz23864, new_esEs0(Neg(Zero), ywz23860), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12),new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12)) (new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12),new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12)) (new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12),new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12)) (new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12),new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12)) ---------------------------------------- (299) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (300) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (301) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (302) 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. ---------------------------------------- (303) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (304) 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_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) ---------------------------------------- (305) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (306) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12),new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12)) ---------------------------------------- (307) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (308) 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. ---------------------------------------- (309) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (310) 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_esEs5 ---------------------------------------- (311) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (312) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12),new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12)) ---------------------------------------- (313) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (314) 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. ---------------------------------------- (315) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) The TRS R consists of the following rules: new_esEs2 -> False The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (316) 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_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) ---------------------------------------- (317) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) The TRS R consists of the following rules: new_esEs2 -> False The set Q consists of the following terms: new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (318) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12),new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12)) ---------------------------------------- (319) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The TRS R consists of the following rules: new_esEs2 -> False The set Q consists of the following terms: new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (320) 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. ---------------------------------------- (321) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) R is empty. The set Q consists of the following terms: new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (322) 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_esEs2 ---------------------------------------- (323) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (324) 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_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 13 >= 13, 14 >= 14 *new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 14 >= 14 *new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 *new_plusFM_CNew_elt0(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, Neg(Succ(ywz238300)), ywz2384, ywz2385, ywz2386, ywz2387, False, h) -> new_plusFM_CNew_elt00(ywz2376, ywz2377, ywz2378, ywz2379, ywz2380, ywz2381, ywz2382, ywz2387, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 12 >= 8, 14 >= 9 *new_plusFM_CNew_elt00(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt0(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 ---------------------------------------- (325) YES ---------------------------------------- (326) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2005, ywz2006, ywz2007, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), ywz2009, True, h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_lt(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_lt(Neg(Zero), ywz20080), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (327) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2005, ywz2006, ywz2007, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), ywz2009, True, h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_lt(Neg(Zero), ywz20080), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2005, ywz2006, ywz2007, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), ywz2009, True, h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h),new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2005, ywz2006, ywz2007, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), ywz2009, True, h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h)) ---------------------------------------- (328) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_lt(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2005, ywz2006, ywz2007, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), ywz2009, True, h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (329) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_lt(Neg(Zero), ywz20080), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h),new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h)) ---------------------------------------- (330) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2005, ywz2006, ywz2007, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), ywz2009, True, h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) The TRS R consists of the following rules: new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (331) 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. ---------------------------------------- (332) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2005, ywz2006, ywz2007, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), ywz2009, True, h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs1(x0, Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs3(Succ(x0), x1) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (333) 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_lt(x0, x1) new_esEs6(Zero, Zero) new_esEs6(Succ(x0), Succ(x1)) new_esEs6(Succ(x0), Zero) new_esEs3(Zero, x0) new_esEs6(Zero, Succ(x0)) new_esEs3(Succ(x0), x1) ---------------------------------------- (334) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2005, ywz2006, ywz2007, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), ywz2009, True, h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (335) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2005, ywz2006, ywz2007, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), ywz2009, True, h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16),new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16)) (new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16),new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16)) (new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16),new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16)) (new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16),new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16)) ---------------------------------------- (336) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y11, y12, y13, y14, new_esEs4, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Zero), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y11, y12, y13, y14, new_esEs4, y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (337) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (338) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (339) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, new_esEs5, y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16),new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16)) ---------------------------------------- (340) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (341) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs1(x0, Zero), y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16),new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16)) ---------------------------------------- (342) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (343) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, new_esEs2, y16) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16),new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16)) ---------------------------------------- (344) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (345) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Branch(ywz20080, ywz20081, ywz20082, ywz20083, ywz20084), h) -> new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz20080, ywz20081, ywz20082, ywz20083, ywz20084, new_esEs0(Neg(Zero), ywz20080), h) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12),new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12)) (new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12),new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12)) (new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12),new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12)) (new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12),new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12)) ---------------------------------------- (346) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Zero), y8, y9, y10, y11, new_esEs4, y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Zero), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Zero), y8, y9, y10, y11, new_esEs4, y12) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (347) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (348) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) The TRS R consists of the following rules: new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (349) 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. ---------------------------------------- (350) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (351) 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_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Pos(Zero)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs4 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_esEs0(Neg(Zero), Neg(Zero)) ---------------------------------------- (352) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (353) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, new_esEs5, y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12),new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12)) ---------------------------------------- (354) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False new_esEs5 -> True The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (355) 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. ---------------------------------------- (356) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs5 new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (357) 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_esEs5 ---------------------------------------- (358) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (359) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs1(x0, Zero), y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12),new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12)) ---------------------------------------- (360) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) The TRS R consists of the following rules: new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs2 -> False The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (361) 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. ---------------------------------------- (362) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) The TRS R consists of the following rules: new_esEs2 -> False The set Q consists of the following terms: new_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (363) 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_esEs1(x0, Succ(x1)) new_esEs1(x0, Zero) ---------------------------------------- (364) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) The TRS R consists of the following rules: new_esEs2 -> False The set Q consists of the following terms: new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (365) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, new_esEs2, y12) at position [12] we obtained the following new rules [LPAR04]: (new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12),new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12)) ---------------------------------------- (366) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The TRS R consists of the following rules: new_esEs2 -> False The set Q consists of the following terms: new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (367) 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. ---------------------------------------- (368) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) R is empty. The set Q consists of the following terms: new_esEs2 We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (369) 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_esEs2 ---------------------------------------- (370) Obligation: Q DP problem: The TRS P consists of the following rules: new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (371) 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_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Pos(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y11, y12, y13, y14, True, y16) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 13 >= 13, 14 >= 14 *new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, y7, y8, y9, Branch(Neg(Succ(x0)), y11, y12, y13, y14), y15, True, y16) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y11, y12, y13, y14, False, y16) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 11 > 8, 11 > 9, 11 > 10, 11 > 11, 11 > 12, 14 >= 14 *new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Pos(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Pos(Succ(x0)), y8, y9, y10, y11, True, y12) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 *new_plusFM_CNew_elt01(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, Neg(Succ(ywz200500)), ywz2006, ywz2007, ywz2008, ywz2009, False, h) -> new_plusFM_CNew_elt02(ywz1998, ywz1999, ywz2000, ywz2001, ywz2002, ywz2003, ywz2004, ywz2009, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 12 >= 8, 14 >= 9 *new_plusFM_CNew_elt02(y0, y1, y2, y3, y4, y5, y6, Branch(Neg(Succ(x0)), y8, y9, y10, y11), y12) -> new_plusFM_CNew_elt01(y0, y1, y2, y3, y4, y5, y6, Neg(Succ(x0)), y8, y9, y10, y11, False, y12) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 > 8, 8 > 9, 8 > 10, 8 > 11, 8 > 12, 9 >= 14 ---------------------------------------- (372) YES ---------------------------------------- (373) Obligation: Q DP problem: The TRS P consists of the following rules: new_mkVBalBranch3(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h) -> new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), h) new_mkVBalBranch3MkVBalBranch1(ywz740, ywz741, ywz742, ywz743, Branch(ywz7440, ywz7441, ywz7442, ywz7443, ywz7444), ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, True, h) -> new_mkVBalBranch3(ywz50, ywz9, ywz7440, ywz7441, ywz7442, ywz7443, ywz7444, ywz630, ywz631, ywz632, ywz633, ywz634, h) new_mkVBalBranch0(ywz50, ywz9, Branch(ywz7440, ywz7441, ywz7442, ywz7443, ywz7444), ywz630, ywz631, ywz632, ywz633, ywz634, h) -> new_mkVBalBranch3(ywz50, ywz9, ywz7440, ywz7441, ywz7442, ywz7443, ywz7444, ywz630, ywz631, ywz632, ywz633, ywz634, h) new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, True, h) -> new_mkVBalBranch(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, ywz633, h) new_mkVBalBranch3MkVBalBranch1(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, True, h) -> new_mkVBalBranch0(ywz50, ywz9, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h) new_mkVBalBranch(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, Branch(ywz6330, ywz6331, ywz6332, ywz6333, ywz6334), h) -> new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), h) new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, Branch(ywz6330, ywz6331, ywz6332, ywz6333, ywz6334), ywz634, ywz50, ywz9, True, h) -> new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), h) new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, False, h) -> new_mkVBalBranch3MkVBalBranch1(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h)), new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h)), h) The TRS R consists of the following rules: new_sr(Pos(ywz10370)) -> Pos(new_primMulNat(ywz10370)) new_sizeFM(Branch(ywz630, ywz631, ywz632, ywz633, ywz634), h) -> ywz632 new_esEs0(Pos(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs2 new_primPlusNat0(Succ(ywz250000), Zero) -> Succ(ywz250000) new_primPlusNat0(Zero, Succ(ywz372000)) -> Succ(ywz372000) new_primPlusNat0(Zero, Zero) -> Zero new_esEs2 -> False new_esEs6(Succ(ywz821000), Zero) -> new_esEs2 new_sizeFM(EmptyFM, h) -> Pos(Zero) new_primMulNat(Zero) -> Zero new_esEs0(Neg(Succ(ywz82100)), Neg(ywz8110)) -> new_esEs3(ywz8110, ywz82100) new_primPlusNat1(Zero) -> Succ(Succ(new_primPlusNat3)) new_esEs6(Succ(ywz821000), Succ(ywz811000)) -> new_esEs6(ywz821000, ywz811000) new_mkVBalBranch3Size_l(ywz70, ywz71, ywz72, ywz73, ywz74, ywz60, ywz61, ywz62, ywz63, ywz64, h) -> new_sizeFM(Branch(ywz70, ywz71, ywz72, ywz73, ywz74), h) new_esEs0(Pos(Zero), Pos(Zero)) -> new_esEs4 new_primPlusNat3 -> Zero new_primPlusNat1(Succ(ywz72000)) -> Succ(Succ(new_primPlusNat2(ywz72000))) new_esEs3(Zero, ywz82100) -> new_esEs5 new_esEs0(Neg(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs5 new_esEs3(Succ(ywz81100), ywz82100) -> new_esEs6(ywz81100, ywz82100) new_esEs6(Zero, Zero) -> new_esEs4 new_primPlusNat2(Succ(ywz720000)) -> Succ(Succ(new_primPlusNat4(ywz720000))) new_primMulNat(Succ(ywz103700)) -> new_primPlusNat0(new_primMulNat0(ywz103700), Succ(ywz103700)) new_primPlusNat4(Zero) -> Succ(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Zero)), Succ(Succ(Zero))), Succ(Zero))) new_mkVBalBranch3Size_r(ywz70, ywz71, ywz72, ywz73, ywz74, ywz60, ywz61, ywz62, ywz63, ywz64, h) -> new_sizeFM(Branch(ywz60, ywz61, ywz62, ywz63, ywz64), h) new_esEs6(Zero, Succ(ywz811000)) -> new_esEs5 new_esEs1(ywz82100, Succ(ywz81100)) -> new_esEs6(ywz82100, ywz81100) new_esEs4 -> False new_esEs1(ywz82100, Zero) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Zero)) -> new_esEs4 new_primPlusNat2(Zero) -> Succ(Succ(new_primPlusNat5(new_primPlusNat3))) new_esEs0(Neg(Zero), Pos(Succ(ywz81100))) -> new_esEs5 new_sr(Neg(ywz10370)) -> Neg(new_primMulNat(ywz10370)) new_primMulNat0(ywz7200) -> Succ(Succ(new_primPlusNat1(ywz7200))) new_esEs5 -> True new_esEs0(Pos(Zero), Neg(Succ(ywz81100))) -> new_esEs2 new_esEs0(Neg(Zero), Neg(Succ(ywz81100))) -> new_esEs1(ywz81100, Zero) new_esEs0(Pos(Zero), Neg(Zero)) -> new_esEs4 new_esEs0(Neg(Zero), Pos(Zero)) -> new_esEs4 new_lt(ywz821, ywz811) -> new_esEs0(ywz821, ywz811) new_primPlusNat0(Succ(ywz250000), Succ(ywz372000)) -> Succ(Succ(new_primPlusNat0(ywz250000, ywz372000))) new_primPlusNat5(ywz302) -> Succ(Succ(ywz302)) new_esEs0(Pos(Succ(ywz82100)), Pos(ywz8110)) -> new_esEs1(ywz82100, ywz8110) new_primPlusNat4(Succ(ywz7200000)) -> Succ(Succ(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(Succ(ywz7200000))), Succ(Succ(Succ(ywz7200000)))), Succ(Succ(ywz7200000))), ywz7200000))) new_esEs0(Pos(Zero), Pos(Succ(ywz81100))) -> new_esEs3(Zero, ywz81100) The set Q consists of the following terms: new_primPlusNat0(Zero, Succ(x0)) new_esEs0(Neg(Zero), Pos(Succ(x0))) new_esEs0(Pos(Zero), Neg(Succ(x0))) new_sizeFM(EmptyFM, x0) new_esEs6(Zero, Zero) new_esEs0(Pos(Zero), Pos(Zero)) new_primPlusNat0(Succ(x0), Zero) new_primPlusNat3 new_esEs6(Succ(x0), Succ(x1)) new_esEs1(x0, Succ(x1)) new_esEs6(Succ(x0), Zero) new_primPlusNat5(x0) new_primPlusNat1(Zero) new_esEs3(Zero, x0) new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) new_primPlusNat2(Zero) new_primPlusNat4(Succ(x0)) new_esEs5 new_primMulNat(Zero) new_esEs0(Neg(Succ(x0)), Neg(x1)) new_esEs0(Neg(Zero), Neg(Succ(x0))) new_esEs2 new_esEs0(Pos(Succ(x0)), Pos(x1)) new_esEs0(Pos(Zero), Pos(Succ(x0))) new_primPlusNat1(Succ(x0)) new_esEs0(Neg(Zero), Neg(Zero)) new_primMulNat0(x0) new_lt(x0, x1) new_primPlusNat2(Succ(x0)) new_esEs0(Pos(Succ(x0)), Neg(x1)) new_esEs0(Neg(Succ(x0)), Pos(x1)) new_sr(Neg(x0)) new_primMulNat(Succ(x0)) new_esEs1(x0, Zero) new_sizeFM(Branch(x0, x1, x2, x3, x4), x5) new_esEs6(Zero, Succ(x0)) new_mkVBalBranch3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) new_sr(Pos(x0)) new_esEs0(Pos(Zero), Neg(Zero)) new_esEs0(Neg(Zero), Pos(Zero)) new_primPlusNat0(Succ(x0), Succ(x1)) new_esEs3(Succ(x0), x1) new_primPlusNat4(Zero) new_esEs4 new_primPlusNat0(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (374) 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_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, False, h) -> new_mkVBalBranch3MkVBalBranch1(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h)), new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h)), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6, 7 >= 7, 8 >= 8, 9 >= 9, 10 >= 10, 11 >= 11, 12 >= 12, 14 >= 14 *new_mkVBalBranch3(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h) -> new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), h) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 8, 11 >= 9, 12 >= 10, 1 >= 11, 2 >= 12, 13 >= 14 *new_mkVBalBranch3MkVBalBranch1(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, True, h) -> new_mkVBalBranch0(ywz50, ywz9, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, h) The graph contains the following edges 11 >= 1, 12 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 >= 6, 9 >= 7, 10 >= 8, 14 >= 9 *new_mkVBalBranch(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, Branch(ywz6330, ywz6331, ywz6332, ywz6333, ywz6334), h) -> new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), h) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 4, 7 >= 5, 8 > 6, 8 > 7, 8 > 8, 8 > 9, 8 > 10, 1 >= 11, 2 >= 12, 9 >= 14 *new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, Branch(ywz6330, ywz6331, ywz6332, ywz6333, ywz6334), ywz634, ywz50, ywz9, True, h) -> new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, ywz50, ywz9, new_lt(new_sr(new_mkVBalBranch3Size_l(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), new_mkVBalBranch3Size_r(ywz740, ywz741, ywz742, ywz743, ywz744, ywz6330, ywz6331, ywz6332, ywz6333, ywz6334, h)), h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 9 > 6, 9 > 7, 9 > 8, 9 > 9, 9 > 10, 11 >= 11, 12 >= 12, 14 >= 14 *new_mkVBalBranch3MkVBalBranch2(ywz740, ywz741, ywz742, ywz743, ywz744, ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, True, h) -> new_mkVBalBranch(ywz50, ywz9, ywz740, ywz741, ywz742, ywz743, ywz744, ywz633, h) The graph contains the following edges 11 >= 1, 12 >= 2, 1 >= 3, 2 >= 4, 3 >= 5, 4 >= 6, 5 >= 7, 9 >= 8, 14 >= 9 *new_mkVBalBranch0(ywz50, ywz9, Branch(ywz7440, ywz7441, ywz7442, ywz7443, ywz7444), ywz630, ywz631, ywz632, ywz633, ywz634, h) -> new_mkVBalBranch3(ywz50, ywz9, ywz7440, ywz7441, ywz7442, ywz7443, ywz7444, ywz630, ywz631, ywz632, ywz633, ywz634, h) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 3 > 7, 4 >= 8, 5 >= 9, 6 >= 10, 7 >= 11, 8 >= 12, 9 >= 13 *new_mkVBalBranch3MkVBalBranch1(ywz740, ywz741, ywz742, ywz743, Branch(ywz7440, ywz7441, ywz7442, ywz7443, ywz7444), ywz630, ywz631, ywz632, ywz633, ywz634, ywz50, ywz9, True, h) -> new_mkVBalBranch3(ywz50, ywz9, ywz7440, ywz7441, ywz7442, ywz7443, ywz7444, ywz630, ywz631, ywz632, ywz633, ywz634, h) The graph contains the following edges 11 >= 1, 12 >= 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 5 > 7, 6 >= 8, 7 >= 9, 8 >= 10, 9 >= 11, 10 >= 12, 14 >= 13 ---------------------------------------- (375) YES ---------------------------------------- (376) Obligation: Q DP problem: The TRS P consists of the following rules: new_esEs(Succ(ywz821000), Succ(ywz811000)) -> new_esEs(ywz821000, ywz811000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (377) 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_esEs(Succ(ywz821000), Succ(ywz811000)) -> new_esEs(ywz821000, ywz811000) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (378) YES