/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) IFR [EQUIVALENT, 0 ms] (4) HASKELL (5) BR [EQUIVALENT, 0 ms] (6) HASKELL (7) COR [EQUIVALENT, 0 ms] (8) HASKELL (9) NumRed [SOUND, 0 ms] (10) HASKELL (11) Narrow [SOUND, 0 ms] (12) AND (13) QDP (14) NonTerminationLoopProof [COMPLETE, 0 ms] (15) NO (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES (19) QDP (20) DependencyGraphProof [EQUIVALENT, 0 ms] (21) QDP (22) TransformationProof [EQUIVALENT, 0 ms] (23) QDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) QDP (26) QReductionProof [EQUIVALENT, 0 ms] (27) QDP (28) MNOCProof [EQUIVALENT, 0 ms] (29) QDP (30) InductionCalculusProof [EQUIVALENT, 0 ms] (31) QDP (32) TransformationProof [EQUIVALENT, 0 ms] (33) QDP (34) DependencyGraphProof [EQUIVALENT, 0 ms] (35) QDP (36) TransformationProof [EQUIVALENT, 0 ms] (37) QDP (38) DependencyGraphProof [EQUIVALENT, 0 ms] (39) QDP (40) TransformationProof [EQUIVALENT, 0 ms] (41) QDP (42) DependencyGraphProof [EQUIVALENT, 0 ms] (43) QDP (44) TransformationProof [EQUIVALENT, 0 ms] (45) QDP (46) DependencyGraphProof [EQUIVALENT, 0 ms] (47) QDP (48) MNOCProof [EQUIVALENT, 0 ms] (49) QDP (50) InductionCalculusProof [EQUIVALENT, 0 ms] (51) QDP (52) QDP (53) NonTerminationLoopProof [COMPLETE, 0 ms] (54) NO (55) QDP (56) NonTerminationLoopProof [COMPLETE, 0 ms] (57) NO (58) QDP (59) QDPSizeChangeProof [EQUIVALENT, 0 ms] (60) YES (61) QDP (62) NonTerminationLoopProof [COMPLETE, 0 ms] (63) NO (64) QDP (65) NonTerminationLoopProof [COMPLETE, 0 ms] (66) NO (67) QDP (68) NonTerminationLoopProof [COMPLETE, 0 ms] (69) NO (70) QDP (71) DependencyGraphProof [EQUIVALENT, 0 ms] (72) QDP (73) QDPOrderProof [EQUIVALENT, 0 ms] (74) QDP (75) DependencyGraphProof [EQUIVALENT, 0 ms] (76) QDP (77) QDPSizeChangeProof [EQUIVALENT, 0 ms] (78) YES (79) QDP (80) NonTerminationLoopProof [COMPLETE, 0 ms] (81) NO (82) QDP (83) NonTerminationLoopProof [COMPLETE, 0 ms] (84) NO (85) QDP (86) DependencyGraphProof [EQUIVALENT, 0 ms] (87) QDP (88) TransformationProof [EQUIVALENT, 30 ms] (89) QDP (90) TransformationProof [EQUIVALENT, 0 ms] (91) QDP (92) TransformationProof [EQUIVALENT, 0 ms] (93) QDP (94) TransformationProof [EQUIVALENT, 0 ms] (95) QDP (96) TransformationProof [EQUIVALENT, 0 ms] (97) QDP (98) TransformationProof [EQUIVALENT, 0 ms] (99) QDP (100) DependencyGraphProof [EQUIVALENT, 0 ms] (101) QDP (102) TransformationProof [EQUIVALENT, 0 ms] (103) QDP (104) DependencyGraphProof [EQUIVALENT, 0 ms] (105) QDP (106) TransformationProof [EQUIVALENT, 0 ms] (107) QDP (108) DependencyGraphProof [EQUIVALENT, 0 ms] (109) QDP (110) TransformationProof [EQUIVALENT, 0 ms] (111) QDP (112) DependencyGraphProof [EQUIVALENT, 0 ms] (113) QDP (114) TransformationProof [EQUIVALENT, 0 ms] (115) QDP (116) DependencyGraphProof [EQUIVALENT, 0 ms] (117) QDP (118) TransformationProof [EQUIVALENT, 0 ms] (119) QDP (120) DependencyGraphProof [EQUIVALENT, 0 ms] (121) QDP (122) TransformationProof [EQUIVALENT, 0 ms] (123) QDP (124) DependencyGraphProof [EQUIVALENT, 0 ms] (125) QDP (126) TransformationProof [EQUIVALENT, 0 ms] (127) QDP (128) DependencyGraphProof [EQUIVALENT, 0 ms] (129) QDP (130) TransformationProof [EQUIVALENT, 0 ms] (131) QDP (132) DependencyGraphProof [EQUIVALENT, 0 ms] (133) QDP (134) TransformationProof [EQUIVALENT, 0 ms] (135) QDP (136) DependencyGraphProof [EQUIVALENT, 0 ms] (137) QDP (138) TransformationProof [EQUIVALENT, 0 ms] (139) QDP (140) DependencyGraphProof [EQUIVALENT, 0 ms] (141) QDP (142) TransformationProof [EQUIVALENT, 0 ms] (143) QDP (144) DependencyGraphProof [EQUIVALENT, 0 ms] (145) QDP (146) TransformationProof [EQUIVALENT, 0 ms] (147) QDP (148) TransformationProof [EQUIVALENT, 0 ms] (149) QDP (150) DependencyGraphProof [EQUIVALENT, 0 ms] (151) QDP (152) TransformationProof [EQUIVALENT, 0 ms] (153) QDP (154) DependencyGraphProof [EQUIVALENT, 0 ms] (155) QDP (156) TransformationProof [EQUIVALENT, 0 ms] (157) QDP (158) DependencyGraphProof [EQUIVALENT, 0 ms] (159) QDP (160) TransformationProof [EQUIVALENT, 0 ms] (161) QDP (162) DependencyGraphProof [EQUIVALENT, 0 ms] (163) QDP (164) TransformationProof [EQUIVALENT, 0 ms] (165) QDP (166) QDPSizeChangeProof [EQUIVALENT, 0 ms] (167) YES (168) QDP (169) NonTerminationLoopProof [COMPLETE, 0 ms] (170) NO (171) QDP (172) NonTerminationLoopProof [COMPLETE, 0 ms] (173) NO (174) QDP (175) NonTerminationLoopProof [COMPLETE, 0 ms] (176) NO (177) QDP (178) NonTerminationLoopProof [COMPLETE, 0 ms] (179) NO (180) QDP (181) NonTerminationLoopProof [COMPLETE, 0 ms] (182) NO (183) QDP (184) NonTerminationLoopProof [COMPLETE, 0 ms] (185) NO (186) QDP (187) DependencyGraphProof [EQUIVALENT, 0 ms] (188) QDP (189) QDPOrderProof [EQUIVALENT, 0 ms] (190) QDP (191) DependencyGraphProof [EQUIVALENT, 0 ms] (192) QDP (193) QDPSizeChangeProof [EQUIVALENT, 0 ms] (194) YES (195) QDP (196) NonTerminationLoopProof [COMPLETE, 0 ms] (197) NO (198) QDP (199) NonTerminationLoopProof [COMPLETE, 0 ms] (200) NO (201) Narrow [COMPLETE, 0 ms] (202) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\_->q" is transformed to "gtGt0 q _ = q; " ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) 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; " The following If expression "if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x" is transformed to "primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y); primModNatP0 x y False = primMinusNatS y x; " The following If expression "if b then (showChar '(') . p . showChar ')' else p" is transformed to "showParen0 p True = (showChar '(') . p . showChar ')'; showParen0 p False = p; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "randomSelect (x : []) = x; randomSelect (x : xs)|terminatorrandomSelect xs|otherwisex; " is transformed to "randomSelect (x : []) = randomSelect3 (x : []); randomSelect (x : xs) = randomSelect2 (x : xs); " "randomSelect1 x xs True = randomSelect xs; randomSelect1 x xs False = randomSelect0 x xs otherwise; " "randomSelect0 x xs True = x; " "randomSelect2 (x : xs) = randomSelect1 x xs terminator; " "randomSelect3 (x : []) = x; randomSelect3 xu = randomSelect2 xu; " The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (10) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (11) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="print",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="print xv3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="putStrLn . show",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="putStrLn (show xv3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6 -> 7[label="",style="dashed", color="red", weight=0]; 6[label="putStr (show xv3) >> putChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];6 -> 8[label="",style="dashed", color="magenta", weight=3]; 6 -> 9[label="",style="dashed", color="magenta", weight=3]; 8[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];9[label="xv3",fontsize=16,color="green",shape="box"];7[label="putStr (show xv5) >> putChar (Char (Succ xv6))",fontsize=16,color="black",shape="triangle"];7 -> 10[label="",style="solid", color="black", weight=3]; 10[label="putStr (show xv5) >>= gtGt0 (putChar (Char (Succ xv6)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 11 -> 533[label="",style="dashed", color="red", weight=0]; 11[label="primbindIO (putStr (show xv5)) (gtGt0 (putChar (Char (Succ xv6))))",fontsize=16,color="magenta"];11 -> 534[label="",style="dashed", color="magenta", weight=3]; 11 -> 535[label="",style="dashed", color="magenta", weight=3]; 534[label="putChar (Char (Succ xv6))",fontsize=16,color="black",shape="box"];534 -> 638[label="",style="solid", color="black", weight=3]; 535 -> 639[label="",style="dashed", color="red", weight=0]; 535[label="putStr (show xv5)",fontsize=16,color="magenta"];535 -> 640[label="",style="dashed", color="magenta", weight=3]; 533[label="primbindIO xv70 (gtGt0 xv68)",fontsize=16,color="burlywood",shape="triangle"];2765[label="xv70/IO xv700",fontsize=10,color="white",style="solid",shape="box"];533 -> 2765[label="",style="solid", color="burlywood", weight=9]; 2765 -> 641[label="",style="solid", color="burlywood", weight=3]; 2766[label="xv70/AProVE_IO xv700",fontsize=10,color="white",style="solid",shape="box"];533 -> 2766[label="",style="solid", color="burlywood", weight=9]; 2766 -> 642[label="",style="solid", color="burlywood", weight=3]; 2767[label="xv70/AProVE_Exception xv700",fontsize=10,color="white",style="solid",shape="box"];533 -> 2767[label="",style="solid", color="burlywood", weight=9]; 2767 -> 643[label="",style="solid", color="burlywood", weight=3]; 2768[label="xv70/AProVE_Error xv700",fontsize=10,color="white",style="solid",shape="box"];533 -> 2768[label="",style="solid", color="burlywood", weight=9]; 2768 -> 644[label="",style="solid", color="burlywood", weight=3]; 638 -> 808[label="",style="dashed", color="red", weight=0]; 638[label="(seq Char (Succ xv6) output)",fontsize=16,color="magenta"];638 -> 809[label="",style="dashed", color="magenta", weight=3]; 638 -> 810[label="",style="dashed", color="magenta", weight=3]; 640[label="show xv5",fontsize=16,color="blue",shape="box"];2769[label="show :: ((@2) a b) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2769[label="",style="solid", color="blue", weight=9]; 2769 -> 646[label="",style="solid", color="blue", weight=3]; 2770[label="show :: Double -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2770[label="",style="solid", color="blue", weight=9]; 2770 -> 647[label="",style="solid", color="blue", weight=3]; 2771[label="show :: Bool -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2771[label="",style="solid", color="blue", weight=9]; 2771 -> 648[label="",style="solid", color="blue", weight=3]; 2772[label="show :: Ordering -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2772[label="",style="solid", color="blue", weight=9]; 2772 -> 649[label="",style="solid", color="blue", weight=3]; 2773[label="show :: Float -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2773[label="",style="solid", color="blue", weight=9]; 2773 -> 650[label="",style="solid", color="blue", weight=3]; 2774[label="show :: (Ratio a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2774[label="",style="solid", color="blue", weight=9]; 2774 -> 651[label="",style="solid", color="blue", weight=3]; 2775[label="show :: (Maybe a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2775[label="",style="solid", color="blue", weight=9]; 2775 -> 652[label="",style="solid", color="blue", weight=3]; 2776[label="show :: HugsException -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2776[label="",style="solid", color="blue", weight=9]; 2776 -> 653[label="",style="solid", color="blue", weight=3]; 2777[label="show :: ((@3) a b c) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2777[label="",style="solid", color="blue", weight=9]; 2777 -> 654[label="",style="solid", color="blue", weight=3]; 2778[label="show :: Char -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2778[label="",style="solid", color="blue", weight=9]; 2778 -> 655[label="",style="solid", color="blue", weight=3]; 2779[label="show :: IOError -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2779[label="",style="solid", color="blue", weight=9]; 2779 -> 656[label="",style="solid", color="blue", weight=3]; 2780[label="show :: (Either a b) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2780[label="",style="solid", color="blue", weight=9]; 2780 -> 657[label="",style="solid", color="blue", weight=3]; 2781[label="show :: () -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2781[label="",style="solid", color="blue", weight=9]; 2781 -> 658[label="",style="solid", color="blue", weight=3]; 2782[label="show :: ([] a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2782[label="",style="solid", color="blue", weight=9]; 2782 -> 659[label="",style="solid", color="blue", weight=3]; 2783[label="show :: Integer -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2783[label="",style="solid", color="blue", weight=9]; 2783 -> 660[label="",style="solid", color="blue", weight=3]; 2784[label="show :: IOErrorKind -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2784[label="",style="solid", color="blue", weight=9]; 2784 -> 661[label="",style="solid", color="blue", weight=3]; 2785[label="show :: Int -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2785[label="",style="solid", color="blue", weight=9]; 2785 -> 662[label="",style="solid", color="blue", weight=3]; 2786[label="show :: (IO a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2786[label="",style="solid", color="blue", weight=9]; 2786 -> 663[label="",style="solid", color="blue", weight=3]; 639[label="putStr xv73",fontsize=16,color="burlywood",shape="triangle"];2787[label="xv73/xv730 : xv731",fontsize=10,color="white",style="solid",shape="box"];639 -> 2787[label="",style="solid", color="burlywood", weight=9]; 2787 -> 664[label="",style="solid", color="burlywood", weight=3]; 2788[label="xv73/[]",fontsize=10,color="white",style="solid",shape="box"];639 -> 2788[label="",style="solid", color="burlywood", weight=9]; 2788 -> 665[label="",style="solid", color="burlywood", weight=3]; 641[label="primbindIO (IO xv700) (gtGt0 xv68)",fontsize=16,color="black",shape="box"];641 -> 666[label="",style="solid", color="black", weight=3]; 642[label="primbindIO (AProVE_IO xv700) (gtGt0 xv68)",fontsize=16,color="black",shape="box"];642 -> 667[label="",style="solid", color="black", weight=3]; 643[label="primbindIO (AProVE_Exception xv700) (gtGt0 xv68)",fontsize=16,color="black",shape="box"];643 -> 668[label="",style="solid", color="black", weight=3]; 644[label="primbindIO (AProVE_Error xv700) (gtGt0 xv68)",fontsize=16,color="black",shape="box"];644 -> 669[label="",style="solid", color="black", weight=3]; 809 -> 670[label="",style="dashed", color="red", weight=0]; 809[label="output",fontsize=16,color="magenta"];810[label="Char (Succ xv6)",fontsize=16,color="green",shape="box"];808[label="(seq xv730 xv102)",fontsize=16,color="black",shape="triangle"];808 -> 812[label="",style="solid", color="black", weight=3]; 646[label="show xv5",fontsize=16,color="black",shape="triangle"];646 -> 671[label="",style="solid", color="black", weight=3]; 647[label="show xv5",fontsize=16,color="black",shape="triangle"];647 -> 672[label="",style="solid", color="black", weight=3]; 648[label="show xv5",fontsize=16,color="black",shape="triangle"];648 -> 673[label="",style="solid", color="black", weight=3]; 649[label="show xv5",fontsize=16,color="black",shape="triangle"];649 -> 674[label="",style="solid", color="black", weight=3]; 650[label="show xv5",fontsize=16,color="black",shape="triangle"];650 -> 675[label="",style="solid", color="black", weight=3]; 651[label="show xv5",fontsize=16,color="black",shape="box"];651 -> 676[label="",style="solid", color="black", weight=3]; 652[label="show xv5",fontsize=16,color="black",shape="triangle"];652 -> 677[label="",style="solid", color="black", weight=3]; 653[label="show xv5",fontsize=16,color="black",shape="triangle"];653 -> 678[label="",style="solid", color="black", weight=3]; 654[label="show xv5",fontsize=16,color="black",shape="triangle"];654 -> 679[label="",style="solid", color="black", weight=3]; 655[label="show xv5",fontsize=16,color="black",shape="triangle"];655 -> 680[label="",style="solid", color="black", weight=3]; 656[label="show xv5",fontsize=16,color="black",shape="triangle"];656 -> 681[label="",style="solid", color="black", weight=3]; 657[label="show xv5",fontsize=16,color="black",shape="triangle"];657 -> 682[label="",style="solid", color="black", weight=3]; 658[label="show xv5",fontsize=16,color="black",shape="triangle"];658 -> 683[label="",style="solid", color="black", weight=3]; 659[label="show xv5",fontsize=16,color="black",shape="triangle"];659 -> 684[label="",style="solid", color="black", weight=3]; 660[label="show xv5",fontsize=16,color="black",shape="triangle"];660 -> 685[label="",style="solid", color="black", weight=3]; 661[label="show xv5",fontsize=16,color="black",shape="triangle"];661 -> 686[label="",style="solid", color="black", weight=3]; 662[label="show xv5",fontsize=16,color="black",shape="triangle"];662 -> 687[label="",style="solid", color="black", weight=3]; 663[label="show xv5",fontsize=16,color="black",shape="triangle"];663 -> 688[label="",style="solid", color="black", weight=3]; 664[label="putStr (xv730 : xv731)",fontsize=16,color="black",shape="box"];664 -> 689[label="",style="solid", color="black", weight=3]; 665[label="putStr []",fontsize=16,color="black",shape="box"];665 -> 690[label="",style="solid", color="black", weight=3]; 666[label="error []",fontsize=16,color="red",shape="box"];667[label="gtGt0 xv68 xv700",fontsize=16,color="black",shape="box"];667 -> 691[label="",style="solid", color="black", weight=3]; 668[label="AProVE_Exception xv700",fontsize=16,color="green",shape="box"];669[label="AProVE_Error xv700",fontsize=16,color="green",shape="box"];670[label="output",fontsize=16,color="black",shape="triangle"];670 -> 692[label="",style="solid", color="black", weight=3]; 812[label="enforceWHNF (WHNF xv730) xv102",fontsize=16,color="black",shape="box"];812 -> 819[label="",style="solid", color="black", weight=3]; 671[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];671 -> 693[label="",style="solid", color="black", weight=3]; 672[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];672 -> 694[label="",style="solid", color="black", weight=3]; 673[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];673 -> 695[label="",style="solid", color="black", weight=3]; 674[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];674 -> 696[label="",style="solid", color="black", weight=3]; 675[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];675 -> 697[label="",style="solid", color="black", weight=3]; 676[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="burlywood",shape="box"];2789[label="xv5/xv50 :% xv51",fontsize=10,color="white",style="solid",shape="box"];676 -> 2789[label="",style="solid", color="burlywood", weight=9]; 2789 -> 698[label="",style="solid", color="burlywood", weight=3]; 677[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];677 -> 699[label="",style="solid", color="black", weight=3]; 678[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];678 -> 700[label="",style="solid", color="black", weight=3]; 679[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];679 -> 701[label="",style="solid", color="black", weight=3]; 680[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];680 -> 702[label="",style="solid", color="black", weight=3]; 681[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];681 -> 703[label="",style="solid", color="black", weight=3]; 682[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];682 -> 704[label="",style="solid", color="black", weight=3]; 683[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];683 -> 705[label="",style="solid", color="black", weight=3]; 684[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];684 -> 706[label="",style="solid", color="black", weight=3]; 685[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];685 -> 707[label="",style="solid", color="black", weight=3]; 686[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];686 -> 708[label="",style="solid", color="black", weight=3]; 687[label="primShowInt xv5",fontsize=16,color="burlywood",shape="triangle"];2790[label="xv5/Pos xv50",fontsize=10,color="white",style="solid",shape="box"];687 -> 2790[label="",style="solid", color="burlywood", weight=9]; 2790 -> 709[label="",style="solid", color="burlywood", weight=3]; 2791[label="xv5/Neg xv50",fontsize=10,color="white",style="solid",shape="box"];687 -> 2791[label="",style="solid", color="burlywood", weight=9]; 2791 -> 710[label="",style="solid", color="burlywood", weight=3]; 688[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];688 -> 711[label="",style="solid", color="black", weight=3]; 689 -> 712[label="",style="dashed", color="red", weight=0]; 689[label="putChar xv730 >> putStr xv731",fontsize=16,color="magenta"];689 -> 713[label="",style="dashed", color="magenta", weight=3]; 690 -> 670[label="",style="dashed", color="red", weight=0]; 690[label="output",fontsize=16,color="magenta"];691[label="xv68",fontsize=16,color="green",shape="box"];692[label="randomSelect (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];692 -> 714[label="",style="solid", color="black", weight=3]; 819[label="xv102",fontsize=16,color="green",shape="box"];693 -> 1484[label="",style="dashed", color="red", weight=0]; 693[label="show xv5 ++ []",fontsize=16,color="magenta"];693 -> 1485[label="",style="dashed", color="magenta", weight=3]; 693 -> 1486[label="",style="dashed", color="magenta", weight=3]; 694 -> 1484[label="",style="dashed", color="red", weight=0]; 694[label="show xv5 ++ []",fontsize=16,color="magenta"];694 -> 1487[label="",style="dashed", color="magenta", weight=3]; 694 -> 1488[label="",style="dashed", color="magenta", weight=3]; 695 -> 1484[label="",style="dashed", color="red", weight=0]; 695[label="show xv5 ++ []",fontsize=16,color="magenta"];695 -> 1489[label="",style="dashed", color="magenta", weight=3]; 695 -> 1490[label="",style="dashed", color="magenta", weight=3]; 696 -> 1484[label="",style="dashed", color="red", weight=0]; 696[label="show xv5 ++ []",fontsize=16,color="magenta"];696 -> 1491[label="",style="dashed", color="magenta", weight=3]; 696 -> 1492[label="",style="dashed", color="magenta", weight=3]; 697 -> 1484[label="",style="dashed", color="red", weight=0]; 697[label="show xv5 ++ []",fontsize=16,color="magenta"];697 -> 1493[label="",style="dashed", color="magenta", weight=3]; 697 -> 1494[label="",style="dashed", color="magenta", weight=3]; 698[label="showsPrec (Pos Zero) (xv50 :% xv51) []",fontsize=16,color="black",shape="box"];698 -> 732[label="",style="solid", color="black", weight=3]; 699 -> 1484[label="",style="dashed", color="red", weight=0]; 699[label="show xv5 ++ []",fontsize=16,color="magenta"];699 -> 1495[label="",style="dashed", color="magenta", weight=3]; 699 -> 1496[label="",style="dashed", color="magenta", weight=3]; 700 -> 1484[label="",style="dashed", color="red", weight=0]; 700[label="show xv5 ++ []",fontsize=16,color="magenta"];700 -> 1497[label="",style="dashed", color="magenta", weight=3]; 700 -> 1498[label="",style="dashed", color="magenta", weight=3]; 701 -> 1484[label="",style="dashed", color="red", weight=0]; 701[label="show xv5 ++ []",fontsize=16,color="magenta"];701 -> 1499[label="",style="dashed", color="magenta", weight=3]; 701 -> 1500[label="",style="dashed", color="magenta", weight=3]; 702 -> 1484[label="",style="dashed", color="red", weight=0]; 702[label="show xv5 ++ []",fontsize=16,color="magenta"];702 -> 1501[label="",style="dashed", color="magenta", weight=3]; 702 -> 1502[label="",style="dashed", color="magenta", weight=3]; 703 -> 1484[label="",style="dashed", color="red", weight=0]; 703[label="show xv5 ++ []",fontsize=16,color="magenta"];703 -> 1503[label="",style="dashed", color="magenta", weight=3]; 703 -> 1504[label="",style="dashed", color="magenta", weight=3]; 704 -> 1484[label="",style="dashed", color="red", weight=0]; 704[label="show xv5 ++ []",fontsize=16,color="magenta"];704 -> 1505[label="",style="dashed", color="magenta", weight=3]; 704 -> 1506[label="",style="dashed", color="magenta", weight=3]; 705 -> 1484[label="",style="dashed", color="red", weight=0]; 705[label="show xv5 ++ []",fontsize=16,color="magenta"];705 -> 1507[label="",style="dashed", color="magenta", weight=3]; 705 -> 1508[label="",style="dashed", color="magenta", weight=3]; 706 -> 1484[label="",style="dashed", color="red", weight=0]; 706[label="show xv5 ++ []",fontsize=16,color="magenta"];706 -> 1509[label="",style="dashed", color="magenta", weight=3]; 706 -> 1510[label="",style="dashed", color="magenta", weight=3]; 707 -> 1484[label="",style="dashed", color="red", weight=0]; 707[label="show xv5 ++ []",fontsize=16,color="magenta"];707 -> 1511[label="",style="dashed", color="magenta", weight=3]; 707 -> 1512[label="",style="dashed", color="magenta", weight=3]; 708 -> 1484[label="",style="dashed", color="red", weight=0]; 708[label="show xv5 ++ []",fontsize=16,color="magenta"];708 -> 1513[label="",style="dashed", color="magenta", weight=3]; 708 -> 1514[label="",style="dashed", color="magenta", weight=3]; 709[label="primShowInt (Pos xv50)",fontsize=16,color="burlywood",shape="box"];2792[label="xv50/Succ xv500",fontsize=10,color="white",style="solid",shape="box"];709 -> 2792[label="",style="solid", color="burlywood", weight=9]; 2792 -> 733[label="",style="solid", color="burlywood", weight=3]; 2793[label="xv50/Zero",fontsize=10,color="white",style="solid",shape="box"];709 -> 2793[label="",style="solid", color="burlywood", weight=9]; 2793 -> 734[label="",style="solid", color="burlywood", weight=3]; 710[label="primShowInt (Neg xv50)",fontsize=16,color="black",shape="box"];710 -> 735[label="",style="solid", color="black", weight=3]; 711 -> 1484[label="",style="dashed", color="red", weight=0]; 711[label="show xv5 ++ []",fontsize=16,color="magenta"];711 -> 1515[label="",style="dashed", color="magenta", weight=3]; 711 -> 1516[label="",style="dashed", color="magenta", weight=3]; 713 -> 639[label="",style="dashed", color="red", weight=0]; 713[label="putStr xv731",fontsize=16,color="magenta"];713 -> 736[label="",style="dashed", color="magenta", weight=3]; 712[label="putChar xv730 >> xv74",fontsize=16,color="black",shape="triangle"];712 -> 737[label="",style="solid", color="black", weight=3]; 714[label="randomSelect2 (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];714 -> 738[label="",style="solid", color="black", weight=3]; 1485 -> 646[label="",style="dashed", color="red", weight=0]; 1485[label="show xv5",fontsize=16,color="magenta"];1486[label="[]",fontsize=16,color="green",shape="box"];1484[label="xv189 ++ xv131",fontsize=16,color="burlywood",shape="triangle"];2794[label="xv189/xv1890 : xv1891",fontsize=10,color="white",style="solid",shape="box"];1484 -> 2794[label="",style="solid", color="burlywood", weight=9]; 2794 -> 1590[label="",style="solid", color="burlywood", weight=3]; 2795[label="xv189/[]",fontsize=10,color="white",style="solid",shape="box"];1484 -> 2795[label="",style="solid", color="burlywood", weight=9]; 2795 -> 1591[label="",style="solid", color="burlywood", weight=3]; 1487 -> 647[label="",style="dashed", color="red", weight=0]; 1487[label="show xv5",fontsize=16,color="magenta"];1488[label="[]",fontsize=16,color="green",shape="box"];1489 -> 648[label="",style="dashed", color="red", weight=0]; 1489[label="show xv5",fontsize=16,color="magenta"];1490[label="[]",fontsize=16,color="green",shape="box"];1491 -> 649[label="",style="dashed", color="red", weight=0]; 1491[label="show xv5",fontsize=16,color="magenta"];1492[label="[]",fontsize=16,color="green",shape="box"];1493 -> 650[label="",style="dashed", color="red", weight=0]; 1493[label="show xv5",fontsize=16,color="magenta"];1494[label="[]",fontsize=16,color="green",shape="box"];732 -> 1735[label="",style="dashed", color="red", weight=0]; 732[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows xv50) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows xv51) []",fontsize=16,color="magenta"];732 -> 1736[label="",style="dashed", color="magenta", weight=3]; 732 -> 1737[label="",style="dashed", color="magenta", weight=3]; 732 -> 1738[label="",style="dashed", color="magenta", weight=3]; 732 -> 1739[label="",style="dashed", color="magenta", weight=3]; 732 -> 1740[label="",style="dashed", color="magenta", weight=3]; 732 -> 1741[label="",style="dashed", color="magenta", weight=3]; 1495 -> 652[label="",style="dashed", color="red", weight=0]; 1495[label="show xv5",fontsize=16,color="magenta"];1496[label="[]",fontsize=16,color="green",shape="box"];1497 -> 653[label="",style="dashed", color="red", weight=0]; 1497[label="show xv5",fontsize=16,color="magenta"];1498[label="[]",fontsize=16,color="green",shape="box"];1499 -> 654[label="",style="dashed", color="red", weight=0]; 1499[label="show xv5",fontsize=16,color="magenta"];1500[label="[]",fontsize=16,color="green",shape="box"];1501 -> 655[label="",style="dashed", color="red", weight=0]; 1501[label="show xv5",fontsize=16,color="magenta"];1502[label="[]",fontsize=16,color="green",shape="box"];1503 -> 656[label="",style="dashed", color="red", weight=0]; 1503[label="show xv5",fontsize=16,color="magenta"];1504[label="[]",fontsize=16,color="green",shape="box"];1505 -> 657[label="",style="dashed", color="red", weight=0]; 1505[label="show xv5",fontsize=16,color="magenta"];1506[label="[]",fontsize=16,color="green",shape="box"];1507 -> 658[label="",style="dashed", color="red", weight=0]; 1507[label="show xv5",fontsize=16,color="magenta"];1508[label="[]",fontsize=16,color="green",shape="box"];1509 -> 659[label="",style="dashed", color="red", weight=0]; 1509[label="show xv5",fontsize=16,color="magenta"];1510[label="[]",fontsize=16,color="green",shape="box"];1511 -> 660[label="",style="dashed", color="red", weight=0]; 1511[label="show xv5",fontsize=16,color="magenta"];1512[label="[]",fontsize=16,color="green",shape="box"];1513 -> 661[label="",style="dashed", color="red", weight=0]; 1513[label="show xv5",fontsize=16,color="magenta"];1514[label="[]",fontsize=16,color="green",shape="box"];733[label="primShowInt (Pos (Succ xv500))",fontsize=16,color="black",shape="box"];733 -> 745[label="",style="solid", color="black", weight=3]; 734[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];734 -> 746[label="",style="solid", color="black", weight=3]; 735[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))) : primShowInt (Pos xv50)",fontsize=16,color="green",shape="box"];735 -> 747[label="",style="dashed", color="green", weight=3]; 1515 -> 663[label="",style="dashed", color="red", weight=0]; 1515[label="show xv5",fontsize=16,color="magenta"];1516[label="[]",fontsize=16,color="green",shape="box"];736[label="xv731",fontsize=16,color="green",shape="box"];737[label="putChar xv730 >>= gtGt0 xv74",fontsize=16,color="black",shape="box"];737 -> 748[label="",style="solid", color="black", weight=3]; 738[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];738 -> 749[label="",style="solid", color="black", weight=3]; 1590[label="(xv1890 : xv1891) ++ xv131",fontsize=16,color="black",shape="box"];1590 -> 1612[label="",style="solid", color="black", weight=3]; 1591[label="[] ++ xv131",fontsize=16,color="black",shape="box"];1591 -> 1613[label="",style="solid", color="black", weight=3]; 1736[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1737[label="xv51",fontsize=16,color="green",shape="box"];1738[label="xv50",fontsize=16,color="green",shape="box"];1739[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1740[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1741[label="[]",fontsize=16,color="green",shape="box"];1735[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) xv216",fontsize=16,color="black",shape="triangle"];1735 -> 1748[label="",style="solid", color="black", weight=3]; 745 -> 1484[label="",style="dashed", color="red", weight=0]; 745[label="primShowInt (div Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];745 -> 1519[label="",style="dashed", color="magenta", weight=3]; 745 -> 1520[label="",style="dashed", color="magenta", weight=3]; 746[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))) : []",fontsize=16,color="green",shape="box"];747 -> 687[label="",style="dashed", color="red", weight=0]; 747[label="primShowInt (Pos xv50)",fontsize=16,color="magenta"];747 -> 776[label="",style="dashed", color="magenta", weight=3]; 748 -> 533[label="",style="dashed", color="red", weight=0]; 748[label="primbindIO (putChar xv730) (gtGt0 xv74)",fontsize=16,color="magenta"];748 -> 777[label="",style="dashed", color="magenta", weight=3]; 748 -> 778[label="",style="dashed", color="magenta", weight=3]; 749[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) ter5m",fontsize=16,color="burlywood",shape="box"];2796[label="ter5m/False",fontsize=10,color="white",style="solid",shape="box"];749 -> 2796[label="",style="solid", color="burlywood", weight=9]; 2796 -> 779[label="",style="solid", color="burlywood", weight=3]; 2797[label="ter5m/True",fontsize=10,color="white",style="solid",shape="box"];749 -> 2797[label="",style="solid", color="burlywood", weight=9]; 2797 -> 780[label="",style="solid", color="burlywood", weight=3]; 1612[label="xv1890 : xv1891 ++ xv131",fontsize=16,color="green",shape="box"];1612 -> 1617[label="",style="dashed", color="green", weight=3]; 1613[label="xv131",fontsize=16,color="green",shape="box"];1748[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) xv216",fontsize=16,color="black",shape="box"];1748 -> 1754[label="",style="solid", color="black", weight=3]; 1519 -> 687[label="",style="dashed", color="red", weight=0]; 1519[label="primShowInt (div Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];1519 -> 1592[label="",style="dashed", color="magenta", weight=3]; 1520[label="toEnum (mod Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];1520 -> 1593[label="",style="dashed", color="green", weight=3]; 776[label="Pos xv50",fontsize=16,color="green",shape="box"];777[label="xv74",fontsize=16,color="green",shape="box"];778[label="putChar xv730",fontsize=16,color="black",shape="box"];778 -> 798[label="",style="solid", color="black", weight=3]; 779[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];779 -> 799[label="",style="solid", color="black", weight=3]; 780[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];780 -> 800[label="",style="solid", color="black", weight=3]; 1617 -> 1484[label="",style="dashed", color="red", weight=0]; 1617[label="xv1891 ++ xv131",fontsize=16,color="magenta"];1617 -> 1621[label="",style="dashed", color="magenta", weight=3]; 1754[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) xv216",fontsize=16,color="black",shape="box"];1754 -> 1760[label="",style="solid", color="black", weight=3]; 1592 -> 1614[label="",style="dashed", color="red", weight=0]; 1592[label="div Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];1592 -> 1615[label="",style="dashed", color="magenta", weight=3]; 1592 -> 1616[label="",style="dashed", color="magenta", weight=3]; 1593[label="toEnum (mod Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];1593 -> 1651[label="",style="solid", color="black", weight=3]; 798 -> 808[label="",style="dashed", color="red", weight=0]; 798[label="(seq xv730 output)",fontsize=16,color="magenta"];798 -> 811[label="",style="dashed", color="magenta", weight=3]; 799[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];799 -> 817[label="",style="solid", color="black", weight=3]; 800[label="randomSelect (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];800 -> 818[label="",style="solid", color="black", weight=3]; 1621[label="xv1891",fontsize=16,color="green",shape="box"];1760[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) xv216",fontsize=16,color="black",shape="box"];1760 -> 1767[label="",style="solid", color="black", weight=3]; 1615[label="xv500",fontsize=16,color="green",shape="box"];1616[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];1614[label="div Pos (Succ xv191) Pos (Succ xv192)",fontsize=16,color="black",shape="triangle"];1614 -> 1622[label="",style="solid", color="black", weight=3]; 1651 -> 1680[label="",style="dashed", color="red", weight=0]; 1651[label="primIntToChar (mod Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];1651 -> 1681[label="",style="dashed", color="magenta", weight=3]; 1651 -> 1682[label="",style="dashed", color="magenta", weight=3]; 811 -> 670[label="",style="dashed", color="red", weight=0]; 811[label="output",fontsize=16,color="magenta"];817[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];817 -> 824[label="",style="solid", color="black", weight=3]; 818[label="randomSelect2 (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];818 -> 825[label="",style="solid", color="black", weight=3]; 1767[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) xv216",fontsize=16,color="black",shape="box"];1767 -> 1776[label="",style="solid", color="black", weight=3]; 1622[label="primDivInt (Pos (Succ xv191)) (Pos (Succ xv192))",fontsize=16,color="black",shape="box"];1622 -> 1650[label="",style="solid", color="black", weight=3]; 1681[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];1682[label="xv500",fontsize=16,color="green",shape="box"];1680[label="primIntToChar (mod Pos (Succ xv197) Pos (Succ xv198))",fontsize=16,color="black",shape="triangle"];1680 -> 1683[label="",style="solid", color="black", weight=3]; 824[label="aIOE IOError_FullError",fontsize=16,color="black",shape="box"];824 -> 829[label="",style="solid", color="black", weight=3]; 825[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];825 -> 830[label="",style="solid", color="black", weight=3]; 1776[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (LT == GT) xv216",fontsize=16,color="black",shape="box"];1776 -> 1787[label="",style="solid", color="black", weight=3]; 1650[label="Pos (primDivNatS (Succ xv191) (Succ xv192))",fontsize=16,color="green",shape="box"];1650 -> 1679[label="",style="dashed", color="green", weight=3]; 1683[label="primIntToChar (primModInt (Pos (Succ xv197)) (Pos (Succ xv198)))",fontsize=16,color="black",shape="box"];1683 -> 1703[label="",style="solid", color="black", weight=3]; 829[label="AProVE_Exception (AET_IOError (IOError IOError_FullError [] [] Nothing))",fontsize=16,color="green",shape="box"];830[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) ter6m",fontsize=16,color="burlywood",shape="box"];2798[label="ter6m/False",fontsize=10,color="white",style="solid",shape="box"];830 -> 2798[label="",style="solid", color="burlywood", weight=9]; 2798 -> 834[label="",style="solid", color="burlywood", weight=3]; 2799[label="ter6m/True",fontsize=10,color="white",style="solid",shape="box"];830 -> 2799[label="",style="solid", color="burlywood", weight=9]; 2799 -> 835[label="",style="solid", color="burlywood", weight=3]; 1787[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) False xv216",fontsize=16,color="black",shape="box"];1787 -> 1800[label="",style="solid", color="black", weight=3]; 1679[label="primDivNatS (Succ xv191) (Succ xv192)",fontsize=16,color="black",shape="triangle"];1679 -> 1684[label="",style="solid", color="black", weight=3]; 1703[label="primIntToChar (Pos (primModNatS (Succ xv197) (Succ xv198)))",fontsize=16,color="black",shape="box"];1703 -> 1749[label="",style="solid", color="black", weight=3]; 834[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];834 -> 840[label="",style="solid", color="black", weight=3]; 835[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];835 -> 841[label="",style="solid", color="black", weight=3]; 1800[label="(shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="black",shape="box"];1800 -> 1812[label="",style="solid", color="black", weight=3]; 1684[label="primDivNatS0 xv191 xv192 (primGEqNatS xv191 xv192)",fontsize=16,color="burlywood",shape="box"];2800[label="xv191/Succ xv1910",fontsize=10,color="white",style="solid",shape="box"];1684 -> 2800[label="",style="solid", color="burlywood", weight=9]; 2800 -> 1704[label="",style="solid", color="burlywood", weight=3]; 2801[label="xv191/Zero",fontsize=10,color="white",style="solid",shape="box"];1684 -> 2801[label="",style="solid", color="burlywood", weight=9]; 2801 -> 1705[label="",style="solid", color="burlywood", weight=3]; 1749[label="Char (primModNatS (Succ xv197) (Succ xv198))",fontsize=16,color="green",shape="box"];1749 -> 1755[label="",style="dashed", color="green", weight=3]; 840[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];840 -> 848[label="",style="solid", color="black", weight=3]; 841[label="randomSelect (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];841 -> 849[label="",style="solid", color="black", weight=3]; 1812[label="shows xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1812 -> 1825[label="",style="solid", color="black", weight=3]; 1704[label="primDivNatS0 (Succ xv1910) xv192 (primGEqNatS (Succ xv1910) xv192)",fontsize=16,color="burlywood",shape="box"];2802[label="xv192/Succ xv1920",fontsize=10,color="white",style="solid",shape="box"];1704 -> 2802[label="",style="solid", color="burlywood", weight=9]; 2802 -> 1750[label="",style="solid", color="burlywood", weight=3]; 2803[label="xv192/Zero",fontsize=10,color="white",style="solid",shape="box"];1704 -> 2803[label="",style="solid", color="burlywood", weight=9]; 2803 -> 1751[label="",style="solid", color="burlywood", weight=3]; 1705[label="primDivNatS0 Zero xv192 (primGEqNatS Zero xv192)",fontsize=16,color="burlywood",shape="box"];2804[label="xv192/Succ xv1920",fontsize=10,color="white",style="solid",shape="box"];1705 -> 2804[label="",style="solid", color="burlywood", weight=9]; 2804 -> 1752[label="",style="solid", color="burlywood", weight=3]; 2805[label="xv192/Zero",fontsize=10,color="white",style="solid",shape="box"];1705 -> 2805[label="",style="solid", color="burlywood", weight=9]; 2805 -> 1753[label="",style="solid", color="burlywood", weight=3]; 1755[label="primModNatS (Succ xv197) (Succ xv198)",fontsize=16,color="black",shape="triangle"];1755 -> 1761[label="",style="solid", color="black", weight=3]; 848[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];848 -> 873[label="",style="solid", color="black", weight=3]; 849[label="randomSelect3 (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];849 -> 874[label="",style="solid", color="black", weight=3]; 1825[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="blue",shape="box"];2806[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2806[label="",style="solid", color="blue", weight=9]; 2806 -> 1840[label="",style="solid", color="blue", weight=3]; 2807[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2807[label="",style="solid", color="blue", weight=9]; 2807 -> 1841[label="",style="solid", color="blue", weight=3]; 2808[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2808[label="",style="solid", color="blue", weight=9]; 2808 -> 1842[label="",style="solid", color="blue", weight=3]; 2809[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2809[label="",style="solid", color="blue", weight=9]; 2809 -> 1843[label="",style="solid", color="blue", weight=3]; 2810[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2810[label="",style="solid", color="blue", weight=9]; 2810 -> 1844[label="",style="solid", color="blue", weight=3]; 2811[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2811[label="",style="solid", color="blue", weight=9]; 2811 -> 1845[label="",style="solid", color="blue", weight=3]; 2812[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2812[label="",style="solid", color="blue", weight=9]; 2812 -> 1846[label="",style="solid", color="blue", weight=3]; 2813[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2813[label="",style="solid", color="blue", weight=9]; 2813 -> 1847[label="",style="solid", color="blue", weight=3]; 2814[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2814[label="",style="solid", color="blue", weight=9]; 2814 -> 1848[label="",style="solid", color="blue", weight=3]; 2815[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2815[label="",style="solid", color="blue", weight=9]; 2815 -> 1849[label="",style="solid", color="blue", weight=3]; 2816[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2816[label="",style="solid", color="blue", weight=9]; 2816 -> 1850[label="",style="solid", color="blue", weight=3]; 2817[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2817[label="",style="solid", color="blue", weight=9]; 2817 -> 1851[label="",style="solid", color="blue", weight=3]; 2818[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2818[label="",style="solid", color="blue", weight=9]; 2818 -> 1852[label="",style="solid", color="blue", weight=3]; 2819[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2819[label="",style="solid", color="blue", weight=9]; 2819 -> 1853[label="",style="solid", color="blue", weight=3]; 2820[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2820[label="",style="solid", color="blue", weight=9]; 2820 -> 1854[label="",style="solid", color="blue", weight=3]; 2821[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2821[label="",style="solid", color="blue", weight=9]; 2821 -> 1855[label="",style="solid", color="blue", weight=3]; 2822[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2822[label="",style="solid", color="blue", weight=9]; 2822 -> 1856[label="",style="solid", color="blue", weight=3]; 2823[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2823[label="",style="solid", color="blue", weight=9]; 2823 -> 1857[label="",style="solid", color="blue", weight=3]; 1750[label="primDivNatS0 (Succ xv1910) (Succ xv1920) (primGEqNatS (Succ xv1910) (Succ xv1920))",fontsize=16,color="black",shape="box"];1750 -> 1756[label="",style="solid", color="black", weight=3]; 1751[label="primDivNatS0 (Succ xv1910) Zero (primGEqNatS (Succ xv1910) Zero)",fontsize=16,color="black",shape="box"];1751 -> 1757[label="",style="solid", color="black", weight=3]; 1752[label="primDivNatS0 Zero (Succ xv1920) (primGEqNatS Zero (Succ xv1920))",fontsize=16,color="black",shape="box"];1752 -> 1758[label="",style="solid", color="black", weight=3]; 1753[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1753 -> 1759[label="",style="solid", color="black", weight=3]; 1761[label="primModNatS0 xv197 xv198 (primGEqNatS xv197 xv198)",fontsize=16,color="burlywood",shape="box"];2824[label="xv197/Succ xv1970",fontsize=10,color="white",style="solid",shape="box"];1761 -> 2824[label="",style="solid", color="burlywood", weight=9]; 2824 -> 1768[label="",style="solid", color="burlywood", weight=3]; 2825[label="xv197/Zero",fontsize=10,color="white",style="solid",shape="box"];1761 -> 2825[label="",style="solid", color="burlywood", weight=9]; 2825 -> 1769[label="",style="solid", color="burlywood", weight=3]; 873[label="aIOE IOError_PermDenied",fontsize=16,color="black",shape="box"];873 -> 900[label="",style="solid", color="black", weight=3]; 874[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];1840[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1840 -> 1872[label="",style="solid", color="black", weight=3]; 1841[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1841 -> 1873[label="",style="solid", color="black", weight=3]; 1842[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1842 -> 1874[label="",style="solid", color="black", weight=3]; 1843[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1843 -> 1875[label="",style="solid", color="black", weight=3]; 1844[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1844 -> 1876[label="",style="solid", color="black", weight=3]; 1845[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="burlywood",shape="box"];2826[label="xv211/xv2110 :% xv2111",fontsize=10,color="white",style="solid",shape="box"];1845 -> 2826[label="",style="solid", color="burlywood", weight=9]; 2826 -> 1877[label="",style="solid", color="burlywood", weight=3]; 1846[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1846 -> 1878[label="",style="solid", color="black", weight=3]; 1847[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1847 -> 1879[label="",style="solid", color="black", weight=3]; 1848[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1848 -> 1880[label="",style="solid", color="black", weight=3]; 1849[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1849 -> 1881[label="",style="solid", color="black", weight=3]; 1850[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1850 -> 1882[label="",style="solid", color="black", weight=3]; 1851[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1851 -> 1883[label="",style="solid", color="black", weight=3]; 1852[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1852 -> 1884[label="",style="solid", color="black", weight=3]; 1853[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1853 -> 1885[label="",style="solid", color="black", weight=3]; 1854[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1854 -> 1886[label="",style="solid", color="black", weight=3]; 1855[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1855 -> 1887[label="",style="solid", color="black", weight=3]; 1856[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1856 -> 1888[label="",style="solid", color="black", weight=3]; 1857[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1857 -> 1889[label="",style="solid", color="black", weight=3]; 1756 -> 2471[label="",style="dashed", color="red", weight=0]; 1756[label="primDivNatS0 (Succ xv1910) (Succ xv1920) (primGEqNatS xv1910 xv1920)",fontsize=16,color="magenta"];1756 -> 2472[label="",style="dashed", color="magenta", weight=3]; 1756 -> 2473[label="",style="dashed", color="magenta", weight=3]; 1756 -> 2474[label="",style="dashed", color="magenta", weight=3]; 1756 -> 2475[label="",style="dashed", color="magenta", weight=3]; 1757[label="primDivNatS0 (Succ xv1910) Zero True",fontsize=16,color="black",shape="box"];1757 -> 1764[label="",style="solid", color="black", weight=3]; 1758[label="primDivNatS0 Zero (Succ xv1920) False",fontsize=16,color="black",shape="box"];1758 -> 1765[label="",style="solid", color="black", weight=3]; 1759[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];1759 -> 1766[label="",style="solid", color="black", weight=3]; 1768[label="primModNatS0 (Succ xv1970) xv198 (primGEqNatS (Succ xv1970) xv198)",fontsize=16,color="burlywood",shape="box"];2827[label="xv198/Succ xv1980",fontsize=10,color="white",style="solid",shape="box"];1768 -> 2827[label="",style="solid", color="burlywood", weight=9]; 2827 -> 1777[label="",style="solid", color="burlywood", weight=3]; 2828[label="xv198/Zero",fontsize=10,color="white",style="solid",shape="box"];1768 -> 2828[label="",style="solid", color="burlywood", weight=9]; 2828 -> 1778[label="",style="solid", color="burlywood", weight=3]; 1769[label="primModNatS0 Zero xv198 (primGEqNatS Zero xv198)",fontsize=16,color="burlywood",shape="box"];2829[label="xv198/Succ xv1980",fontsize=10,color="white",style="solid",shape="box"];1769 -> 2829[label="",style="solid", color="burlywood", weight=9]; 2829 -> 1779[label="",style="solid", color="burlywood", weight=3]; 2830[label="xv198/Zero",fontsize=10,color="white",style="solid",shape="box"];1769 -> 2830[label="",style="solid", color="burlywood", weight=9]; 2830 -> 1780[label="",style="solid", color="burlywood", weight=3]; 900[label="AProVE_Exception (AET_IOError (IOError IOError_PermDenied [] [] Nothing))",fontsize=16,color="green",shape="box"];1872 -> 1484[label="",style="dashed", color="red", weight=0]; 1872[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1872 -> 1902[label="",style="dashed", color="magenta", weight=3]; 1872 -> 1903[label="",style="dashed", color="magenta", weight=3]; 1873 -> 1484[label="",style="dashed", color="red", weight=0]; 1873[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1873 -> 1904[label="",style="dashed", color="magenta", weight=3]; 1873 -> 1905[label="",style="dashed", color="magenta", weight=3]; 1874 -> 1484[label="",style="dashed", color="red", weight=0]; 1874[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1874 -> 1906[label="",style="dashed", color="magenta", weight=3]; 1874 -> 1907[label="",style="dashed", color="magenta", weight=3]; 1875 -> 1484[label="",style="dashed", color="red", weight=0]; 1875[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1875 -> 1908[label="",style="dashed", color="magenta", weight=3]; 1875 -> 1909[label="",style="dashed", color="magenta", weight=3]; 1876 -> 1484[label="",style="dashed", color="red", weight=0]; 1876[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1876 -> 1910[label="",style="dashed", color="magenta", weight=3]; 1876 -> 1911[label="",style="dashed", color="magenta", weight=3]; 1877[label="showsPrec (Pos Zero) (xv2110 :% xv2111) ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1877 -> 1912[label="",style="solid", color="black", weight=3]; 1878 -> 1484[label="",style="dashed", color="red", weight=0]; 1878[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1878 -> 1913[label="",style="dashed", color="magenta", weight=3]; 1878 -> 1914[label="",style="dashed", color="magenta", weight=3]; 1879 -> 1484[label="",style="dashed", color="red", weight=0]; 1879[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1879 -> 1915[label="",style="dashed", color="magenta", weight=3]; 1879 -> 1916[label="",style="dashed", color="magenta", weight=3]; 1880 -> 1484[label="",style="dashed", color="red", weight=0]; 1880[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1880 -> 1917[label="",style="dashed", color="magenta", weight=3]; 1880 -> 1918[label="",style="dashed", color="magenta", weight=3]; 1881 -> 1484[label="",style="dashed", color="red", weight=0]; 1881[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1881 -> 1919[label="",style="dashed", color="magenta", weight=3]; 1881 -> 1920[label="",style="dashed", color="magenta", weight=3]; 1882 -> 1484[label="",style="dashed", color="red", weight=0]; 1882[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1882 -> 1921[label="",style="dashed", color="magenta", weight=3]; 1882 -> 1922[label="",style="dashed", color="magenta", weight=3]; 1883 -> 1484[label="",style="dashed", color="red", weight=0]; 1883[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1883 -> 1923[label="",style="dashed", color="magenta", weight=3]; 1883 -> 1924[label="",style="dashed", color="magenta", weight=3]; 1884 -> 1484[label="",style="dashed", color="red", weight=0]; 1884[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1884 -> 1925[label="",style="dashed", color="magenta", weight=3]; 1884 -> 1926[label="",style="dashed", color="magenta", weight=3]; 1885 -> 1484[label="",style="dashed", color="red", weight=0]; 1885[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1885 -> 1927[label="",style="dashed", color="magenta", weight=3]; 1885 -> 1928[label="",style="dashed", color="magenta", weight=3]; 1886 -> 1484[label="",style="dashed", color="red", weight=0]; 1886[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1886 -> 1929[label="",style="dashed", color="magenta", weight=3]; 1886 -> 1930[label="",style="dashed", color="magenta", weight=3]; 1887 -> 1484[label="",style="dashed", color="red", weight=0]; 1887[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1887 -> 1931[label="",style="dashed", color="magenta", weight=3]; 1887 -> 1932[label="",style="dashed", color="magenta", weight=3]; 1888 -> 1484[label="",style="dashed", color="red", weight=0]; 1888[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1888 -> 1933[label="",style="dashed", color="magenta", weight=3]; 1888 -> 1934[label="",style="dashed", color="magenta", weight=3]; 1889 -> 1484[label="",style="dashed", color="red", weight=0]; 1889[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1889 -> 1935[label="",style="dashed", color="magenta", weight=3]; 1889 -> 1936[label="",style="dashed", color="magenta", weight=3]; 2472[label="xv1910",fontsize=16,color="green",shape="box"];2473[label="xv1920",fontsize=16,color="green",shape="box"];2474[label="xv1910",fontsize=16,color="green",shape="box"];2475[label="xv1920",fontsize=16,color="green",shape="box"];2471[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS xv261 xv262)",fontsize=16,color="burlywood",shape="triangle"];2831[label="xv261/Succ xv2610",fontsize=10,color="white",style="solid",shape="box"];2471 -> 2831[label="",style="solid", color="burlywood", weight=9]; 2831 -> 2512[label="",style="solid", color="burlywood", weight=3]; 2832[label="xv261/Zero",fontsize=10,color="white",style="solid",shape="box"];2471 -> 2832[label="",style="solid", color="burlywood", weight=9]; 2832 -> 2513[label="",style="solid", color="burlywood", weight=3]; 1764[label="Succ (primDivNatS (primMinusNatS (Succ xv1910) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1764 -> 1774[label="",style="dashed", color="green", weight=3]; 1765[label="Zero",fontsize=16,color="green",shape="box"];1766[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1766 -> 1775[label="",style="dashed", color="green", weight=3]; 1777[label="primModNatS0 (Succ xv1970) (Succ xv1980) (primGEqNatS (Succ xv1970) (Succ xv1980))",fontsize=16,color="black",shape="box"];1777 -> 1788[label="",style="solid", color="black", weight=3]; 1778[label="primModNatS0 (Succ xv1970) Zero (primGEqNatS (Succ xv1970) Zero)",fontsize=16,color="black",shape="box"];1778 -> 1789[label="",style="solid", color="black", weight=3]; 1779[label="primModNatS0 Zero (Succ xv1980) (primGEqNatS Zero (Succ xv1980))",fontsize=16,color="black",shape="box"];1779 -> 1790[label="",style="solid", color="black", weight=3]; 1780[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1780 -> 1791[label="",style="solid", color="black", weight=3]; 1902 -> 646[label="",style="dashed", color="red", weight=0]; 1902[label="show xv211",fontsize=16,color="magenta"];1902 -> 1950[label="",style="dashed", color="magenta", weight=3]; 1903[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="black",shape="triangle"];1903 -> 1951[label="",style="solid", color="black", weight=3]; 1904 -> 647[label="",style="dashed", color="red", weight=0]; 1904[label="show xv211",fontsize=16,color="magenta"];1904 -> 1952[label="",style="dashed", color="magenta", weight=3]; 1905 -> 1903[label="",style="dashed", color="red", weight=0]; 1905[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1906 -> 648[label="",style="dashed", color="red", weight=0]; 1906[label="show xv211",fontsize=16,color="magenta"];1906 -> 1953[label="",style="dashed", color="magenta", weight=3]; 1907 -> 1903[label="",style="dashed", color="red", weight=0]; 1907[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1908 -> 649[label="",style="dashed", color="red", weight=0]; 1908[label="show xv211",fontsize=16,color="magenta"];1908 -> 1954[label="",style="dashed", color="magenta", weight=3]; 1909 -> 1903[label="",style="dashed", color="red", weight=0]; 1909[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1910 -> 650[label="",style="dashed", color="red", weight=0]; 1910[label="show xv211",fontsize=16,color="magenta"];1910 -> 1955[label="",style="dashed", color="magenta", weight=3]; 1911 -> 1903[label="",style="dashed", color="red", weight=0]; 1911[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1912 -> 1735[label="",style="dashed", color="red", weight=0]; 1912[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows xv2110) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows xv2111) ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="magenta"];1912 -> 1956[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1957[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1958[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1959[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1960[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1961[label="",style="dashed", color="magenta", weight=3]; 1913 -> 652[label="",style="dashed", color="red", weight=0]; 1913[label="show xv211",fontsize=16,color="magenta"];1913 -> 1962[label="",style="dashed", color="magenta", weight=3]; 1914 -> 1903[label="",style="dashed", color="red", weight=0]; 1914[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1915 -> 653[label="",style="dashed", color="red", weight=0]; 1915[label="show xv211",fontsize=16,color="magenta"];1915 -> 1963[label="",style="dashed", color="magenta", weight=3]; 1916 -> 1903[label="",style="dashed", color="red", weight=0]; 1916[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1917 -> 654[label="",style="dashed", color="red", weight=0]; 1917[label="show xv211",fontsize=16,color="magenta"];1917 -> 1964[label="",style="dashed", color="magenta", weight=3]; 1918 -> 1903[label="",style="dashed", color="red", weight=0]; 1918[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1919 -> 655[label="",style="dashed", color="red", weight=0]; 1919[label="show xv211",fontsize=16,color="magenta"];1919 -> 1965[label="",style="dashed", color="magenta", weight=3]; 1920 -> 1903[label="",style="dashed", color="red", weight=0]; 1920[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1921 -> 656[label="",style="dashed", color="red", weight=0]; 1921[label="show xv211",fontsize=16,color="magenta"];1921 -> 1966[label="",style="dashed", color="magenta", weight=3]; 1922 -> 1903[label="",style="dashed", color="red", weight=0]; 1922[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1923 -> 657[label="",style="dashed", color="red", weight=0]; 1923[label="show xv211",fontsize=16,color="magenta"];1923 -> 1967[label="",style="dashed", color="magenta", weight=3]; 1924 -> 1903[label="",style="dashed", color="red", weight=0]; 1924[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1925 -> 658[label="",style="dashed", color="red", weight=0]; 1925[label="show xv211",fontsize=16,color="magenta"];1925 -> 1968[label="",style="dashed", color="magenta", weight=3]; 1926 -> 1903[label="",style="dashed", color="red", weight=0]; 1926[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1927 -> 659[label="",style="dashed", color="red", weight=0]; 1927[label="show xv211",fontsize=16,color="magenta"];1927 -> 1969[label="",style="dashed", color="magenta", weight=3]; 1928 -> 1903[label="",style="dashed", color="red", weight=0]; 1928[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1929 -> 660[label="",style="dashed", color="red", weight=0]; 1929[label="show xv211",fontsize=16,color="magenta"];1929 -> 1970[label="",style="dashed", color="magenta", weight=3]; 1930 -> 1903[label="",style="dashed", color="red", weight=0]; 1930[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1931 -> 661[label="",style="dashed", color="red", weight=0]; 1931[label="show xv211",fontsize=16,color="magenta"];1931 -> 1971[label="",style="dashed", color="magenta", weight=3]; 1932 -> 1903[label="",style="dashed", color="red", weight=0]; 1932[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1933 -> 662[label="",style="dashed", color="red", weight=0]; 1933[label="show xv211",fontsize=16,color="magenta"];1933 -> 1972[label="",style="dashed", color="magenta", weight=3]; 1934 -> 1903[label="",style="dashed", color="red", weight=0]; 1934[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1935 -> 663[label="",style="dashed", color="red", weight=0]; 1935[label="show xv211",fontsize=16,color="magenta"];1935 -> 1973[label="",style="dashed", color="magenta", weight=3]; 1936 -> 1903[label="",style="dashed", color="red", weight=0]; 1936[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];2512[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS (Succ xv2610) xv262)",fontsize=16,color="burlywood",shape="box"];2833[label="xv262/Succ xv2620",fontsize=10,color="white",style="solid",shape="box"];2512 -> 2833[label="",style="solid", color="burlywood", weight=9]; 2833 -> 2524[label="",style="solid", color="burlywood", weight=3]; 2834[label="xv262/Zero",fontsize=10,color="white",style="solid",shape="box"];2512 -> 2834[label="",style="solid", color="burlywood", weight=9]; 2834 -> 2525[label="",style="solid", color="burlywood", weight=3]; 2513[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS Zero xv262)",fontsize=16,color="burlywood",shape="box"];2835[label="xv262/Succ xv2620",fontsize=10,color="white",style="solid",shape="box"];2513 -> 2835[label="",style="solid", color="burlywood", weight=9]; 2835 -> 2526[label="",style="solid", color="burlywood", weight=3]; 2836[label="xv262/Zero",fontsize=10,color="white",style="solid",shape="box"];2513 -> 2836[label="",style="solid", color="burlywood", weight=9]; 2836 -> 2527[label="",style="solid", color="burlywood", weight=3]; 1774 -> 2725[label="",style="dashed", color="red", weight=0]; 1774[label="primDivNatS (primMinusNatS (Succ xv1910) Zero) (Succ Zero)",fontsize=16,color="magenta"];1774 -> 2726[label="",style="dashed", color="magenta", weight=3]; 1774 -> 2727[label="",style="dashed", color="magenta", weight=3]; 1774 -> 2728[label="",style="dashed", color="magenta", weight=3]; 1775 -> 2725[label="",style="dashed", color="red", weight=0]; 1775[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1775 -> 2729[label="",style="dashed", color="magenta", weight=3]; 1775 -> 2730[label="",style="dashed", color="magenta", weight=3]; 1775 -> 2731[label="",style="dashed", color="magenta", weight=3]; 1788 -> 2546[label="",style="dashed", color="red", weight=0]; 1788[label="primModNatS0 (Succ xv1970) (Succ xv1980) (primGEqNatS xv1970 xv1980)",fontsize=16,color="magenta"];1788 -> 2547[label="",style="dashed", color="magenta", weight=3]; 1788 -> 2548[label="",style="dashed", color="magenta", weight=3]; 1788 -> 2549[label="",style="dashed", color="magenta", weight=3]; 1788 -> 2550[label="",style="dashed", color="magenta", weight=3]; 1789[label="primModNatS0 (Succ xv1970) Zero True",fontsize=16,color="black",shape="box"];1789 -> 1803[label="",style="solid", color="black", weight=3]; 1790[label="primModNatS0 Zero (Succ xv1980) False",fontsize=16,color="black",shape="box"];1790 -> 1804[label="",style="solid", color="black", weight=3]; 1791[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];1791 -> 1805[label="",style="solid", color="black", weight=3]; 1950[label="xv211",fontsize=16,color="green",shape="box"];1951[label="showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : []) (shows xv215 xv216)",fontsize=16,color="black",shape="box"];1951 -> 1990[label="",style="solid", color="black", weight=3]; 1952[label="xv211",fontsize=16,color="green",shape="box"];1953[label="xv211",fontsize=16,color="green",shape="box"];1954[label="xv211",fontsize=16,color="green",shape="box"];1955[label="xv211",fontsize=16,color="green",shape="box"];1956[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1957[label="xv2111",fontsize=16,color="green",shape="box"];1958[label="xv2110",fontsize=16,color="green",shape="box"];1959[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1960[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1961 -> 1903[label="",style="dashed", color="red", weight=0]; 1961[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1962[label="xv211",fontsize=16,color="green",shape="box"];1963[label="xv211",fontsize=16,color="green",shape="box"];1964[label="xv211",fontsize=16,color="green",shape="box"];1965[label="xv211",fontsize=16,color="green",shape="box"];1966[label="xv211",fontsize=16,color="green",shape="box"];1967[label="xv211",fontsize=16,color="green",shape="box"];1968[label="xv211",fontsize=16,color="green",shape="box"];1969[label="xv211",fontsize=16,color="green",shape="box"];1970[label="xv211",fontsize=16,color="green",shape="box"];1971[label="xv211",fontsize=16,color="green",shape="box"];1972[label="xv211",fontsize=16,color="green",shape="box"];1973[label="xv211",fontsize=16,color="green",shape="box"];2524[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS (Succ xv2610) (Succ xv2620))",fontsize=16,color="black",shape="box"];2524 -> 2538[label="",style="solid", color="black", weight=3]; 2525[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS (Succ xv2610) Zero)",fontsize=16,color="black",shape="box"];2525 -> 2539[label="",style="solid", color="black", weight=3]; 2526[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS Zero (Succ xv2620))",fontsize=16,color="black",shape="box"];2526 -> 2540[label="",style="solid", color="black", weight=3]; 2527[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2527 -> 2541[label="",style="solid", color="black", weight=3]; 2726[label="Zero",fontsize=16,color="green",shape="box"];2727[label="Succ xv1910",fontsize=16,color="green",shape="box"];2728[label="Zero",fontsize=16,color="green",shape="box"];2725[label="primDivNatS (primMinusNatS xv273 xv274) (Succ xv275)",fontsize=16,color="burlywood",shape="triangle"];2837[label="xv273/Succ xv2730",fontsize=10,color="white",style="solid",shape="box"];2725 -> 2837[label="",style="solid", color="burlywood", weight=9]; 2837 -> 2750[label="",style="solid", color="burlywood", weight=3]; 2838[label="xv273/Zero",fontsize=10,color="white",style="solid",shape="box"];2725 -> 2838[label="",style="solid", color="burlywood", weight=9]; 2838 -> 2751[label="",style="solid", color="burlywood", weight=3]; 2729[label="Zero",fontsize=16,color="green",shape="box"];2730[label="Zero",fontsize=16,color="green",shape="box"];2731[label="Zero",fontsize=16,color="green",shape="box"];2547[label="xv1970",fontsize=16,color="green",shape="box"];2548[label="xv1980",fontsize=16,color="green",shape="box"];2549[label="xv1980",fontsize=16,color="green",shape="box"];2550[label="xv1970",fontsize=16,color="green",shape="box"];2546[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS xv266 xv267)",fontsize=16,color="burlywood",shape="triangle"];2839[label="xv266/Succ xv2660",fontsize=10,color="white",style="solid",shape="box"];2546 -> 2839[label="",style="solid", color="burlywood", weight=9]; 2839 -> 2587[label="",style="solid", color="burlywood", weight=3]; 2840[label="xv266/Zero",fontsize=10,color="white",style="solid",shape="box"];2546 -> 2840[label="",style="solid", color="burlywood", weight=9]; 2840 -> 2588[label="",style="solid", color="burlywood", weight=3]; 1803 -> 2633[label="",style="dashed", color="red", weight=0]; 1803[label="primModNatS (primMinusNatS (Succ xv1970) Zero) (Succ Zero)",fontsize=16,color="magenta"];1803 -> 2634[label="",style="dashed", color="magenta", weight=3]; 1803 -> 2635[label="",style="dashed", color="magenta", weight=3]; 1803 -> 2636[label="",style="dashed", color="magenta", weight=3]; 1804[label="Succ Zero",fontsize=16,color="green",shape="box"];1805 -> 2633[label="",style="dashed", color="red", weight=0]; 1805[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1805 -> 2637[label="",style="dashed", color="magenta", weight=3]; 1805 -> 2638[label="",style="dashed", color="magenta", weight=3]; 1805 -> 2639[label="",style="dashed", color="magenta", weight=3]; 1990 -> 1484[label="",style="dashed", color="red", weight=0]; 1990[label="(++) (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : []) shows xv215 xv216",fontsize=16,color="magenta"];1990 -> 2006[label="",style="dashed", color="magenta", weight=3]; 1990 -> 2007[label="",style="dashed", color="magenta", weight=3]; 2538 -> 2471[label="",style="dashed", color="red", weight=0]; 2538[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS xv2610 xv2620)",fontsize=16,color="magenta"];2538 -> 2589[label="",style="dashed", color="magenta", weight=3]; 2538 -> 2590[label="",style="dashed", color="magenta", weight=3]; 2539[label="primDivNatS0 (Succ xv259) (Succ xv260) True",fontsize=16,color="black",shape="triangle"];2539 -> 2591[label="",style="solid", color="black", weight=3]; 2540[label="primDivNatS0 (Succ xv259) (Succ xv260) False",fontsize=16,color="black",shape="box"];2540 -> 2592[label="",style="solid", color="black", weight=3]; 2541 -> 2539[label="",style="dashed", color="red", weight=0]; 2541[label="primDivNatS0 (Succ xv259) (Succ xv260) True",fontsize=16,color="magenta"];2750[label="primDivNatS (primMinusNatS (Succ xv2730) xv274) (Succ xv275)",fontsize=16,color="burlywood",shape="box"];2841[label="xv274/Succ xv2740",fontsize=10,color="white",style="solid",shape="box"];2750 -> 2841[label="",style="solid", color="burlywood", weight=9]; 2841 -> 2752[label="",style="solid", color="burlywood", weight=3]; 2842[label="xv274/Zero",fontsize=10,color="white",style="solid",shape="box"];2750 -> 2842[label="",style="solid", color="burlywood", weight=9]; 2842 -> 2753[label="",style="solid", color="burlywood", weight=3]; 2751[label="primDivNatS (primMinusNatS Zero xv274) (Succ xv275)",fontsize=16,color="burlywood",shape="box"];2843[label="xv274/Succ xv2740",fontsize=10,color="white",style="solid",shape="box"];2751 -> 2843[label="",style="solid", color="burlywood", weight=9]; 2843 -> 2754[label="",style="solid", color="burlywood", weight=3]; 2844[label="xv274/Zero",fontsize=10,color="white",style="solid",shape="box"];2751 -> 2844[label="",style="solid", color="burlywood", weight=9]; 2844 -> 2755[label="",style="solid", color="burlywood", weight=3]; 2587[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS (Succ xv2660) xv267)",fontsize=16,color="burlywood",shape="box"];2845[label="xv267/Succ xv2670",fontsize=10,color="white",style="solid",shape="box"];2587 -> 2845[label="",style="solid", color="burlywood", weight=9]; 2845 -> 2597[label="",style="solid", color="burlywood", weight=3]; 2846[label="xv267/Zero",fontsize=10,color="white",style="solid",shape="box"];2587 -> 2846[label="",style="solid", color="burlywood", weight=9]; 2846 -> 2598[label="",style="solid", color="burlywood", weight=3]; 2588[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS Zero xv267)",fontsize=16,color="burlywood",shape="box"];2847[label="xv267/Succ xv2670",fontsize=10,color="white",style="solid",shape="box"];2588 -> 2847[label="",style="solid", color="burlywood", weight=9]; 2847 -> 2599[label="",style="solid", color="burlywood", weight=3]; 2848[label="xv267/Zero",fontsize=10,color="white",style="solid",shape="box"];2588 -> 2848[label="",style="solid", color="burlywood", weight=9]; 2848 -> 2600[label="",style="solid", color="burlywood", weight=3]; 2634[label="Zero",fontsize=16,color="green",shape="box"];2635[label="Zero",fontsize=16,color="green",shape="box"];2636[label="Succ xv1970",fontsize=16,color="green",shape="box"];2633[label="primModNatS (primMinusNatS xv269 xv270) (Succ xv271)",fontsize=16,color="burlywood",shape="triangle"];2849[label="xv269/Succ xv2690",fontsize=10,color="white",style="solid",shape="box"];2633 -> 2849[label="",style="solid", color="burlywood", weight=9]; 2849 -> 2664[label="",style="solid", color="burlywood", weight=3]; 2850[label="xv269/Zero",fontsize=10,color="white",style="solid",shape="box"];2633 -> 2850[label="",style="solid", color="burlywood", weight=9]; 2850 -> 2665[label="",style="solid", color="burlywood", weight=3]; 2637[label="Zero",fontsize=16,color="green",shape="box"];2638[label="Zero",fontsize=16,color="green",shape="box"];2639[label="Zero",fontsize=16,color="green",shape="box"];2006[label="Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : []",fontsize=16,color="green",shape="box"];2007[label="shows xv215 xv216",fontsize=16,color="black",shape="box"];2007 -> 2021[label="",style="solid", color="black", weight=3]; 2589[label="xv2610",fontsize=16,color="green",shape="box"];2590[label="xv2620",fontsize=16,color="green",shape="box"];2591[label="Succ (primDivNatS (primMinusNatS (Succ xv259) (Succ xv260)) (Succ (Succ xv260)))",fontsize=16,color="green",shape="box"];2591 -> 2601[label="",style="dashed", color="green", weight=3]; 2592[label="Zero",fontsize=16,color="green",shape="box"];2752[label="primDivNatS (primMinusNatS (Succ xv2730) (Succ xv2740)) (Succ xv275)",fontsize=16,color="black",shape="box"];2752 -> 2756[label="",style="solid", color="black", weight=3]; 2753[label="primDivNatS (primMinusNatS (Succ xv2730) Zero) (Succ xv275)",fontsize=16,color="black",shape="box"];2753 -> 2757[label="",style="solid", color="black", weight=3]; 2754[label="primDivNatS (primMinusNatS Zero (Succ xv2740)) (Succ xv275)",fontsize=16,color="black",shape="box"];2754 -> 2758[label="",style="solid", color="black", weight=3]; 2755[label="primDivNatS (primMinusNatS Zero Zero) (Succ xv275)",fontsize=16,color="black",shape="box"];2755 -> 2759[label="",style="solid", color="black", weight=3]; 2597[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS (Succ xv2660) (Succ xv2670))",fontsize=16,color="black",shape="box"];2597 -> 2608[label="",style="solid", color="black", weight=3]; 2598[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS (Succ xv2660) Zero)",fontsize=16,color="black",shape="box"];2598 -> 2609[label="",style="solid", color="black", weight=3]; 2599[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS Zero (Succ xv2670))",fontsize=16,color="black",shape="box"];2599 -> 2610[label="",style="solid", color="black", weight=3]; 2600[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2600 -> 2611[label="",style="solid", color="black", weight=3]; 2664[label="primModNatS (primMinusNatS (Succ xv2690) xv270) (Succ xv271)",fontsize=16,color="burlywood",shape="box"];2851[label="xv270/Succ xv2700",fontsize=10,color="white",style="solid",shape="box"];2664 -> 2851[label="",style="solid", color="burlywood", weight=9]; 2851 -> 2670[label="",style="solid", color="burlywood", weight=3]; 2852[label="xv270/Zero",fontsize=10,color="white",style="solid",shape="box"];2664 -> 2852[label="",style="solid", color="burlywood", weight=9]; 2852 -> 2671[label="",style="solid", color="burlywood", weight=3]; 2665[label="primModNatS (primMinusNatS Zero xv270) (Succ xv271)",fontsize=16,color="burlywood",shape="box"];2853[label="xv270/Succ xv2700",fontsize=10,color="white",style="solid",shape="box"];2665 -> 2853[label="",style="solid", color="burlywood", weight=9]; 2853 -> 2672[label="",style="solid", color="burlywood", weight=3]; 2854[label="xv270/Zero",fontsize=10,color="white",style="solid",shape="box"];2665 -> 2854[label="",style="solid", color="burlywood", weight=9]; 2854 -> 2673[label="",style="solid", color="burlywood", weight=3]; 2021[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="blue",shape="box"];2855[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2855[label="",style="solid", color="blue", weight=9]; 2855 -> 2037[label="",style="solid", color="blue", weight=3]; 2856[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2856[label="",style="solid", color="blue", weight=9]; 2856 -> 2038[label="",style="solid", color="blue", weight=3]; 2857[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2857[label="",style="solid", color="blue", weight=9]; 2857 -> 2039[label="",style="solid", color="blue", weight=3]; 2858[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2858[label="",style="solid", color="blue", weight=9]; 2858 -> 2040[label="",style="solid", color="blue", weight=3]; 2859[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2859[label="",style="solid", color="blue", weight=9]; 2859 -> 2041[label="",style="solid", color="blue", weight=3]; 2860[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2860[label="",style="solid", color="blue", weight=9]; 2860 -> 2042[label="",style="solid", color="blue", weight=3]; 2861[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2861[label="",style="solid", color="blue", weight=9]; 2861 -> 2043[label="",style="solid", color="blue", weight=3]; 2862[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2862[label="",style="solid", color="blue", weight=9]; 2862 -> 2044[label="",style="solid", color="blue", weight=3]; 2863[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2863[label="",style="solid", color="blue", weight=9]; 2863 -> 2045[label="",style="solid", color="blue", weight=3]; 2864[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2864[label="",style="solid", color="blue", weight=9]; 2864 -> 2046[label="",style="solid", color="blue", weight=3]; 2865[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2865[label="",style="solid", color="blue", weight=9]; 2865 -> 2047[label="",style="solid", color="blue", weight=3]; 2866[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2866[label="",style="solid", color="blue", weight=9]; 2866 -> 2048[label="",style="solid", color="blue", weight=3]; 2867[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2867[label="",style="solid", color="blue", weight=9]; 2867 -> 2049[label="",style="solid", color="blue", weight=3]; 2868[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2868[label="",style="solid", color="blue", weight=9]; 2868 -> 2050[label="",style="solid", color="blue", weight=3]; 2869[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2869[label="",style="solid", color="blue", weight=9]; 2869 -> 2051[label="",style="solid", color="blue", weight=3]; 2870[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2870[label="",style="solid", color="blue", weight=9]; 2870 -> 2052[label="",style="solid", color="blue", weight=3]; 2871[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2871[label="",style="solid", color="blue", weight=9]; 2871 -> 2053[label="",style="solid", color="blue", weight=3]; 2872[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2872[label="",style="solid", color="blue", weight=9]; 2872 -> 2054[label="",style="solid", color="blue", weight=3]; 2601 -> 2725[label="",style="dashed", color="red", weight=0]; 2601[label="primDivNatS (primMinusNatS (Succ xv259) (Succ xv260)) (Succ (Succ xv260))",fontsize=16,color="magenta"];2601 -> 2732[label="",style="dashed", color="magenta", weight=3]; 2601 -> 2733[label="",style="dashed", color="magenta", weight=3]; 2601 -> 2734[label="",style="dashed", color="magenta", weight=3]; 2756 -> 2725[label="",style="dashed", color="red", weight=0]; 2756[label="primDivNatS (primMinusNatS xv2730 xv2740) (Succ xv275)",fontsize=16,color="magenta"];2756 -> 2760[label="",style="dashed", color="magenta", weight=3]; 2756 -> 2761[label="",style="dashed", color="magenta", weight=3]; 2757 -> 1679[label="",style="dashed", color="red", weight=0]; 2757[label="primDivNatS (Succ xv2730) (Succ xv275)",fontsize=16,color="magenta"];2757 -> 2762[label="",style="dashed", color="magenta", weight=3]; 2757 -> 2763[label="",style="dashed", color="magenta", weight=3]; 2758[label="primDivNatS Zero (Succ xv275)",fontsize=16,color="black",shape="triangle"];2758 -> 2764[label="",style="solid", color="black", weight=3]; 2759 -> 2758[label="",style="dashed", color="red", weight=0]; 2759[label="primDivNatS Zero (Succ xv275)",fontsize=16,color="magenta"];2608 -> 2546[label="",style="dashed", color="red", weight=0]; 2608[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS xv2660 xv2670)",fontsize=16,color="magenta"];2608 -> 2617[label="",style="dashed", color="magenta", weight=3]; 2608 -> 2618[label="",style="dashed", color="magenta", weight=3]; 2609[label="primModNatS0 (Succ xv264) (Succ xv265) True",fontsize=16,color="black",shape="triangle"];2609 -> 2619[label="",style="solid", color="black", weight=3]; 2610[label="primModNatS0 (Succ xv264) (Succ xv265) False",fontsize=16,color="black",shape="box"];2610 -> 2620[label="",style="solid", color="black", weight=3]; 2611 -> 2609[label="",style="dashed", color="red", weight=0]; 2611[label="primModNatS0 (Succ xv264) (Succ xv265) True",fontsize=16,color="magenta"];2670[label="primModNatS (primMinusNatS (Succ xv2690) (Succ xv2700)) (Succ xv271)",fontsize=16,color="black",shape="box"];2670 -> 2680[label="",style="solid", color="black", weight=3]; 2671[label="primModNatS (primMinusNatS (Succ xv2690) Zero) (Succ xv271)",fontsize=16,color="black",shape="box"];2671 -> 2681[label="",style="solid", color="black", weight=3]; 2672[label="primModNatS (primMinusNatS Zero (Succ xv2700)) (Succ xv271)",fontsize=16,color="black",shape="box"];2672 -> 2682[label="",style="solid", color="black", weight=3]; 2673[label="primModNatS (primMinusNatS Zero Zero) (Succ xv271)",fontsize=16,color="black",shape="box"];2673 -> 2683[label="",style="solid", color="black", weight=3]; 2037[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2037 -> 2072[label="",style="solid", color="black", weight=3]; 2038[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2038 -> 2073[label="",style="solid", color="black", weight=3]; 2039[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2039 -> 2074[label="",style="solid", color="black", weight=3]; 2040[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2040 -> 2075[label="",style="solid", color="black", weight=3]; 2041[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2041 -> 2076[label="",style="solid", color="black", weight=3]; 2042[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="burlywood",shape="box"];2873[label="xv215/xv2150 :% xv2151",fontsize=10,color="white",style="solid",shape="box"];2042 -> 2873[label="",style="solid", color="burlywood", weight=9]; 2873 -> 2077[label="",style="solid", color="burlywood", weight=3]; 2043[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2043 -> 2078[label="",style="solid", color="black", weight=3]; 2044[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2044 -> 2079[label="",style="solid", color="black", weight=3]; 2045[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2045 -> 2080[label="",style="solid", color="black", weight=3]; 2046[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2046 -> 2081[label="",style="solid", color="black", weight=3]; 2047[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2047 -> 2082[label="",style="solid", color="black", weight=3]; 2048[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2048 -> 2083[label="",style="solid", color="black", weight=3]; 2049[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2049 -> 2084[label="",style="solid", color="black", weight=3]; 2050[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2050 -> 2085[label="",style="solid", color="black", weight=3]; 2051[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2051 -> 2086[label="",style="solid", color="black", weight=3]; 2052[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2052 -> 2087[label="",style="solid", color="black", weight=3]; 2053[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2053 -> 2088[label="",style="solid", color="black", weight=3]; 2054[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2054 -> 2089[label="",style="solid", color="black", weight=3]; 2732[label="Succ xv260",fontsize=16,color="green",shape="box"];2733[label="Succ xv259",fontsize=16,color="green",shape="box"];2734[label="Succ xv260",fontsize=16,color="green",shape="box"];2760[label="xv2730",fontsize=16,color="green",shape="box"];2761[label="xv2740",fontsize=16,color="green",shape="box"];2762[label="xv2730",fontsize=16,color="green",shape="box"];2763[label="xv275",fontsize=16,color="green",shape="box"];2764[label="Zero",fontsize=16,color="green",shape="box"];2617[label="xv2660",fontsize=16,color="green",shape="box"];2618[label="xv2670",fontsize=16,color="green",shape="box"];2619 -> 2633[label="",style="dashed", color="red", weight=0]; 2619[label="primModNatS (primMinusNatS (Succ xv264) (Succ xv265)) (Succ (Succ xv265))",fontsize=16,color="magenta"];2619 -> 2646[label="",style="dashed", color="magenta", weight=3]; 2619 -> 2647[label="",style="dashed", color="magenta", weight=3]; 2619 -> 2648[label="",style="dashed", color="magenta", weight=3]; 2620[label="Succ (Succ xv264)",fontsize=16,color="green",shape="box"];2680 -> 2633[label="",style="dashed", color="red", weight=0]; 2680[label="primModNatS (primMinusNatS xv2690 xv2700) (Succ xv271)",fontsize=16,color="magenta"];2680 -> 2688[label="",style="dashed", color="magenta", weight=3]; 2680 -> 2689[label="",style="dashed", color="magenta", weight=3]; 2681 -> 1755[label="",style="dashed", color="red", weight=0]; 2681[label="primModNatS (Succ xv2690) (Succ xv271)",fontsize=16,color="magenta"];2681 -> 2690[label="",style="dashed", color="magenta", weight=3]; 2681 -> 2691[label="",style="dashed", color="magenta", weight=3]; 2682[label="primModNatS Zero (Succ xv271)",fontsize=16,color="black",shape="triangle"];2682 -> 2692[label="",style="solid", color="black", weight=3]; 2683 -> 2682[label="",style="dashed", color="red", weight=0]; 2683[label="primModNatS Zero (Succ xv271)",fontsize=16,color="magenta"];2072 -> 1484[label="",style="dashed", color="red", weight=0]; 2072[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2072 -> 2100[label="",style="dashed", color="magenta", weight=3]; 2072 -> 2101[label="",style="dashed", color="magenta", weight=3]; 2073 -> 1484[label="",style="dashed", color="red", weight=0]; 2073[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2073 -> 2102[label="",style="dashed", color="magenta", weight=3]; 2073 -> 2103[label="",style="dashed", color="magenta", weight=3]; 2074 -> 1484[label="",style="dashed", color="red", weight=0]; 2074[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2074 -> 2104[label="",style="dashed", color="magenta", weight=3]; 2074 -> 2105[label="",style="dashed", color="magenta", weight=3]; 2075 -> 1484[label="",style="dashed", color="red", weight=0]; 2075[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2075 -> 2106[label="",style="dashed", color="magenta", weight=3]; 2075 -> 2107[label="",style="dashed", color="magenta", weight=3]; 2076 -> 1484[label="",style="dashed", color="red", weight=0]; 2076[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2076 -> 2108[label="",style="dashed", color="magenta", weight=3]; 2076 -> 2109[label="",style="dashed", color="magenta", weight=3]; 2077[label="showsPrec (Pos Zero) (xv2150 :% xv2151) xv216",fontsize=16,color="black",shape="box"];2077 -> 2110[label="",style="solid", color="black", weight=3]; 2078 -> 1484[label="",style="dashed", color="red", weight=0]; 2078[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2078 -> 2111[label="",style="dashed", color="magenta", weight=3]; 2078 -> 2112[label="",style="dashed", color="magenta", weight=3]; 2079 -> 1484[label="",style="dashed", color="red", weight=0]; 2079[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2079 -> 2113[label="",style="dashed", color="magenta", weight=3]; 2079 -> 2114[label="",style="dashed", color="magenta", weight=3]; 2080 -> 1484[label="",style="dashed", color="red", weight=0]; 2080[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2080 -> 2115[label="",style="dashed", color="magenta", weight=3]; 2080 -> 2116[label="",style="dashed", color="magenta", weight=3]; 2081 -> 1484[label="",style="dashed", color="red", weight=0]; 2081[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2081 -> 2117[label="",style="dashed", color="magenta", weight=3]; 2081 -> 2118[label="",style="dashed", color="magenta", weight=3]; 2082 -> 1484[label="",style="dashed", color="red", weight=0]; 2082[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2082 -> 2119[label="",style="dashed", color="magenta", weight=3]; 2082 -> 2120[label="",style="dashed", color="magenta", weight=3]; 2083 -> 1484[label="",style="dashed", color="red", weight=0]; 2083[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2083 -> 2121[label="",style="dashed", color="magenta", weight=3]; 2083 -> 2122[label="",style="dashed", color="magenta", weight=3]; 2084 -> 1484[label="",style="dashed", color="red", weight=0]; 2084[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2084 -> 2123[label="",style="dashed", color="magenta", weight=3]; 2084 -> 2124[label="",style="dashed", color="magenta", weight=3]; 2085 -> 1484[label="",style="dashed", color="red", weight=0]; 2085[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2085 -> 2125[label="",style="dashed", color="magenta", weight=3]; 2085 -> 2126[label="",style="dashed", color="magenta", weight=3]; 2086 -> 1484[label="",style="dashed", color="red", weight=0]; 2086[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2086 -> 2127[label="",style="dashed", color="magenta", weight=3]; 2086 -> 2128[label="",style="dashed", color="magenta", weight=3]; 2087 -> 1484[label="",style="dashed", color="red", weight=0]; 2087[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2087 -> 2129[label="",style="dashed", color="magenta", weight=3]; 2087 -> 2130[label="",style="dashed", color="magenta", weight=3]; 2088 -> 1484[label="",style="dashed", color="red", weight=0]; 2088[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2088 -> 2131[label="",style="dashed", color="magenta", weight=3]; 2088 -> 2132[label="",style="dashed", color="magenta", weight=3]; 2089 -> 1484[label="",style="dashed", color="red", weight=0]; 2089[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2089 -> 2133[label="",style="dashed", color="magenta", weight=3]; 2089 -> 2134[label="",style="dashed", color="magenta", weight=3]; 2646[label="Succ xv265",fontsize=16,color="green",shape="box"];2647[label="Succ xv265",fontsize=16,color="green",shape="box"];2648[label="Succ xv264",fontsize=16,color="green",shape="box"];2688[label="xv2700",fontsize=16,color="green",shape="box"];2689[label="xv2690",fontsize=16,color="green",shape="box"];2690[label="xv271",fontsize=16,color="green",shape="box"];2691[label="xv2690",fontsize=16,color="green",shape="box"];2692[label="Zero",fontsize=16,color="green",shape="box"];2100 -> 646[label="",style="dashed", color="red", weight=0]; 2100[label="show xv215",fontsize=16,color="magenta"];2100 -> 2145[label="",style="dashed", color="magenta", weight=3]; 2101[label="xv216",fontsize=16,color="green",shape="box"];2102 -> 647[label="",style="dashed", color="red", weight=0]; 2102[label="show xv215",fontsize=16,color="magenta"];2102 -> 2146[label="",style="dashed", color="magenta", weight=3]; 2103[label="xv216",fontsize=16,color="green",shape="box"];2104 -> 648[label="",style="dashed", color="red", weight=0]; 2104[label="show xv215",fontsize=16,color="magenta"];2104 -> 2147[label="",style="dashed", color="magenta", weight=3]; 2105[label="xv216",fontsize=16,color="green",shape="box"];2106 -> 649[label="",style="dashed", color="red", weight=0]; 2106[label="show xv215",fontsize=16,color="magenta"];2106 -> 2148[label="",style="dashed", color="magenta", weight=3]; 2107[label="xv216",fontsize=16,color="green",shape="box"];2108 -> 650[label="",style="dashed", color="red", weight=0]; 2108[label="show xv215",fontsize=16,color="magenta"];2108 -> 2149[label="",style="dashed", color="magenta", weight=3]; 2109[label="xv216",fontsize=16,color="green",shape="box"];2110 -> 1735[label="",style="dashed", color="red", weight=0]; 2110[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows xv2150) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows xv2151) xv216",fontsize=16,color="magenta"];2110 -> 2150[label="",style="dashed", color="magenta", weight=3]; 2110 -> 2151[label="",style="dashed", color="magenta", weight=3]; 2110 -> 2152[label="",style="dashed", color="magenta", weight=3]; 2110 -> 2153[label="",style="dashed", color="magenta", weight=3]; 2110 -> 2154[label="",style="dashed", color="magenta", weight=3]; 2111 -> 652[label="",style="dashed", color="red", weight=0]; 2111[label="show xv215",fontsize=16,color="magenta"];2111 -> 2155[label="",style="dashed", color="magenta", weight=3]; 2112[label="xv216",fontsize=16,color="green",shape="box"];2113 -> 653[label="",style="dashed", color="red", weight=0]; 2113[label="show xv215",fontsize=16,color="magenta"];2113 -> 2156[label="",style="dashed", color="magenta", weight=3]; 2114[label="xv216",fontsize=16,color="green",shape="box"];2115 -> 654[label="",style="dashed", color="red", weight=0]; 2115[label="show xv215",fontsize=16,color="magenta"];2115 -> 2157[label="",style="dashed", color="magenta", weight=3]; 2116[label="xv216",fontsize=16,color="green",shape="box"];2117 -> 655[label="",style="dashed", color="red", weight=0]; 2117[label="show xv215",fontsize=16,color="magenta"];2117 -> 2158[label="",style="dashed", color="magenta", weight=3]; 2118[label="xv216",fontsize=16,color="green",shape="box"];2119 -> 656[label="",style="dashed", color="red", weight=0]; 2119[label="show xv215",fontsize=16,color="magenta"];2119 -> 2159[label="",style="dashed", color="magenta", weight=3]; 2120[label="xv216",fontsize=16,color="green",shape="box"];2121 -> 657[label="",style="dashed", color="red", weight=0]; 2121[label="show xv215",fontsize=16,color="magenta"];2121 -> 2160[label="",style="dashed", color="magenta", weight=3]; 2122[label="xv216",fontsize=16,color="green",shape="box"];2123 -> 658[label="",style="dashed", color="red", weight=0]; 2123[label="show xv215",fontsize=16,color="magenta"];2123 -> 2161[label="",style="dashed", color="magenta", weight=3]; 2124[label="xv216",fontsize=16,color="green",shape="box"];2125 -> 659[label="",style="dashed", color="red", weight=0]; 2125[label="show xv215",fontsize=16,color="magenta"];2125 -> 2162[label="",style="dashed", color="magenta", weight=3]; 2126[label="xv216",fontsize=16,color="green",shape="box"];2127 -> 660[label="",style="dashed", color="red", weight=0]; 2127[label="show xv215",fontsize=16,color="magenta"];2127 -> 2163[label="",style="dashed", color="magenta", weight=3]; 2128[label="xv216",fontsize=16,color="green",shape="box"];2129 -> 661[label="",style="dashed", color="red", weight=0]; 2129[label="show xv215",fontsize=16,color="magenta"];2129 -> 2164[label="",style="dashed", color="magenta", weight=3]; 2130[label="xv216",fontsize=16,color="green",shape="box"];2131 -> 662[label="",style="dashed", color="red", weight=0]; 2131[label="show xv215",fontsize=16,color="magenta"];2131 -> 2165[label="",style="dashed", color="magenta", weight=3]; 2132[label="xv216",fontsize=16,color="green",shape="box"];2133 -> 663[label="",style="dashed", color="red", weight=0]; 2133[label="show xv215",fontsize=16,color="magenta"];2133 -> 2166[label="",style="dashed", color="magenta", weight=3]; 2134[label="xv216",fontsize=16,color="green",shape="box"];2145[label="xv215",fontsize=16,color="green",shape="box"];2146[label="xv215",fontsize=16,color="green",shape="box"];2147[label="xv215",fontsize=16,color="green",shape="box"];2148[label="xv215",fontsize=16,color="green",shape="box"];2149[label="xv215",fontsize=16,color="green",shape="box"];2150[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];2151[label="xv2151",fontsize=16,color="green",shape="box"];2152[label="xv2150",fontsize=16,color="green",shape="box"];2153[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];2154[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];2155[label="xv215",fontsize=16,color="green",shape="box"];2156[label="xv215",fontsize=16,color="green",shape="box"];2157[label="xv215",fontsize=16,color="green",shape="box"];2158[label="xv215",fontsize=16,color="green",shape="box"];2159[label="xv215",fontsize=16,color="green",shape="box"];2160[label="xv215",fontsize=16,color="green",shape="box"];2161[label="xv215",fontsize=16,color="green",shape="box"];2162[label="xv215",fontsize=16,color="green",shape="box"];2163[label="xv215",fontsize=16,color="green",shape="box"];2164[label="xv215",fontsize=16,color="green",shape="box"];2165[label="xv215",fontsize=16,color="green",shape="box"];2166[label="xv215",fontsize=16,color="green",shape="box"];} ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: new_show3(xv5) -> new_show3(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (14) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show3(xv5) evaluates to t =new_show3(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show3(xv5) to new_show3(xv5). ---------------------------------------- (15) NO ---------------------------------------- (16) Obligation: Q DP problem: The TRS P consists of the following rules: new_putStr(:(xv730, xv731)) -> new_putStr(xv731) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (17) 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_putStr(:(xv730, xv731)) -> new_putStr(xv731) The graph contains the following edges 1 > 1 ---------------------------------------- (18) YES ---------------------------------------- (19) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Neg(xv50)) -> new_primShowInt(Pos(xv50)) new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS3(xv275) -> Zero new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_div(x0, x1) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (20) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (21) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS3(xv275) -> Zero new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_div(x0, x1) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (22) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ---------------------------------------- (23) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS3(xv275) -> Zero new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_div(x0, x1) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) 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. ---------------------------------------- (25) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_div(x0, x1) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (26) 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_div(x0, x1) ---------------------------------------- (27) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (28) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (29) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (30) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) the following chains were created: *We consider the chain new_primShowInt(Pos(Succ(x0))) -> new_primShowInt(Pos(new_primDivNatS4(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), new_primShowInt(Pos(Succ(x1))) -> new_primShowInt(Pos(new_primDivNatS4(x1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) which results in the following constraint: (1) (new_primShowInt(Pos(new_primDivNatS4(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))=new_primShowInt(Pos(Succ(x1))) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS4(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: (2) (Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=x2 & new_primDivNatS4(x0, x2)=Succ(x1) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS4(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS4(x0, x2)=Succ(x1) which results in the following new constraints: (3) (new_primDivNatS02(x4, x3, x4, x3)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Succ(x3) ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (4) (Succ(new_primDivNatS2(Succ(x6), Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero ==> new_primShowInt(Pos(Succ(Succ(x6))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x6), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (5) (Succ(new_primDivNatS2(Zero, Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero ==> new_primShowInt(Pos(Succ(Zero)))_>=_new_primShowInt(Pos(new_primDivNatS4(Zero, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint: (6) (x4=x7 & x3=x8 & new_primDivNatS02(x4, x3, x7, x8)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS02(x4, x3, x7, x8)=Succ(x1) which results in the following new constraints: (7) (new_primDivNatS02(x12, x11, x10, x9)=Succ(x1) & x12=Succ(x10) & x11=Succ(x9) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 & (\/x13:new_primDivNatS02(x12, x11, x10, x9)=Succ(x13) & x12=x10 & x11=x9 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 ==> new_primShowInt(Pos(Succ(Succ(x12))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x12), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ==> new_primShowInt(Pos(Succ(Succ(x12))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x12), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (8) (new_primDivNatS01(x16, x15)=Succ(x1) & x16=Succ(x14) & x15=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 ==> new_primShowInt(Pos(Succ(Succ(x16))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x16), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (9) (new_primDivNatS01(x18, x17)=Succ(x1) & x18=Zero & x17=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x17 ==> new_primShowInt(Pos(Succ(Succ(x18))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x18), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We simplified constraint (7) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint: (10) (new_primShowInt(Pos(Succ(Succ(Succ(x10)))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(Succ(x10)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We solved constraint (8) using rules (I), (II), (III).We solved constraint (9) using rules (I), (II), (III). To summarize, we get the following constraints P__>=_ for the following pairs. *new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) *(new_primShowInt(Pos(Succ(Succ(Succ(x10)))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(Succ(x10)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (31) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (32) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(xv500))) -> new_primShowInt(Pos(new_primDivNatS4(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))),new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) (new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero))) ---------------------------------------- (33) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (34) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (35) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (36) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))),new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) (new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero))) ---------------------------------------- (37) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (38) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (39) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (40) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) (new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero))) ---------------------------------------- (41) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (42) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (43) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (44) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) at position [0,0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))) (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero))) ---------------------------------------- (45) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (46) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (47) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (48) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (49) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (50) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) the following chains were created: *We consider the chain new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))), new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x1))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x1, Succ(Succ(Succ(Succ(Succ(Zero)))))))) which results in the following constraint: (1) (new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))=new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: (2) (Succ(Succ(Succ(x0)))=x2 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x4 & new_primDivNatS02(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS02(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: (3) (new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x6))))=x8 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x7 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Succ(x5) & (\/x9:new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x9))))) & Succ(Succ(Succ(x6)))=x8 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x7 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x5 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x6)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x6, Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x6))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x6)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x6), Succ(Succ(Succ(Succ(Succ(Zero))))))))) (4) (new_primDivNatS01(x12, x11)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x10))))=x12 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x10))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x10)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x10), Succ(Succ(Succ(Succ(Succ(Zero))))))))) (5) (new_primDivNatS01(x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Zero)))=x14 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x13 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Zero, Succ(Succ(Succ(Succ(Succ(Zero))))))))) We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint: (6) (new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x6))))=x8 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x7 & Succ(Succ(Succ(Succ(Zero))))=x5 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x6))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x6)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x6), Succ(Succ(Succ(Succ(Succ(Zero))))))))) We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: (7) (new_primDivNatS02(x21, x20, x19, x18)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x19)))))=x21 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x20 & Succ(Succ(Succ(Succ(Zero))))=Succ(x18) & (\/x22:new_primDivNatS02(x21, x20, x19, x18)=Succ(Succ(Succ(Succ(Succ(x22))))) & Succ(Succ(Succ(Succ(x19))))=x21 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x20 & Succ(Succ(Succ(Succ(Zero))))=x18 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x19))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x19)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x19), Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x19)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x19))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x19)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) (8) (new_primDivNatS01(x25, x24)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x23)))))=x25 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x24 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x23)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x23))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x23)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) (9) (new_primDivNatS01(x27, x26)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Zero))))=x27 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x26 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))))))) We simplified constraint (7) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x19)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x19))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x19)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) We solved constraint (8) using rules (I), (II).We solved constraint (9) using rules (I), (II). To summarize, we get the following constraints P__>=_ for the following pairs. *new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) *(new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x19)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x19))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x19)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) The constraints for P_> respective P_bound are constructed from P__>=_ where we just replace every occurence of "t _>=_ s" in P__>=_ by "t > s" respective "t _>=_ c". Here c stands for the fresh constant used for P_bound. ---------------------------------------- (51) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) The TRS R consists of the following rules: new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(xv275) -> Zero The set Q consists of the following terms: new_primDivNatS4(Succ(x0), Zero) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS3(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(Zero, Zero) new_primDivNatS4(Zero, Succ(x0)) new_primDivNatS01(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (52) Obligation: Q DP problem: The TRS P consists of the following rules: new_show5(xv5) -> new_show5(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (53) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show5(xv5) evaluates to t =new_show5(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show5(xv5) to new_show5(xv5). ---------------------------------------- (54) NO ---------------------------------------- (55) Obligation: Q DP problem: The TRS P consists of the following rules: new_show11(xv5) -> new_show11(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (56) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show11(xv5) evaluates to t =new_show11(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show11(xv5) to new_show11(xv5). ---------------------------------------- (57) NO ---------------------------------------- (58) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(xv1890, xv1891), xv131) -> new_psPs(xv1891, xv131) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (59) 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_psPs(:(xv1890, xv1891), xv131) -> new_psPs(xv1891, xv131) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (60) YES ---------------------------------------- (61) Obligation: Q DP problem: The TRS P consists of the following rules: new_show10(xv5) -> new_show10(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (62) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show10(xv5) evaluates to t =new_show10(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show10(xv5) to new_show10(xv5). ---------------------------------------- (63) NO ---------------------------------------- (64) Obligation: Q DP problem: The TRS P consists of the following rules: new_show2(xv5, h) -> new_show2(xv5, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (65) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show2(xv5, h) evaluates to t =new_show2(xv5, h) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show2(xv5, h) to new_show2(xv5, h). ---------------------------------------- (66) NO ---------------------------------------- (67) Obligation: Q DP problem: The TRS P consists of the following rules: new_show14(xv5, h, ba) -> new_show14(xv5, h, ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (68) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show14(xv5, h, ba) evaluates to t =new_show14(xv5, h, ba) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show14(xv5, h, ba) to new_show14(xv5, h, ba). ---------------------------------------- (69) NO ---------------------------------------- (70) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(xv259, xv260, Zero, Zero) -> new_primDivNatS00(xv259, xv260) new_primDivNatS00(xv259, xv260) -> new_primDivNatS(Succ(xv259), Succ(xv260), Succ(xv260)) new_primDivNatS(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS(xv2730, xv2740, xv275) new_primDivNatS1(Succ(xv1910), Zero) -> new_primDivNatS(Succ(xv1910), Zero, Zero) new_primDivNatS0(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS0(xv259, xv260, xv2610, xv2620) new_primDivNatS0(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS(Succ(xv259), Succ(xv260), Succ(xv260)) new_primDivNatS1(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS0(xv1910, xv1920, xv1910, xv1920) new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) new_primDivNatS(Succ(xv2730), Zero, xv275) -> new_primDivNatS1(xv2730, xv275) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (71) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (72) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(xv259, xv260) -> new_primDivNatS(Succ(xv259), Succ(xv260), Succ(xv260)) new_primDivNatS(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS(xv2730, xv2740, xv275) new_primDivNatS(Succ(xv2730), Zero, xv275) -> new_primDivNatS1(xv2730, xv275) new_primDivNatS1(Succ(xv1910), Zero) -> new_primDivNatS(Succ(xv1910), Zero, Zero) new_primDivNatS1(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS0(xv1910, xv1920, xv1910, xv1920) new_primDivNatS0(xv259, xv260, Zero, Zero) -> new_primDivNatS00(xv259, xv260) new_primDivNatS0(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS0(xv259, xv260, xv2610, xv2620) new_primDivNatS0(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS(Succ(xv259), Succ(xv260), Succ(xv260)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (73) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primDivNatS(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS(xv2730, xv2740, xv275) new_primDivNatS1(Succ(xv1910), Zero) -> new_primDivNatS(Succ(xv1910), Zero, Zero) new_primDivNatS1(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS0(xv1910, xv1920, xv1910, xv1920) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 POL(new_primDivNatS1(x_1, x_2)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: none ---------------------------------------- (74) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(xv259, xv260) -> new_primDivNatS(Succ(xv259), Succ(xv260), Succ(xv260)) new_primDivNatS(Succ(xv2730), Zero, xv275) -> new_primDivNatS1(xv2730, xv275) new_primDivNatS0(xv259, xv260, Zero, Zero) -> new_primDivNatS00(xv259, xv260) new_primDivNatS0(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS0(xv259, xv260, xv2610, xv2620) new_primDivNatS0(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS(Succ(xv259), Succ(xv260), Succ(xv260)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (75) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (76) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS0(xv259, xv260, xv2610, xv2620) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (77) 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_primDivNatS0(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS0(xv259, xv260, xv2610, xv2620) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (78) YES ---------------------------------------- (79) Obligation: Q DP problem: The TRS P consists of the following rules: new_show13(xv5) -> new_show13(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (80) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show13(xv5) evaluates to t =new_show13(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show13(xv5) to new_show13(xv5). ---------------------------------------- (81) NO ---------------------------------------- (82) Obligation: Q DP problem: The TRS P consists of the following rules: new_show8(xv5) -> new_show8(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (83) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show8(xv5) evaluates to t =new_show8(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show8(xv5) to new_show8(xv5). ---------------------------------------- (84) NO ---------------------------------------- (85) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(app(ty_@2, ba), bb), app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (86) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (87) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (88) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) at position [5] we obtained the following new rules [LPAR04]: (new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bd)), bd, bd),new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bd)), bd, bd)) ---------------------------------------- (89) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bd)), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (90) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bd)), bd, bd) at position [5] we obtained the following new rules [LPAR04]: (new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), new_psPs0(:(Char(Succ(xv213)), :(Char(Succ(xv214)), [])), new_showsPrec(xv215, xv216, bd))), bd, bd),new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), new_psPs0(:(Char(Succ(xv213)), :(Char(Succ(xv214)), [])), new_showsPrec(xv215, xv216, bd))), bd, bd)) ---------------------------------------- (91) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), new_psPs0(:(Char(Succ(xv213)), :(Char(Succ(xv214)), [])), new_showsPrec(xv215, xv216, bd))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (92) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), new_psPs0(:(Char(Succ(xv213)), :(Char(Succ(xv214)), [])), new_showsPrec(xv215, xv216, bd))), bd, bd) at position [5,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), new_psPs0(:(Char(Succ(xv214)), []), new_showsPrec(xv215, xv216, bd)))), bd, bd),new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), new_psPs0(:(Char(Succ(xv214)), []), new_showsPrec(xv215, xv216, bd)))), bd, bd)) ---------------------------------------- (93) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), new_psPs0(:(Char(Succ(xv214)), []), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (94) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), new_psPs0(:(Char(Succ(xv214)), []), new_showsPrec(xv215, xv216, bd)))), bd, bd) at position [5,1,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_psPs0([], new_showsPrec(xv215, xv216, bd))))), bd, bd),new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_psPs0([], new_showsPrec(xv215, xv216, bd))))), bd, bd)) ---------------------------------------- (95) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_psPs0([], new_showsPrec(xv215, xv216, bd))))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (96) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_psPs0([], new_showsPrec(xv215, xv216, bd))))), bd, bd) at position [5,1,1,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd),new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd)) ---------------------------------------- (97) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (98) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError)) ---------------------------------------- (99) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (100) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (101) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (102) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6))) ---------------------------------------- (103) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (104) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (105) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (106) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering)) ---------------------------------------- (107) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (108) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (109) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (110) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int)) ---------------------------------------- (111) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (112) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (113) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (114) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6))) ---------------------------------------- (115) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (116) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (117) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (118) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool)) ---------------------------------------- (119) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (120) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (121) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (122) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double)) ---------------------------------------- (123) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (124) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (125) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (126) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char)) ---------------------------------------- (127) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (128) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (129) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (130) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float)) ---------------------------------------- (131) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 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_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (134) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6))) ---------------------------------------- (135) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (136) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (137) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (138) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException)) ---------------------------------------- (139) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (140) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (141) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (142) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7))) ---------------------------------------- (143) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (144) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (145) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (146) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7))) (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7))) ---------------------------------------- (147) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (148) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer)) ---------------------------------------- (149) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (150) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (151) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (152) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0)) ---------------------------------------- (153) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (154) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (155) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (156) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8))) ---------------------------------------- (157) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (158) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (159) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (160) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_pt(xv212, xv213, xv214, xv215, xv216, bc) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind)) ---------------------------------------- (161) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (162) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (163) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (164) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, :(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), new_showsPrec(xv215, xv216, bd)))), bd, bd) we obtained the following new rules [LPAR04]: (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7)) (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7)) ---------------------------------------- (165) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7) The TRS R consists of the following rules: new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Int, bc) -> new_psPs0(new_show30(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Succ(xv1910), Succ(xv1920)) -> new_primDivNatS02(xv1910, xv1920, xv1910, xv1920) new_show15(xv5) -> new_psPs0(new_show15(xv5), []) new_primDivNatS2(Zero, Succ(xv2740), xv275) -> new_primDivNatS3(xv275) new_show20(xv5) -> new_psPs0(new_show20(xv5), []) new_primIntToChar(xv197, xv198) -> Char(new_primModNatS2(xv197, xv198)) new_showsPrec(xv215, xv216, app(app(ty_@2, dd), de)) -> new_psPs0(new_show17(xv215, dd, de), xv216) new_showsPrec(xv215, xv216, ty_IOErrorKind) -> new_psPs0(new_show29(xv215), xv216) new_showsPrec(xv215, xv216, ty_Ordering) -> new_psPs0(new_show15(xv215), xv216) new_showsPrec(xv215, xv216, app(app(app(ty_@3, dg), dh), ea)) -> new_psPs0(new_show24(xv215, dg, dh, ea), xv216) new_show22(xv5, db) -> new_psPs0(new_show22(xv5, db), []) new_primShowInt0(Neg(xv50)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(xv50))) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Char, bc) -> new_psPs0(new_show25(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Double) -> new_psPs0(new_show19(xv215), xv216) new_primModNatS3(Zero, Succ(xv2700), xv271) -> new_primModNatS4(xv271) new_primModNatS2(Succ(xv1970), Succ(xv1980)) -> new_primModNatS01(xv1970, xv1980, xv1970, xv1980) new_show27(xv5) -> new_psPs0(new_show27(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Integer, bc) -> new_psPs0(new_show16(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS2(Zero, Zero, xv275) -> new_primDivNatS3(xv275) new_showsPrec(xv215, xv216, ty_Float) -> new_psPs0(new_show21(xv215), xv216) new_show19(xv5) -> new_psPs0(new_show19(xv5), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Bool, bc) -> new_psPs0(new_show20(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS02(xv264, xv265) -> new_primModNatS3(Succ(xv264), Succ(xv265), Succ(xv265)) new_showsPrec(xv215, xv216, app(app(ty_Either, eb), ec)) -> new_psPs0(new_show18(xv215, eb, ec), xv216) new_show28(xv5, ef) -> new_psPs0(new_show28(xv5, ef), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_HugsException, bc) -> new_psPs0(new_show23(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primDivNatS4(Zero, Succ(xv1920)) -> Zero new_primModNatS4(xv271) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_IO, cd), bc) -> new_psPs0(new_show31(xv211, cd), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show23(xv5) -> new_psPs0(new_show23(xv5), []) new_primDivNatS02(xv259, xv260, Zero, Zero) -> new_primDivNatS01(xv259, xv260) new_psPs0(:(xv1890, xv1891), xv131) -> :(xv1890, new_psPs0(xv1891, xv131)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_show30(xv5) -> new_primShowInt0(xv5) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(app(ty_@3, bf), bg), bh), bc) -> new_psPs0(new_show24(xv211, bf, bg, bh), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show31(xv5, dc) -> new_psPs0(new_show31(xv5, dc), []) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Ordering, bc) -> new_psPs0(new_show15(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOError, bc) -> new_psPs0(new_show26(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_primModNatS3(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS3(xv2690, xv2700, xv271) new_primModNatS01(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS01(xv264, xv265, xv2660, xv2670) new_showsPrec(xv215, xv216, app(ty_Maybe, df)) -> new_psPs0(new_show22(xv215, df), xv216) new_showParen0(:%(xv2110, xv2111), xv212, xv213, xv214, xv215, xv216, app(ty_Ratio, bd), bc) -> new_showParen0(xv2110, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2111, new_pt0(xv212, xv213, xv214, xv215, xv216, bd), bd, bd) new_show25(xv5) -> new_psPs0(new_show25(xv5), []) new_primModNatS3(Succ(xv2690), Zero, xv271) -> new_primModNatS2(xv2690, xv271) new_showsPrec(xv215, xv216, ty_@0) -> new_psPs0(new_show27(xv215), xv216) new_psPs0([], xv131) -> xv131 new_primModNatS01(xv264, xv265, Zero, Succ(xv2670)) -> Succ(Succ(xv264)) new_primDivNatS02(xv259, xv260, Succ(xv2610), Zero) -> new_primDivNatS01(xv259, xv260) new_primDivNatS3(xv275) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_@0, bc) -> new_psPs0(new_show27(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_[], cc), bc) -> new_psPs0(new_show28(xv211, cc), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_IOErrorKind, bc) -> new_psPs0(new_show29(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show17(xv5, ce, cf) -> new_psPs0(new_show17(xv5, ce, cf), []) new_pt0(xv212, xv213, xv214, xv215, xv216, bc) -> new_psPs0(:(Char(Succ(xv212)), :(Char(Succ(xv213)), :(Char(Succ(xv214)), []))), new_showsPrec(xv215, xv216, bc)) new_primDivNatS02(xv259, xv260, Zero, Succ(xv2620)) -> Zero new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Float, bc) -> new_psPs0(new_show21(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_div(xv191, xv192) -> Pos(new_primDivNatS4(xv191, xv192)) new_primModNatS2(Succ(xv1970), Zero) -> new_primModNatS3(Succ(xv1970), Zero, Zero) new_primDivNatS2(Succ(xv2730), Zero, xv275) -> new_primDivNatS4(xv2730, xv275) new_primModNatS2(Zero, Succ(xv1980)) -> Succ(Zero) new_show24(xv5, eg, eh, fa) -> new_psPs0(new_show24(xv5, eg, eh, fa), []) new_primDivNatS01(xv259, xv260) -> Succ(new_primDivNatS2(Succ(xv259), Succ(xv260), Succ(xv260))) new_showsPrec(xv215, xv216, ty_Int) -> new_psPs0(new_show30(xv215), xv216) new_primDivNatS4(Succ(xv1910), Zero) -> Succ(new_primDivNatS2(Succ(xv1910), Zero, Zero)) new_show21(xv5) -> new_psPs0(new_show21(xv5), []) new_showsPrec(xv215, xv216, ty_IOError) -> new_psPs0(new_show26(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_@2, ba), bb), bc) -> new_psPs0(new_show17(xv211, ba, bb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show29(xv5) -> new_psPs0(new_show29(xv5), []) new_primShowInt0(Pos(Succ(xv500))) -> new_psPs0(new_primShowInt0(new_div(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(xv500, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(xv264, xv265, Zero, Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, ty_Char) -> new_psPs0(new_show25(xv215), xv216) new_primModNatS01(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS02(xv264, xv265) new_showsPrec(xv215, xv216, app(ty_[], ed)) -> new_psPs0(new_show28(xv215, ed), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show18(xv211, ca, cb), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, app(ty_Maybe, be), bc) -> new_psPs0(new_show22(xv211, be), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_show26(xv5) -> new_psPs0(new_show26(xv5), []) new_showsPrec(xv215, xv216, app(ty_IO, ee)) -> new_psPs0(new_show31(xv215, ee), xv216) new_primDivNatS02(xv259, xv260, Succ(xv2610), Succ(xv2620)) -> new_primDivNatS02(xv259, xv260, xv2610, xv2620) new_show18(xv5, cg, da) -> new_psPs0(new_show18(xv5, cg, da), []) new_primDivNatS2(Succ(xv2730), Succ(xv2740), xv275) -> new_primDivNatS2(xv2730, xv2740, xv275) new_showsPrec(:%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen0(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) new_showsPrec(xv215, xv216, ty_HugsException) -> new_psPs0(new_show23(xv215), xv216) new_primModNatS3(Zero, Zero, xv271) -> new_primModNatS4(xv271) new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_show16(xv5) -> new_psPs0(new_show16(xv5), []) new_showsPrec(xv215, xv216, ty_Bool) -> new_psPs0(new_show20(xv215), xv216) new_showParen0(xv211, xv212, xv213, xv214, xv215, xv216, ty_Double, bc) -> new_psPs0(new_show19(xv211), new_pt0(xv212, xv213, xv214, xv215, xv216, bc)) new_showsPrec(xv215, xv216, ty_Integer) -> new_psPs0(new_show16(xv215), xv216) The set Q consists of the following terms: new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS4(Succ(x0), Zero) new_primDivNatS3(x0) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_show17(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Zero) new_primModNatS4(x0) new_primIntToChar(x0, x1) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, ty_IOErrorKind) new_showsPrec(x0, x1, ty_Ordering) new_div(x0, x1) new_show25(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_showsPrec(x0, x1, ty_Bool) new_show31(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show26(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show16(x0) new_showsPrec(x0, x1, ty_@0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS4(Zero, Zero) new_show20(x0) new_showsPrec(x0, x1, ty_IOError) new_primModNatS2(Succ(x0), Succ(x1)) new_show23(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show30(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1) new_show28(x0, x1) new_primModNatS2(Zero, Zero) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_show29(x0) new_show18(x0, x1, x2) new_showsPrec(x0, x1, ty_HugsException) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS4(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show24(x0, x1, x2, x3) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_primModNatS2(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_show19(x0) new_primModNatS3(Zero, Zero, x0) new_primModNatS3(Zero, Succ(x0), x1) new_primModNatS3(Succ(x0), Zero, x1) new_show21(x0) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, ty_Double) new_psPs0([], x0) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS2(Succ(x0), Zero) new_primShowInt0(Pos(Succ(x0))) new_show22(x0, x1) new_show27(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showsPrec(x0, x1, ty_Float) new_primDivNatS4(Zero, Succ(x0)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (166) 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_pt(xv212, xv213, xv214, :%(xv2150, xv2151), xv216, app(ty_Ratio, h)) -> new_showParen(xv2150, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), xv2151, xv216, h, h) The graph contains the following edges 4 > 1, 4 > 5, 5 >= 6, 6 > 7, 6 > 8 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7) The graph contains the following edges 1 > 1, 2 >= 2, 3 > 2, 4 >= 2, 3 >= 3, 2 >= 4, 3 > 4, 4 >= 4, 1 > 5, 7 > 7, 8 > 7, 7 > 8, 8 > 8 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7) The graph contains the following edges 1 > 1, 2 >= 2, 3 > 2, 4 >= 2, 3 >= 3, 2 >= 4, 3 > 4, 4 >= 4, 1 > 5, 7 > 7, 8 > 7, 7 > 8, 8 > 8 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) The graph contains the following edges 2 >= 1, 3 > 1, 4 >= 1, 3 >= 2, 2 >= 3, 3 > 3, 4 >= 3, 5 >= 4, 6 >= 5, 7 >= 6, 8 >= 6 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The graph contains the following edges 2 >= 1, 3 > 1, 4 >= 1, 3 >= 2, 2 >= 3, 3 > 3, 4 >= 3, 5 >= 4, 6 >= 5, 7 >= 6, 8 >= 6 ---------------------------------------- (167) YES ---------------------------------------- (168) Obligation: Q DP problem: The TRS P consists of the following rules: new_show12(xv5) -> new_show12(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (169) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show12(xv5) evaluates to t =new_show12(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show12(xv5) to new_show12(xv5). ---------------------------------------- (170) NO ---------------------------------------- (171) Obligation: Q DP problem: The TRS P consists of the following rules: new_show7(xv5, h, ba, bb) -> new_show7(xv5, h, ba, bb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (172) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show7(xv5, h, ba, bb) evaluates to t =new_show7(xv5, h, ba, bb) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show7(xv5, h, ba, bb) to new_show7(xv5, h, ba, bb). ---------------------------------------- (173) NO ---------------------------------------- (174) Obligation: Q DP problem: The TRS P consists of the following rules: new_show0(xv5) -> new_show0(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (175) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show0(xv5) evaluates to t =new_show0(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show0(xv5) to new_show0(xv5). ---------------------------------------- (176) NO ---------------------------------------- (177) Obligation: Q DP problem: The TRS P consists of the following rules: new_show1(xv5) -> new_show1(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (178) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show1(xv5) evaluates to t =new_show1(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show1(xv5) to new_show1(xv5). ---------------------------------------- (179) NO ---------------------------------------- (180) Obligation: Q DP problem: The TRS P consists of the following rules: new_show9(xv5, h) -> new_show9(xv5, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (181) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show9(xv5, h) evaluates to t =new_show9(xv5, h) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show9(xv5, h) to new_show9(xv5, h). ---------------------------------------- (182) NO ---------------------------------------- (183) Obligation: Q DP problem: The TRS P consists of the following rules: new_show4(xv5, h, ba) -> new_show4(xv5, h, ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (184) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show4(xv5, h, ba) evaluates to t =new_show4(xv5, h, ba) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show4(xv5, h, ba) to new_show4(xv5, h, ba). ---------------------------------------- (185) NO ---------------------------------------- (186) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(xv2690), Zero, xv271) -> new_primModNatS1(xv2690, xv271) new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero) new_primModNatS00(xv264, xv265) -> new_primModNatS(Succ(xv264), Succ(xv265), Succ(xv265)) new_primModNatS0(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS(Succ(xv264), Succ(xv265), Succ(xv265)) new_primModNatS(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS(xv2690, xv2700, xv271) new_primModNatS0(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS0(xv264, xv265, xv2660, xv2670) new_primModNatS1(Succ(xv1970), Succ(xv1980)) -> new_primModNatS0(xv1970, xv1980, xv1970, xv1980) new_primModNatS0(xv264, xv265, Zero, Zero) -> new_primModNatS00(xv264, xv265) new_primModNatS1(Succ(xv1970), Zero) -> new_primModNatS(Succ(xv1970), Zero, Zero) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (187) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (188) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS1(Succ(xv1970), Succ(xv1980)) -> new_primModNatS0(xv1970, xv1980, xv1970, xv1980) new_primModNatS0(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS(Succ(xv264), Succ(xv265), Succ(xv265)) new_primModNatS(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS(xv2690, xv2700, xv271) new_primModNatS(Succ(xv2690), Zero, xv271) -> new_primModNatS1(xv2690, xv271) new_primModNatS1(Succ(xv1970), Zero) -> new_primModNatS(Succ(xv1970), Zero, Zero) new_primModNatS0(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS0(xv264, xv265, xv2660, xv2670) new_primModNatS0(xv264, xv265, Zero, Zero) -> new_primModNatS00(xv264, xv265) new_primModNatS00(xv264, xv265) -> new_primModNatS(Succ(xv264), Succ(xv265), Succ(xv265)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (189) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primModNatS1(Succ(xv1970), Succ(xv1980)) -> new_primModNatS0(xv1970, xv1980, xv1970, xv1980) new_primModNatS(Succ(xv2690), Succ(xv2700), xv271) -> new_primModNatS(xv2690, xv2700, xv271) new_primModNatS1(Succ(xv1970), Zero) -> new_primModNatS(Succ(xv1970), Zero, Zero) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_primModNatS(x_1, x_2, x_3)) = x_1 POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 POL(new_primModNatS00(x_1, x_2)) = 1 + x_1 POL(new_primModNatS1(x_1, x_2)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: none ---------------------------------------- (190) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(xv264, xv265, Succ(xv2660), Zero) -> new_primModNatS(Succ(xv264), Succ(xv265), Succ(xv265)) new_primModNatS(Succ(xv2690), Zero, xv271) -> new_primModNatS1(xv2690, xv271) new_primModNatS0(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS0(xv264, xv265, xv2660, xv2670) new_primModNatS0(xv264, xv265, Zero, Zero) -> new_primModNatS00(xv264, xv265) new_primModNatS00(xv264, xv265) -> new_primModNatS(Succ(xv264), Succ(xv265), Succ(xv265)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (191) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (192) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS0(xv264, xv265, xv2660, xv2670) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (193) 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_primModNatS0(xv264, xv265, Succ(xv2660), Succ(xv2670)) -> new_primModNatS0(xv264, xv265, xv2660, xv2670) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (194) YES ---------------------------------------- (195) Obligation: Q DP problem: The TRS P consists of the following rules: new_show(xv5, h) -> new_show(xv5, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (196) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show(xv5, h) evaluates to t =new_show(xv5, h) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show(xv5, h) to new_show(xv5, h). ---------------------------------------- (197) NO ---------------------------------------- (198) Obligation: Q DP problem: The TRS P consists of the following rules: new_show6(xv5) -> new_show6(xv5) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (199) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show6(xv5) evaluates to t =new_show6(xv5) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show6(xv5) to new_show6(xv5). ---------------------------------------- (200) NO ---------------------------------------- (201) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="print",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="print xv3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="putStrLn . show",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="putStrLn (show xv3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6 -> 7[label="",style="dashed", color="red", weight=0]; 6[label="putStr (show xv3) >> putChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];6 -> 8[label="",style="dashed", color="magenta", weight=3]; 6 -> 9[label="",style="dashed", color="magenta", weight=3]; 8[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];9[label="xv3",fontsize=16,color="green",shape="box"];7[label="putStr (show xv5) >> putChar (Char (Succ xv6))",fontsize=16,color="black",shape="triangle"];7 -> 10[label="",style="solid", color="black", weight=3]; 10[label="putStr (show xv5) >>= gtGt0 (putChar (Char (Succ xv6)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 11 -> 533[label="",style="dashed", color="red", weight=0]; 11[label="primbindIO (putStr (show xv5)) (gtGt0 (putChar (Char (Succ xv6))))",fontsize=16,color="magenta"];11 -> 534[label="",style="dashed", color="magenta", weight=3]; 11 -> 535[label="",style="dashed", color="magenta", weight=3]; 534[label="putChar (Char (Succ xv6))",fontsize=16,color="black",shape="box"];534 -> 638[label="",style="solid", color="black", weight=3]; 535 -> 639[label="",style="dashed", color="red", weight=0]; 535[label="putStr (show xv5)",fontsize=16,color="magenta"];535 -> 640[label="",style="dashed", color="magenta", weight=3]; 533[label="primbindIO xv70 (gtGt0 xv68)",fontsize=16,color="burlywood",shape="triangle"];2765[label="xv70/IO xv700",fontsize=10,color="white",style="solid",shape="box"];533 -> 2765[label="",style="solid", color="burlywood", weight=9]; 2765 -> 641[label="",style="solid", color="burlywood", weight=3]; 2766[label="xv70/AProVE_IO xv700",fontsize=10,color="white",style="solid",shape="box"];533 -> 2766[label="",style="solid", color="burlywood", weight=9]; 2766 -> 642[label="",style="solid", color="burlywood", weight=3]; 2767[label="xv70/AProVE_Exception xv700",fontsize=10,color="white",style="solid",shape="box"];533 -> 2767[label="",style="solid", color="burlywood", weight=9]; 2767 -> 643[label="",style="solid", color="burlywood", weight=3]; 2768[label="xv70/AProVE_Error xv700",fontsize=10,color="white",style="solid",shape="box"];533 -> 2768[label="",style="solid", color="burlywood", weight=9]; 2768 -> 644[label="",style="solid", color="burlywood", weight=3]; 638 -> 808[label="",style="dashed", color="red", weight=0]; 638[label="(seq Char (Succ xv6) output)",fontsize=16,color="magenta"];638 -> 809[label="",style="dashed", color="magenta", weight=3]; 638 -> 810[label="",style="dashed", color="magenta", weight=3]; 640[label="show xv5",fontsize=16,color="blue",shape="box"];2769[label="show :: ((@2) a b) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2769[label="",style="solid", color="blue", weight=9]; 2769 -> 646[label="",style="solid", color="blue", weight=3]; 2770[label="show :: Double -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2770[label="",style="solid", color="blue", weight=9]; 2770 -> 647[label="",style="solid", color="blue", weight=3]; 2771[label="show :: Bool -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2771[label="",style="solid", color="blue", weight=9]; 2771 -> 648[label="",style="solid", color="blue", weight=3]; 2772[label="show :: Ordering -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2772[label="",style="solid", color="blue", weight=9]; 2772 -> 649[label="",style="solid", color="blue", weight=3]; 2773[label="show :: Float -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2773[label="",style="solid", color="blue", weight=9]; 2773 -> 650[label="",style="solid", color="blue", weight=3]; 2774[label="show :: (Ratio a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2774[label="",style="solid", color="blue", weight=9]; 2774 -> 651[label="",style="solid", color="blue", weight=3]; 2775[label="show :: (Maybe a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2775[label="",style="solid", color="blue", weight=9]; 2775 -> 652[label="",style="solid", color="blue", weight=3]; 2776[label="show :: HugsException -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2776[label="",style="solid", color="blue", weight=9]; 2776 -> 653[label="",style="solid", color="blue", weight=3]; 2777[label="show :: ((@3) a b c) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2777[label="",style="solid", color="blue", weight=9]; 2777 -> 654[label="",style="solid", color="blue", weight=3]; 2778[label="show :: Char -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2778[label="",style="solid", color="blue", weight=9]; 2778 -> 655[label="",style="solid", color="blue", weight=3]; 2779[label="show :: IOError -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2779[label="",style="solid", color="blue", weight=9]; 2779 -> 656[label="",style="solid", color="blue", weight=3]; 2780[label="show :: (Either a b) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2780[label="",style="solid", color="blue", weight=9]; 2780 -> 657[label="",style="solid", color="blue", weight=3]; 2781[label="show :: () -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2781[label="",style="solid", color="blue", weight=9]; 2781 -> 658[label="",style="solid", color="blue", weight=3]; 2782[label="show :: ([] a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2782[label="",style="solid", color="blue", weight=9]; 2782 -> 659[label="",style="solid", color="blue", weight=3]; 2783[label="show :: Integer -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2783[label="",style="solid", color="blue", weight=9]; 2783 -> 660[label="",style="solid", color="blue", weight=3]; 2784[label="show :: IOErrorKind -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2784[label="",style="solid", color="blue", weight=9]; 2784 -> 661[label="",style="solid", color="blue", weight=3]; 2785[label="show :: Int -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2785[label="",style="solid", color="blue", weight=9]; 2785 -> 662[label="",style="solid", color="blue", weight=3]; 2786[label="show :: (IO a) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];640 -> 2786[label="",style="solid", color="blue", weight=9]; 2786 -> 663[label="",style="solid", color="blue", weight=3]; 639[label="putStr xv73",fontsize=16,color="burlywood",shape="triangle"];2787[label="xv73/xv730 : xv731",fontsize=10,color="white",style="solid",shape="box"];639 -> 2787[label="",style="solid", color="burlywood", weight=9]; 2787 -> 664[label="",style="solid", color="burlywood", weight=3]; 2788[label="xv73/[]",fontsize=10,color="white",style="solid",shape="box"];639 -> 2788[label="",style="solid", color="burlywood", weight=9]; 2788 -> 665[label="",style="solid", color="burlywood", weight=3]; 641[label="primbindIO (IO xv700) (gtGt0 xv68)",fontsize=16,color="black",shape="box"];641 -> 666[label="",style="solid", color="black", weight=3]; 642[label="primbindIO (AProVE_IO xv700) (gtGt0 xv68)",fontsize=16,color="black",shape="box"];642 -> 667[label="",style="solid", color="black", weight=3]; 643[label="primbindIO (AProVE_Exception xv700) (gtGt0 xv68)",fontsize=16,color="black",shape="box"];643 -> 668[label="",style="solid", color="black", weight=3]; 644[label="primbindIO (AProVE_Error xv700) (gtGt0 xv68)",fontsize=16,color="black",shape="box"];644 -> 669[label="",style="solid", color="black", weight=3]; 809 -> 670[label="",style="dashed", color="red", weight=0]; 809[label="output",fontsize=16,color="magenta"];810[label="Char (Succ xv6)",fontsize=16,color="green",shape="box"];808[label="(seq xv730 xv102)",fontsize=16,color="black",shape="triangle"];808 -> 812[label="",style="solid", color="black", weight=3]; 646[label="show xv5",fontsize=16,color="black",shape="triangle"];646 -> 671[label="",style="solid", color="black", weight=3]; 647[label="show xv5",fontsize=16,color="black",shape="triangle"];647 -> 672[label="",style="solid", color="black", weight=3]; 648[label="show xv5",fontsize=16,color="black",shape="triangle"];648 -> 673[label="",style="solid", color="black", weight=3]; 649[label="show xv5",fontsize=16,color="black",shape="triangle"];649 -> 674[label="",style="solid", color="black", weight=3]; 650[label="show xv5",fontsize=16,color="black",shape="triangle"];650 -> 675[label="",style="solid", color="black", weight=3]; 651[label="show xv5",fontsize=16,color="black",shape="box"];651 -> 676[label="",style="solid", color="black", weight=3]; 652[label="show xv5",fontsize=16,color="black",shape="triangle"];652 -> 677[label="",style="solid", color="black", weight=3]; 653[label="show xv5",fontsize=16,color="black",shape="triangle"];653 -> 678[label="",style="solid", color="black", weight=3]; 654[label="show xv5",fontsize=16,color="black",shape="triangle"];654 -> 679[label="",style="solid", color="black", weight=3]; 655[label="show xv5",fontsize=16,color="black",shape="triangle"];655 -> 680[label="",style="solid", color="black", weight=3]; 656[label="show xv5",fontsize=16,color="black",shape="triangle"];656 -> 681[label="",style="solid", color="black", weight=3]; 657[label="show xv5",fontsize=16,color="black",shape="triangle"];657 -> 682[label="",style="solid", color="black", weight=3]; 658[label="show xv5",fontsize=16,color="black",shape="triangle"];658 -> 683[label="",style="solid", color="black", weight=3]; 659[label="show xv5",fontsize=16,color="black",shape="triangle"];659 -> 684[label="",style="solid", color="black", weight=3]; 660[label="show xv5",fontsize=16,color="black",shape="triangle"];660 -> 685[label="",style="solid", color="black", weight=3]; 661[label="show xv5",fontsize=16,color="black",shape="triangle"];661 -> 686[label="",style="solid", color="black", weight=3]; 662[label="show xv5",fontsize=16,color="black",shape="triangle"];662 -> 687[label="",style="solid", color="black", weight=3]; 663[label="show xv5",fontsize=16,color="black",shape="triangle"];663 -> 688[label="",style="solid", color="black", weight=3]; 664[label="putStr (xv730 : xv731)",fontsize=16,color="black",shape="box"];664 -> 689[label="",style="solid", color="black", weight=3]; 665[label="putStr []",fontsize=16,color="black",shape="box"];665 -> 690[label="",style="solid", color="black", weight=3]; 666[label="error []",fontsize=16,color="red",shape="box"];667[label="gtGt0 xv68 xv700",fontsize=16,color="black",shape="box"];667 -> 691[label="",style="solid", color="black", weight=3]; 668[label="AProVE_Exception xv700",fontsize=16,color="green",shape="box"];669[label="AProVE_Error xv700",fontsize=16,color="green",shape="box"];670[label="output",fontsize=16,color="black",shape="triangle"];670 -> 692[label="",style="solid", color="black", weight=3]; 812[label="enforceWHNF (WHNF xv730) xv102",fontsize=16,color="black",shape="box"];812 -> 819[label="",style="solid", color="black", weight=3]; 671[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];671 -> 693[label="",style="solid", color="black", weight=3]; 672[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];672 -> 694[label="",style="solid", color="black", weight=3]; 673[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];673 -> 695[label="",style="solid", color="black", weight=3]; 674[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];674 -> 696[label="",style="solid", color="black", weight=3]; 675[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];675 -> 697[label="",style="solid", color="black", weight=3]; 676[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="burlywood",shape="box"];2789[label="xv5/xv50 :% xv51",fontsize=10,color="white",style="solid",shape="box"];676 -> 2789[label="",style="solid", color="burlywood", weight=9]; 2789 -> 698[label="",style="solid", color="burlywood", weight=3]; 677[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];677 -> 699[label="",style="solid", color="black", weight=3]; 678[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];678 -> 700[label="",style="solid", color="black", weight=3]; 679[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];679 -> 701[label="",style="solid", color="black", weight=3]; 680[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];680 -> 702[label="",style="solid", color="black", weight=3]; 681[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];681 -> 703[label="",style="solid", color="black", weight=3]; 682[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];682 -> 704[label="",style="solid", color="black", weight=3]; 683[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];683 -> 705[label="",style="solid", color="black", weight=3]; 684[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];684 -> 706[label="",style="solid", color="black", weight=3]; 685[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];685 -> 707[label="",style="solid", color="black", weight=3]; 686[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];686 -> 708[label="",style="solid", color="black", weight=3]; 687[label="primShowInt xv5",fontsize=16,color="burlywood",shape="triangle"];2790[label="xv5/Pos xv50",fontsize=10,color="white",style="solid",shape="box"];687 -> 2790[label="",style="solid", color="burlywood", weight=9]; 2790 -> 709[label="",style="solid", color="burlywood", weight=3]; 2791[label="xv5/Neg xv50",fontsize=10,color="white",style="solid",shape="box"];687 -> 2791[label="",style="solid", color="burlywood", weight=9]; 2791 -> 710[label="",style="solid", color="burlywood", weight=3]; 688[label="showsPrec (Pos Zero) xv5 []",fontsize=16,color="black",shape="box"];688 -> 711[label="",style="solid", color="black", weight=3]; 689 -> 712[label="",style="dashed", color="red", weight=0]; 689[label="putChar xv730 >> putStr xv731",fontsize=16,color="magenta"];689 -> 713[label="",style="dashed", color="magenta", weight=3]; 690 -> 670[label="",style="dashed", color="red", weight=0]; 690[label="output",fontsize=16,color="magenta"];691[label="xv68",fontsize=16,color="green",shape="box"];692[label="randomSelect (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];692 -> 714[label="",style="solid", color="black", weight=3]; 819[label="xv102",fontsize=16,color="green",shape="box"];693 -> 1484[label="",style="dashed", color="red", weight=0]; 693[label="show xv5 ++ []",fontsize=16,color="magenta"];693 -> 1485[label="",style="dashed", color="magenta", weight=3]; 693 -> 1486[label="",style="dashed", color="magenta", weight=3]; 694 -> 1484[label="",style="dashed", color="red", weight=0]; 694[label="show xv5 ++ []",fontsize=16,color="magenta"];694 -> 1487[label="",style="dashed", color="magenta", weight=3]; 694 -> 1488[label="",style="dashed", color="magenta", weight=3]; 695 -> 1484[label="",style="dashed", color="red", weight=0]; 695[label="show xv5 ++ []",fontsize=16,color="magenta"];695 -> 1489[label="",style="dashed", color="magenta", weight=3]; 695 -> 1490[label="",style="dashed", color="magenta", weight=3]; 696 -> 1484[label="",style="dashed", color="red", weight=0]; 696[label="show xv5 ++ []",fontsize=16,color="magenta"];696 -> 1491[label="",style="dashed", color="magenta", weight=3]; 696 -> 1492[label="",style="dashed", color="magenta", weight=3]; 697 -> 1484[label="",style="dashed", color="red", weight=0]; 697[label="show xv5 ++ []",fontsize=16,color="magenta"];697 -> 1493[label="",style="dashed", color="magenta", weight=3]; 697 -> 1494[label="",style="dashed", color="magenta", weight=3]; 698[label="showsPrec (Pos Zero) (xv50 :% xv51) []",fontsize=16,color="black",shape="box"];698 -> 732[label="",style="solid", color="black", weight=3]; 699 -> 1484[label="",style="dashed", color="red", weight=0]; 699[label="show xv5 ++ []",fontsize=16,color="magenta"];699 -> 1495[label="",style="dashed", color="magenta", weight=3]; 699 -> 1496[label="",style="dashed", color="magenta", weight=3]; 700 -> 1484[label="",style="dashed", color="red", weight=0]; 700[label="show xv5 ++ []",fontsize=16,color="magenta"];700 -> 1497[label="",style="dashed", color="magenta", weight=3]; 700 -> 1498[label="",style="dashed", color="magenta", weight=3]; 701 -> 1484[label="",style="dashed", color="red", weight=0]; 701[label="show xv5 ++ []",fontsize=16,color="magenta"];701 -> 1499[label="",style="dashed", color="magenta", weight=3]; 701 -> 1500[label="",style="dashed", color="magenta", weight=3]; 702 -> 1484[label="",style="dashed", color="red", weight=0]; 702[label="show xv5 ++ []",fontsize=16,color="magenta"];702 -> 1501[label="",style="dashed", color="magenta", weight=3]; 702 -> 1502[label="",style="dashed", color="magenta", weight=3]; 703 -> 1484[label="",style="dashed", color="red", weight=0]; 703[label="show xv5 ++ []",fontsize=16,color="magenta"];703 -> 1503[label="",style="dashed", color="magenta", weight=3]; 703 -> 1504[label="",style="dashed", color="magenta", weight=3]; 704 -> 1484[label="",style="dashed", color="red", weight=0]; 704[label="show xv5 ++ []",fontsize=16,color="magenta"];704 -> 1505[label="",style="dashed", color="magenta", weight=3]; 704 -> 1506[label="",style="dashed", color="magenta", weight=3]; 705 -> 1484[label="",style="dashed", color="red", weight=0]; 705[label="show xv5 ++ []",fontsize=16,color="magenta"];705 -> 1507[label="",style="dashed", color="magenta", weight=3]; 705 -> 1508[label="",style="dashed", color="magenta", weight=3]; 706 -> 1484[label="",style="dashed", color="red", weight=0]; 706[label="show xv5 ++ []",fontsize=16,color="magenta"];706 -> 1509[label="",style="dashed", color="magenta", weight=3]; 706 -> 1510[label="",style="dashed", color="magenta", weight=3]; 707 -> 1484[label="",style="dashed", color="red", weight=0]; 707[label="show xv5 ++ []",fontsize=16,color="magenta"];707 -> 1511[label="",style="dashed", color="magenta", weight=3]; 707 -> 1512[label="",style="dashed", color="magenta", weight=3]; 708 -> 1484[label="",style="dashed", color="red", weight=0]; 708[label="show xv5 ++ []",fontsize=16,color="magenta"];708 -> 1513[label="",style="dashed", color="magenta", weight=3]; 708 -> 1514[label="",style="dashed", color="magenta", weight=3]; 709[label="primShowInt (Pos xv50)",fontsize=16,color="burlywood",shape="box"];2792[label="xv50/Succ xv500",fontsize=10,color="white",style="solid",shape="box"];709 -> 2792[label="",style="solid", color="burlywood", weight=9]; 2792 -> 733[label="",style="solid", color="burlywood", weight=3]; 2793[label="xv50/Zero",fontsize=10,color="white",style="solid",shape="box"];709 -> 2793[label="",style="solid", color="burlywood", weight=9]; 2793 -> 734[label="",style="solid", color="burlywood", weight=3]; 710[label="primShowInt (Neg xv50)",fontsize=16,color="black",shape="box"];710 -> 735[label="",style="solid", color="black", weight=3]; 711 -> 1484[label="",style="dashed", color="red", weight=0]; 711[label="show xv5 ++ []",fontsize=16,color="magenta"];711 -> 1515[label="",style="dashed", color="magenta", weight=3]; 711 -> 1516[label="",style="dashed", color="magenta", weight=3]; 713 -> 639[label="",style="dashed", color="red", weight=0]; 713[label="putStr xv731",fontsize=16,color="magenta"];713 -> 736[label="",style="dashed", color="magenta", weight=3]; 712[label="putChar xv730 >> xv74",fontsize=16,color="black",shape="triangle"];712 -> 737[label="",style="solid", color="black", weight=3]; 714[label="randomSelect2 (aIOE IOError_FullError : aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];714 -> 738[label="",style="solid", color="black", weight=3]; 1485 -> 646[label="",style="dashed", color="red", weight=0]; 1485[label="show xv5",fontsize=16,color="magenta"];1486[label="[]",fontsize=16,color="green",shape="box"];1484[label="xv189 ++ xv131",fontsize=16,color="burlywood",shape="triangle"];2794[label="xv189/xv1890 : xv1891",fontsize=10,color="white",style="solid",shape="box"];1484 -> 2794[label="",style="solid", color="burlywood", weight=9]; 2794 -> 1590[label="",style="solid", color="burlywood", weight=3]; 2795[label="xv189/[]",fontsize=10,color="white",style="solid",shape="box"];1484 -> 2795[label="",style="solid", color="burlywood", weight=9]; 2795 -> 1591[label="",style="solid", color="burlywood", weight=3]; 1487 -> 647[label="",style="dashed", color="red", weight=0]; 1487[label="show xv5",fontsize=16,color="magenta"];1488[label="[]",fontsize=16,color="green",shape="box"];1489 -> 648[label="",style="dashed", color="red", weight=0]; 1489[label="show xv5",fontsize=16,color="magenta"];1490[label="[]",fontsize=16,color="green",shape="box"];1491 -> 649[label="",style="dashed", color="red", weight=0]; 1491[label="show xv5",fontsize=16,color="magenta"];1492[label="[]",fontsize=16,color="green",shape="box"];1493 -> 650[label="",style="dashed", color="red", weight=0]; 1493[label="show xv5",fontsize=16,color="magenta"];1494[label="[]",fontsize=16,color="green",shape="box"];732 -> 1735[label="",style="dashed", color="red", weight=0]; 732[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows xv50) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows xv51) []",fontsize=16,color="magenta"];732 -> 1736[label="",style="dashed", color="magenta", weight=3]; 732 -> 1737[label="",style="dashed", color="magenta", weight=3]; 732 -> 1738[label="",style="dashed", color="magenta", weight=3]; 732 -> 1739[label="",style="dashed", color="magenta", weight=3]; 732 -> 1740[label="",style="dashed", color="magenta", weight=3]; 732 -> 1741[label="",style="dashed", color="magenta", weight=3]; 1495 -> 652[label="",style="dashed", color="red", weight=0]; 1495[label="show xv5",fontsize=16,color="magenta"];1496[label="[]",fontsize=16,color="green",shape="box"];1497 -> 653[label="",style="dashed", color="red", weight=0]; 1497[label="show xv5",fontsize=16,color="magenta"];1498[label="[]",fontsize=16,color="green",shape="box"];1499 -> 654[label="",style="dashed", color="red", weight=0]; 1499[label="show xv5",fontsize=16,color="magenta"];1500[label="[]",fontsize=16,color="green",shape="box"];1501 -> 655[label="",style="dashed", color="red", weight=0]; 1501[label="show xv5",fontsize=16,color="magenta"];1502[label="[]",fontsize=16,color="green",shape="box"];1503 -> 656[label="",style="dashed", color="red", weight=0]; 1503[label="show xv5",fontsize=16,color="magenta"];1504[label="[]",fontsize=16,color="green",shape="box"];1505 -> 657[label="",style="dashed", color="red", weight=0]; 1505[label="show xv5",fontsize=16,color="magenta"];1506[label="[]",fontsize=16,color="green",shape="box"];1507 -> 658[label="",style="dashed", color="red", weight=0]; 1507[label="show xv5",fontsize=16,color="magenta"];1508[label="[]",fontsize=16,color="green",shape="box"];1509 -> 659[label="",style="dashed", color="red", weight=0]; 1509[label="show xv5",fontsize=16,color="magenta"];1510[label="[]",fontsize=16,color="green",shape="box"];1511 -> 660[label="",style="dashed", color="red", weight=0]; 1511[label="show xv5",fontsize=16,color="magenta"];1512[label="[]",fontsize=16,color="green",shape="box"];1513 -> 661[label="",style="dashed", color="red", weight=0]; 1513[label="show xv5",fontsize=16,color="magenta"];1514[label="[]",fontsize=16,color="green",shape="box"];733[label="primShowInt (Pos (Succ xv500))",fontsize=16,color="black",shape="box"];733 -> 745[label="",style="solid", color="black", weight=3]; 734[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];734 -> 746[label="",style="solid", color="black", weight=3]; 735[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))) : primShowInt (Pos xv50)",fontsize=16,color="green",shape="box"];735 -> 747[label="",style="dashed", color="green", weight=3]; 1515 -> 663[label="",style="dashed", color="red", weight=0]; 1515[label="show xv5",fontsize=16,color="magenta"];1516[label="[]",fontsize=16,color="green",shape="box"];736[label="xv731",fontsize=16,color="green",shape="box"];737[label="putChar xv730 >>= gtGt0 xv74",fontsize=16,color="black",shape="box"];737 -> 748[label="",style="solid", color="black", weight=3]; 738[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];738 -> 749[label="",style="solid", color="black", weight=3]; 1590[label="(xv1890 : xv1891) ++ xv131",fontsize=16,color="black",shape="box"];1590 -> 1612[label="",style="solid", color="black", weight=3]; 1591[label="[] ++ xv131",fontsize=16,color="black",shape="box"];1591 -> 1613[label="",style="solid", color="black", weight=3]; 1736[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1737[label="xv51",fontsize=16,color="green",shape="box"];1738[label="xv50",fontsize=16,color="green",shape="box"];1739[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1740[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1741[label="[]",fontsize=16,color="green",shape="box"];1735[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) xv216",fontsize=16,color="black",shape="triangle"];1735 -> 1748[label="",style="solid", color="black", weight=3]; 745 -> 1484[label="",style="dashed", color="red", weight=0]; 745[label="primShowInt (div Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];745 -> 1519[label="",style="dashed", color="magenta", weight=3]; 745 -> 1520[label="",style="dashed", color="magenta", weight=3]; 746[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))) : []",fontsize=16,color="green",shape="box"];747 -> 687[label="",style="dashed", color="red", weight=0]; 747[label="primShowInt (Pos xv50)",fontsize=16,color="magenta"];747 -> 776[label="",style="dashed", color="magenta", weight=3]; 748 -> 533[label="",style="dashed", color="red", weight=0]; 748[label="primbindIO (putChar xv730) (gtGt0 xv74)",fontsize=16,color="magenta"];748 -> 777[label="",style="dashed", color="magenta", weight=3]; 748 -> 778[label="",style="dashed", color="magenta", weight=3]; 749[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) ter5m",fontsize=16,color="burlywood",shape="box"];2796[label="ter5m/False",fontsize=10,color="white",style="solid",shape="box"];749 -> 2796[label="",style="solid", color="burlywood", weight=9]; 2796 -> 779[label="",style="solid", color="burlywood", weight=3]; 2797[label="ter5m/True",fontsize=10,color="white",style="solid",shape="box"];749 -> 2797[label="",style="solid", color="burlywood", weight=9]; 2797 -> 780[label="",style="solid", color="burlywood", weight=3]; 1612[label="xv1890 : xv1891 ++ xv131",fontsize=16,color="green",shape="box"];1612 -> 1617[label="",style="dashed", color="green", weight=3]; 1613[label="xv131",fontsize=16,color="green",shape="box"];1748[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) xv216",fontsize=16,color="black",shape="box"];1748 -> 1754[label="",style="solid", color="black", weight=3]; 1519 -> 687[label="",style="dashed", color="red", weight=0]; 1519[label="primShowInt (div Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];1519 -> 1592[label="",style="dashed", color="magenta", weight=3]; 1520[label="toEnum (mod Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];1520 -> 1593[label="",style="dashed", color="green", weight=3]; 776[label="Pos xv50",fontsize=16,color="green",shape="box"];777[label="xv74",fontsize=16,color="green",shape="box"];778[label="putChar xv730",fontsize=16,color="black",shape="box"];778 -> 798[label="",style="solid", color="black", weight=3]; 779[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];779 -> 799[label="",style="solid", color="black", weight=3]; 780[label="randomSelect1 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];780 -> 800[label="",style="solid", color="black", weight=3]; 1617 -> 1484[label="",style="dashed", color="red", weight=0]; 1617[label="xv1891 ++ xv131",fontsize=16,color="magenta"];1617 -> 1621[label="",style="dashed", color="magenta", weight=3]; 1754[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) xv216",fontsize=16,color="black",shape="box"];1754 -> 1760[label="",style="solid", color="black", weight=3]; 1592 -> 1614[label="",style="dashed", color="red", weight=0]; 1592[label="div Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];1592 -> 1615[label="",style="dashed", color="magenta", weight=3]; 1592 -> 1616[label="",style="dashed", color="magenta", weight=3]; 1593[label="toEnum (mod Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];1593 -> 1651[label="",style="solid", color="black", weight=3]; 798 -> 808[label="",style="dashed", color="red", weight=0]; 798[label="(seq xv730 output)",fontsize=16,color="magenta"];798 -> 811[label="",style="dashed", color="magenta", weight=3]; 799[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];799 -> 817[label="",style="solid", color="black", weight=3]; 800[label="randomSelect (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];800 -> 818[label="",style="solid", color="black", weight=3]; 1621[label="xv1891",fontsize=16,color="green",shape="box"];1760[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) xv216",fontsize=16,color="black",shape="box"];1760 -> 1767[label="",style="solid", color="black", weight=3]; 1615[label="xv500",fontsize=16,color="green",shape="box"];1616[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];1614[label="div Pos (Succ xv191) Pos (Succ xv192)",fontsize=16,color="black",shape="triangle"];1614 -> 1622[label="",style="solid", color="black", weight=3]; 1651 -> 1680[label="",style="dashed", color="red", weight=0]; 1651[label="primIntToChar (mod Pos (Succ xv500) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];1651 -> 1681[label="",style="dashed", color="magenta", weight=3]; 1651 -> 1682[label="",style="dashed", color="magenta", weight=3]; 811 -> 670[label="",style="dashed", color="red", weight=0]; 811[label="output",fontsize=16,color="magenta"];817[label="randomSelect0 (aIOE IOError_FullError) (aIOE IOError_PermDenied : AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];817 -> 824[label="",style="solid", color="black", weight=3]; 818[label="randomSelect2 (aIOE IOError_PermDenied : AProVE_IO () : [])",fontsize=16,color="black",shape="box"];818 -> 825[label="",style="solid", color="black", weight=3]; 1767[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) xv216",fontsize=16,color="black",shape="box"];1767 -> 1776[label="",style="solid", color="black", weight=3]; 1622[label="primDivInt (Pos (Succ xv191)) (Pos (Succ xv192))",fontsize=16,color="black",shape="box"];1622 -> 1650[label="",style="solid", color="black", weight=3]; 1681[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];1682[label="xv500",fontsize=16,color="green",shape="box"];1680[label="primIntToChar (mod Pos (Succ xv197) Pos (Succ xv198))",fontsize=16,color="black",shape="triangle"];1680 -> 1683[label="",style="solid", color="black", weight=3]; 824[label="aIOE IOError_FullError",fontsize=16,color="black",shape="box"];824 -> 829[label="",style="solid", color="black", weight=3]; 825[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) terminator",fontsize=16,color="black",shape="box"];825 -> 830[label="",style="solid", color="black", weight=3]; 1776[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) (LT == GT) xv216",fontsize=16,color="black",shape="box"];1776 -> 1787[label="",style="solid", color="black", weight=3]; 1650[label="Pos (primDivNatS (Succ xv191) (Succ xv192))",fontsize=16,color="green",shape="box"];1650 -> 1679[label="",style="dashed", color="green", weight=3]; 1683[label="primIntToChar (primModInt (Pos (Succ xv197)) (Pos (Succ xv198)))",fontsize=16,color="black",shape="box"];1683 -> 1703[label="",style="solid", color="black", weight=3]; 829[label="AProVE_Exception (AET_IOError (IOError IOError_FullError [] [] Nothing))",fontsize=16,color="green",shape="box"];830[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) ter6m",fontsize=16,color="burlywood",shape="box"];2798[label="ter6m/False",fontsize=10,color="white",style="solid",shape="box"];830 -> 2798[label="",style="solid", color="burlywood", weight=9]; 2798 -> 834[label="",style="solid", color="burlywood", weight=3]; 2799[label="ter6m/True",fontsize=10,color="white",style="solid",shape="box"];830 -> 2799[label="",style="solid", color="burlywood", weight=9]; 2799 -> 835[label="",style="solid", color="burlywood", weight=3]; 1787[label="showParen0 ((shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215) False xv216",fontsize=16,color="black",shape="box"];1787 -> 1800[label="",style="solid", color="black", weight=3]; 1679[label="primDivNatS (Succ xv191) (Succ xv192)",fontsize=16,color="black",shape="triangle"];1679 -> 1684[label="",style="solid", color="black", weight=3]; 1703[label="primIntToChar (Pos (primModNatS (Succ xv197) (Succ xv198)))",fontsize=16,color="black",shape="box"];1703 -> 1749[label="",style="solid", color="black", weight=3]; 834[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) False",fontsize=16,color="black",shape="box"];834 -> 840[label="",style="solid", color="black", weight=3]; 835[label="randomSelect1 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];835 -> 841[label="",style="solid", color="black", weight=3]; 1800[label="(shows xv211) . (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="black",shape="box"];1800 -> 1812[label="",style="solid", color="black", weight=3]; 1684[label="primDivNatS0 xv191 xv192 (primGEqNatS xv191 xv192)",fontsize=16,color="burlywood",shape="box"];2800[label="xv191/Succ xv1910",fontsize=10,color="white",style="solid",shape="box"];1684 -> 2800[label="",style="solid", color="burlywood", weight=9]; 2800 -> 1704[label="",style="solid", color="burlywood", weight=3]; 2801[label="xv191/Zero",fontsize=10,color="white",style="solid",shape="box"];1684 -> 2801[label="",style="solid", color="burlywood", weight=9]; 2801 -> 1705[label="",style="solid", color="burlywood", weight=3]; 1749[label="Char (primModNatS (Succ xv197) (Succ xv198))",fontsize=16,color="green",shape="box"];1749 -> 1755[label="",style="dashed", color="green", weight=3]; 840[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) otherwise",fontsize=16,color="black",shape="box"];840 -> 848[label="",style="solid", color="black", weight=3]; 841[label="randomSelect (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];841 -> 849[label="",style="solid", color="black", weight=3]; 1812[label="shows xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1812 -> 1825[label="",style="solid", color="black", weight=3]; 1704[label="primDivNatS0 (Succ xv1910) xv192 (primGEqNatS (Succ xv1910) xv192)",fontsize=16,color="burlywood",shape="box"];2802[label="xv192/Succ xv1920",fontsize=10,color="white",style="solid",shape="box"];1704 -> 2802[label="",style="solid", color="burlywood", weight=9]; 2802 -> 1750[label="",style="solid", color="burlywood", weight=3]; 2803[label="xv192/Zero",fontsize=10,color="white",style="solid",shape="box"];1704 -> 2803[label="",style="solid", color="burlywood", weight=9]; 2803 -> 1751[label="",style="solid", color="burlywood", weight=3]; 1705[label="primDivNatS0 Zero xv192 (primGEqNatS Zero xv192)",fontsize=16,color="burlywood",shape="box"];2804[label="xv192/Succ xv1920",fontsize=10,color="white",style="solid",shape="box"];1705 -> 2804[label="",style="solid", color="burlywood", weight=9]; 2804 -> 1752[label="",style="solid", color="burlywood", weight=3]; 2805[label="xv192/Zero",fontsize=10,color="white",style="solid",shape="box"];1705 -> 2805[label="",style="solid", color="burlywood", weight=9]; 2805 -> 1753[label="",style="solid", color="burlywood", weight=3]; 1755[label="primModNatS (Succ xv197) (Succ xv198)",fontsize=16,color="black",shape="triangle"];1755 -> 1761[label="",style="solid", color="black", weight=3]; 848[label="randomSelect0 (aIOE IOError_PermDenied) (AProVE_IO () : []) True",fontsize=16,color="black",shape="box"];848 -> 873[label="",style="solid", color="black", weight=3]; 849[label="randomSelect3 (AProVE_IO () : [])",fontsize=16,color="black",shape="box"];849 -> 874[label="",style="solid", color="black", weight=3]; 1825[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="blue",shape="box"];2806[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2806[label="",style="solid", color="blue", weight=9]; 2806 -> 1840[label="",style="solid", color="blue", weight=3]; 2807[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2807[label="",style="solid", color="blue", weight=9]; 2807 -> 1841[label="",style="solid", color="blue", weight=3]; 2808[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2808[label="",style="solid", color="blue", weight=9]; 2808 -> 1842[label="",style="solid", color="blue", weight=3]; 2809[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2809[label="",style="solid", color="blue", weight=9]; 2809 -> 1843[label="",style="solid", color="blue", weight=3]; 2810[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2810[label="",style="solid", color="blue", weight=9]; 2810 -> 1844[label="",style="solid", color="blue", weight=3]; 2811[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2811[label="",style="solid", color="blue", weight=9]; 2811 -> 1845[label="",style="solid", color="blue", weight=3]; 2812[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2812[label="",style="solid", color="blue", weight=9]; 2812 -> 1846[label="",style="solid", color="blue", weight=3]; 2813[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2813[label="",style="solid", color="blue", weight=9]; 2813 -> 1847[label="",style="solid", color="blue", weight=3]; 2814[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2814[label="",style="solid", color="blue", weight=9]; 2814 -> 1848[label="",style="solid", color="blue", weight=3]; 2815[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2815[label="",style="solid", color="blue", weight=9]; 2815 -> 1849[label="",style="solid", color="blue", weight=3]; 2816[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2816[label="",style="solid", color="blue", weight=9]; 2816 -> 1850[label="",style="solid", color="blue", weight=3]; 2817[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2817[label="",style="solid", color="blue", weight=9]; 2817 -> 1851[label="",style="solid", color="blue", weight=3]; 2818[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2818[label="",style="solid", color="blue", weight=9]; 2818 -> 1852[label="",style="solid", color="blue", weight=3]; 2819[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2819[label="",style="solid", color="blue", weight=9]; 2819 -> 1853[label="",style="solid", color="blue", weight=3]; 2820[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2820[label="",style="solid", color="blue", weight=9]; 2820 -> 1854[label="",style="solid", color="blue", weight=3]; 2821[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2821[label="",style="solid", color="blue", weight=9]; 2821 -> 1855[label="",style="solid", color="blue", weight=3]; 2822[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2822[label="",style="solid", color="blue", weight=9]; 2822 -> 1856[label="",style="solid", color="blue", weight=3]; 2823[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1825 -> 2823[label="",style="solid", color="blue", weight=9]; 2823 -> 1857[label="",style="solid", color="blue", weight=3]; 1750[label="primDivNatS0 (Succ xv1910) (Succ xv1920) (primGEqNatS (Succ xv1910) (Succ xv1920))",fontsize=16,color="black",shape="box"];1750 -> 1756[label="",style="solid", color="black", weight=3]; 1751[label="primDivNatS0 (Succ xv1910) Zero (primGEqNatS (Succ xv1910) Zero)",fontsize=16,color="black",shape="box"];1751 -> 1757[label="",style="solid", color="black", weight=3]; 1752[label="primDivNatS0 Zero (Succ xv1920) (primGEqNatS Zero (Succ xv1920))",fontsize=16,color="black",shape="box"];1752 -> 1758[label="",style="solid", color="black", weight=3]; 1753[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1753 -> 1759[label="",style="solid", color="black", weight=3]; 1761[label="primModNatS0 xv197 xv198 (primGEqNatS xv197 xv198)",fontsize=16,color="burlywood",shape="box"];2824[label="xv197/Succ xv1970",fontsize=10,color="white",style="solid",shape="box"];1761 -> 2824[label="",style="solid", color="burlywood", weight=9]; 2824 -> 1768[label="",style="solid", color="burlywood", weight=3]; 2825[label="xv197/Zero",fontsize=10,color="white",style="solid",shape="box"];1761 -> 2825[label="",style="solid", color="burlywood", weight=9]; 2825 -> 1769[label="",style="solid", color="burlywood", weight=3]; 873[label="aIOE IOError_PermDenied",fontsize=16,color="black",shape="box"];873 -> 900[label="",style="solid", color="black", weight=3]; 874[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];1840[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1840 -> 1872[label="",style="solid", color="black", weight=3]; 1841[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1841 -> 1873[label="",style="solid", color="black", weight=3]; 1842[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1842 -> 1874[label="",style="solid", color="black", weight=3]; 1843[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1843 -> 1875[label="",style="solid", color="black", weight=3]; 1844[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1844 -> 1876[label="",style="solid", color="black", weight=3]; 1845[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="burlywood",shape="box"];2826[label="xv211/xv2110 :% xv2111",fontsize=10,color="white",style="solid",shape="box"];1845 -> 2826[label="",style="solid", color="burlywood", weight=9]; 2826 -> 1877[label="",style="solid", color="burlywood", weight=3]; 1846[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1846 -> 1878[label="",style="solid", color="black", weight=3]; 1847[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1847 -> 1879[label="",style="solid", color="black", weight=3]; 1848[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1848 -> 1880[label="",style="solid", color="black", weight=3]; 1849[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1849 -> 1881[label="",style="solid", color="black", weight=3]; 1850[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1850 -> 1882[label="",style="solid", color="black", weight=3]; 1851[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1851 -> 1883[label="",style="solid", color="black", weight=3]; 1852[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1852 -> 1884[label="",style="solid", color="black", weight=3]; 1853[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1853 -> 1885[label="",style="solid", color="black", weight=3]; 1854[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1854 -> 1886[label="",style="solid", color="black", weight=3]; 1855[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1855 -> 1887[label="",style="solid", color="black", weight=3]; 1856[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1856 -> 1888[label="",style="solid", color="black", weight=3]; 1857[label="showsPrec (Pos Zero) xv211 ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1857 -> 1889[label="",style="solid", color="black", weight=3]; 1756 -> 2471[label="",style="dashed", color="red", weight=0]; 1756[label="primDivNatS0 (Succ xv1910) (Succ xv1920) (primGEqNatS xv1910 xv1920)",fontsize=16,color="magenta"];1756 -> 2472[label="",style="dashed", color="magenta", weight=3]; 1756 -> 2473[label="",style="dashed", color="magenta", weight=3]; 1756 -> 2474[label="",style="dashed", color="magenta", weight=3]; 1756 -> 2475[label="",style="dashed", color="magenta", weight=3]; 1757[label="primDivNatS0 (Succ xv1910) Zero True",fontsize=16,color="black",shape="box"];1757 -> 1764[label="",style="solid", color="black", weight=3]; 1758[label="primDivNatS0 Zero (Succ xv1920) False",fontsize=16,color="black",shape="box"];1758 -> 1765[label="",style="solid", color="black", weight=3]; 1759[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];1759 -> 1766[label="",style="solid", color="black", weight=3]; 1768[label="primModNatS0 (Succ xv1970) xv198 (primGEqNatS (Succ xv1970) xv198)",fontsize=16,color="burlywood",shape="box"];2827[label="xv198/Succ xv1980",fontsize=10,color="white",style="solid",shape="box"];1768 -> 2827[label="",style="solid", color="burlywood", weight=9]; 2827 -> 1777[label="",style="solid", color="burlywood", weight=3]; 2828[label="xv198/Zero",fontsize=10,color="white",style="solid",shape="box"];1768 -> 2828[label="",style="solid", color="burlywood", weight=9]; 2828 -> 1778[label="",style="solid", color="burlywood", weight=3]; 1769[label="primModNatS0 Zero xv198 (primGEqNatS Zero xv198)",fontsize=16,color="burlywood",shape="box"];2829[label="xv198/Succ xv1980",fontsize=10,color="white",style="solid",shape="box"];1769 -> 2829[label="",style="solid", color="burlywood", weight=9]; 2829 -> 1779[label="",style="solid", color="burlywood", weight=3]; 2830[label="xv198/Zero",fontsize=10,color="white",style="solid",shape="box"];1769 -> 2830[label="",style="solid", color="burlywood", weight=9]; 2830 -> 1780[label="",style="solid", color="burlywood", weight=3]; 900[label="AProVE_Exception (AET_IOError (IOError IOError_PermDenied [] [] Nothing))",fontsize=16,color="green",shape="box"];1872 -> 1484[label="",style="dashed", color="red", weight=0]; 1872[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1872 -> 1902[label="",style="dashed", color="magenta", weight=3]; 1872 -> 1903[label="",style="dashed", color="magenta", weight=3]; 1873 -> 1484[label="",style="dashed", color="red", weight=0]; 1873[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1873 -> 1904[label="",style="dashed", color="magenta", weight=3]; 1873 -> 1905[label="",style="dashed", color="magenta", weight=3]; 1874 -> 1484[label="",style="dashed", color="red", weight=0]; 1874[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1874 -> 1906[label="",style="dashed", color="magenta", weight=3]; 1874 -> 1907[label="",style="dashed", color="magenta", weight=3]; 1875 -> 1484[label="",style="dashed", color="red", weight=0]; 1875[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1875 -> 1908[label="",style="dashed", color="magenta", weight=3]; 1875 -> 1909[label="",style="dashed", color="magenta", weight=3]; 1876 -> 1484[label="",style="dashed", color="red", weight=0]; 1876[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1876 -> 1910[label="",style="dashed", color="magenta", weight=3]; 1876 -> 1911[label="",style="dashed", color="magenta", weight=3]; 1877[label="showsPrec (Pos Zero) (xv2110 :% xv2111) ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="black",shape="box"];1877 -> 1912[label="",style="solid", color="black", weight=3]; 1878 -> 1484[label="",style="dashed", color="red", weight=0]; 1878[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1878 -> 1913[label="",style="dashed", color="magenta", weight=3]; 1878 -> 1914[label="",style="dashed", color="magenta", weight=3]; 1879 -> 1484[label="",style="dashed", color="red", weight=0]; 1879[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1879 -> 1915[label="",style="dashed", color="magenta", weight=3]; 1879 -> 1916[label="",style="dashed", color="magenta", weight=3]; 1880 -> 1484[label="",style="dashed", color="red", weight=0]; 1880[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1880 -> 1917[label="",style="dashed", color="magenta", weight=3]; 1880 -> 1918[label="",style="dashed", color="magenta", weight=3]; 1881 -> 1484[label="",style="dashed", color="red", weight=0]; 1881[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1881 -> 1919[label="",style="dashed", color="magenta", weight=3]; 1881 -> 1920[label="",style="dashed", color="magenta", weight=3]; 1882 -> 1484[label="",style="dashed", color="red", weight=0]; 1882[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1882 -> 1921[label="",style="dashed", color="magenta", weight=3]; 1882 -> 1922[label="",style="dashed", color="magenta", weight=3]; 1883 -> 1484[label="",style="dashed", color="red", weight=0]; 1883[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1883 -> 1923[label="",style="dashed", color="magenta", weight=3]; 1883 -> 1924[label="",style="dashed", color="magenta", weight=3]; 1884 -> 1484[label="",style="dashed", color="red", weight=0]; 1884[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1884 -> 1925[label="",style="dashed", color="magenta", weight=3]; 1884 -> 1926[label="",style="dashed", color="magenta", weight=3]; 1885 -> 1484[label="",style="dashed", color="red", weight=0]; 1885[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1885 -> 1927[label="",style="dashed", color="magenta", weight=3]; 1885 -> 1928[label="",style="dashed", color="magenta", weight=3]; 1886 -> 1484[label="",style="dashed", color="red", weight=0]; 1886[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1886 -> 1929[label="",style="dashed", color="magenta", weight=3]; 1886 -> 1930[label="",style="dashed", color="magenta", weight=3]; 1887 -> 1484[label="",style="dashed", color="red", weight=0]; 1887[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1887 -> 1931[label="",style="dashed", color="magenta", weight=3]; 1887 -> 1932[label="",style="dashed", color="magenta", weight=3]; 1888 -> 1484[label="",style="dashed", color="red", weight=0]; 1888[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1888 -> 1933[label="",style="dashed", color="magenta", weight=3]; 1888 -> 1934[label="",style="dashed", color="magenta", weight=3]; 1889 -> 1484[label="",style="dashed", color="red", weight=0]; 1889[label="show xv211 ++ (showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1889 -> 1935[label="",style="dashed", color="magenta", weight=3]; 1889 -> 1936[label="",style="dashed", color="magenta", weight=3]; 2472[label="xv1910",fontsize=16,color="green",shape="box"];2473[label="xv1920",fontsize=16,color="green",shape="box"];2474[label="xv1910",fontsize=16,color="green",shape="box"];2475[label="xv1920",fontsize=16,color="green",shape="box"];2471[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS xv261 xv262)",fontsize=16,color="burlywood",shape="triangle"];2831[label="xv261/Succ xv2610",fontsize=10,color="white",style="solid",shape="box"];2471 -> 2831[label="",style="solid", color="burlywood", weight=9]; 2831 -> 2512[label="",style="solid", color="burlywood", weight=3]; 2832[label="xv261/Zero",fontsize=10,color="white",style="solid",shape="box"];2471 -> 2832[label="",style="solid", color="burlywood", weight=9]; 2832 -> 2513[label="",style="solid", color="burlywood", weight=3]; 1764[label="Succ (primDivNatS (primMinusNatS (Succ xv1910) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1764 -> 1774[label="",style="dashed", color="green", weight=3]; 1765[label="Zero",fontsize=16,color="green",shape="box"];1766[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1766 -> 1775[label="",style="dashed", color="green", weight=3]; 1777[label="primModNatS0 (Succ xv1970) (Succ xv1980) (primGEqNatS (Succ xv1970) (Succ xv1980))",fontsize=16,color="black",shape="box"];1777 -> 1788[label="",style="solid", color="black", weight=3]; 1778[label="primModNatS0 (Succ xv1970) Zero (primGEqNatS (Succ xv1970) Zero)",fontsize=16,color="black",shape="box"];1778 -> 1789[label="",style="solid", color="black", weight=3]; 1779[label="primModNatS0 Zero (Succ xv1980) (primGEqNatS Zero (Succ xv1980))",fontsize=16,color="black",shape="box"];1779 -> 1790[label="",style="solid", color="black", weight=3]; 1780[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1780 -> 1791[label="",style="solid", color="black", weight=3]; 1902 -> 646[label="",style="dashed", color="red", weight=0]; 1902[label="show xv211",fontsize=16,color="magenta"];1902 -> 1950[label="",style="dashed", color="magenta", weight=3]; 1903[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="black",shape="triangle"];1903 -> 1951[label="",style="solid", color="black", weight=3]; 1904 -> 647[label="",style="dashed", color="red", weight=0]; 1904[label="show xv211",fontsize=16,color="magenta"];1904 -> 1952[label="",style="dashed", color="magenta", weight=3]; 1905 -> 1903[label="",style="dashed", color="red", weight=0]; 1905[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1906 -> 648[label="",style="dashed", color="red", weight=0]; 1906[label="show xv211",fontsize=16,color="magenta"];1906 -> 1953[label="",style="dashed", color="magenta", weight=3]; 1907 -> 1903[label="",style="dashed", color="red", weight=0]; 1907[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1908 -> 649[label="",style="dashed", color="red", weight=0]; 1908[label="show xv211",fontsize=16,color="magenta"];1908 -> 1954[label="",style="dashed", color="magenta", weight=3]; 1909 -> 1903[label="",style="dashed", color="red", weight=0]; 1909[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1910 -> 650[label="",style="dashed", color="red", weight=0]; 1910[label="show xv211",fontsize=16,color="magenta"];1910 -> 1955[label="",style="dashed", color="magenta", weight=3]; 1911 -> 1903[label="",style="dashed", color="red", weight=0]; 1911[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1912 -> 1735[label="",style="dashed", color="red", weight=0]; 1912[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows xv2110) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows xv2111) ((showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215)",fontsize=16,color="magenta"];1912 -> 1956[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1957[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1958[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1959[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1960[label="",style="dashed", color="magenta", weight=3]; 1912 -> 1961[label="",style="dashed", color="magenta", weight=3]; 1913 -> 652[label="",style="dashed", color="red", weight=0]; 1913[label="show xv211",fontsize=16,color="magenta"];1913 -> 1962[label="",style="dashed", color="magenta", weight=3]; 1914 -> 1903[label="",style="dashed", color="red", weight=0]; 1914[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1915 -> 653[label="",style="dashed", color="red", weight=0]; 1915[label="show xv211",fontsize=16,color="magenta"];1915 -> 1963[label="",style="dashed", color="magenta", weight=3]; 1916 -> 1903[label="",style="dashed", color="red", weight=0]; 1916[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1917 -> 654[label="",style="dashed", color="red", weight=0]; 1917[label="show xv211",fontsize=16,color="magenta"];1917 -> 1964[label="",style="dashed", color="magenta", weight=3]; 1918 -> 1903[label="",style="dashed", color="red", weight=0]; 1918[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1919 -> 655[label="",style="dashed", color="red", weight=0]; 1919[label="show xv211",fontsize=16,color="magenta"];1919 -> 1965[label="",style="dashed", color="magenta", weight=3]; 1920 -> 1903[label="",style="dashed", color="red", weight=0]; 1920[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1921 -> 656[label="",style="dashed", color="red", weight=0]; 1921[label="show xv211",fontsize=16,color="magenta"];1921 -> 1966[label="",style="dashed", color="magenta", weight=3]; 1922 -> 1903[label="",style="dashed", color="red", weight=0]; 1922[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1923 -> 657[label="",style="dashed", color="red", weight=0]; 1923[label="show xv211",fontsize=16,color="magenta"];1923 -> 1967[label="",style="dashed", color="magenta", weight=3]; 1924 -> 1903[label="",style="dashed", color="red", weight=0]; 1924[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1925 -> 658[label="",style="dashed", color="red", weight=0]; 1925[label="show xv211",fontsize=16,color="magenta"];1925 -> 1968[label="",style="dashed", color="magenta", weight=3]; 1926 -> 1903[label="",style="dashed", color="red", weight=0]; 1926[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1927 -> 659[label="",style="dashed", color="red", weight=0]; 1927[label="show xv211",fontsize=16,color="magenta"];1927 -> 1969[label="",style="dashed", color="magenta", weight=3]; 1928 -> 1903[label="",style="dashed", color="red", weight=0]; 1928[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1929 -> 660[label="",style="dashed", color="red", weight=0]; 1929[label="show xv211",fontsize=16,color="magenta"];1929 -> 1970[label="",style="dashed", color="magenta", weight=3]; 1930 -> 1903[label="",style="dashed", color="red", weight=0]; 1930[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1931 -> 661[label="",style="dashed", color="red", weight=0]; 1931[label="show xv211",fontsize=16,color="magenta"];1931 -> 1971[label="",style="dashed", color="magenta", weight=3]; 1932 -> 1903[label="",style="dashed", color="red", weight=0]; 1932[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1933 -> 662[label="",style="dashed", color="red", weight=0]; 1933[label="show xv211",fontsize=16,color="magenta"];1933 -> 1972[label="",style="dashed", color="magenta", weight=3]; 1934 -> 1903[label="",style="dashed", color="red", weight=0]; 1934[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1935 -> 663[label="",style="dashed", color="red", weight=0]; 1935[label="show xv211",fontsize=16,color="magenta"];1935 -> 1973[label="",style="dashed", color="magenta", weight=3]; 1936 -> 1903[label="",style="dashed", color="red", weight=0]; 1936[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];2512[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS (Succ xv2610) xv262)",fontsize=16,color="burlywood",shape="box"];2833[label="xv262/Succ xv2620",fontsize=10,color="white",style="solid",shape="box"];2512 -> 2833[label="",style="solid", color="burlywood", weight=9]; 2833 -> 2524[label="",style="solid", color="burlywood", weight=3]; 2834[label="xv262/Zero",fontsize=10,color="white",style="solid",shape="box"];2512 -> 2834[label="",style="solid", color="burlywood", weight=9]; 2834 -> 2525[label="",style="solid", color="burlywood", weight=3]; 2513[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS Zero xv262)",fontsize=16,color="burlywood",shape="box"];2835[label="xv262/Succ xv2620",fontsize=10,color="white",style="solid",shape="box"];2513 -> 2835[label="",style="solid", color="burlywood", weight=9]; 2835 -> 2526[label="",style="solid", color="burlywood", weight=3]; 2836[label="xv262/Zero",fontsize=10,color="white",style="solid",shape="box"];2513 -> 2836[label="",style="solid", color="burlywood", weight=9]; 2836 -> 2527[label="",style="solid", color="burlywood", weight=3]; 1774 -> 2725[label="",style="dashed", color="red", weight=0]; 1774[label="primDivNatS (primMinusNatS (Succ xv1910) Zero) (Succ Zero)",fontsize=16,color="magenta"];1774 -> 2726[label="",style="dashed", color="magenta", weight=3]; 1774 -> 2727[label="",style="dashed", color="magenta", weight=3]; 1774 -> 2728[label="",style="dashed", color="magenta", weight=3]; 1775 -> 2725[label="",style="dashed", color="red", weight=0]; 1775[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1775 -> 2729[label="",style="dashed", color="magenta", weight=3]; 1775 -> 2730[label="",style="dashed", color="magenta", weight=3]; 1775 -> 2731[label="",style="dashed", color="magenta", weight=3]; 1788 -> 2546[label="",style="dashed", color="red", weight=0]; 1788[label="primModNatS0 (Succ xv1970) (Succ xv1980) (primGEqNatS xv1970 xv1980)",fontsize=16,color="magenta"];1788 -> 2547[label="",style="dashed", color="magenta", weight=3]; 1788 -> 2548[label="",style="dashed", color="magenta", weight=3]; 1788 -> 2549[label="",style="dashed", color="magenta", weight=3]; 1788 -> 2550[label="",style="dashed", color="magenta", weight=3]; 1789[label="primModNatS0 (Succ xv1970) Zero True",fontsize=16,color="black",shape="box"];1789 -> 1803[label="",style="solid", color="black", weight=3]; 1790[label="primModNatS0 Zero (Succ xv1980) False",fontsize=16,color="black",shape="box"];1790 -> 1804[label="",style="solid", color="black", weight=3]; 1791[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];1791 -> 1805[label="",style="solid", color="black", weight=3]; 1950[label="xv211",fontsize=16,color="green",shape="box"];1951[label="showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : []) (shows xv215 xv216)",fontsize=16,color="black",shape="box"];1951 -> 1990[label="",style="solid", color="black", weight=3]; 1952[label="xv211",fontsize=16,color="green",shape="box"];1953[label="xv211",fontsize=16,color="green",shape="box"];1954[label="xv211",fontsize=16,color="green",shape="box"];1955[label="xv211",fontsize=16,color="green",shape="box"];1956[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1957[label="xv2111",fontsize=16,color="green",shape="box"];1958[label="xv2110",fontsize=16,color="green",shape="box"];1959[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1960[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1961 -> 1903[label="",style="dashed", color="red", weight=0]; 1961[label="(showString (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : [])) . shows xv215",fontsize=16,color="magenta"];1962[label="xv211",fontsize=16,color="green",shape="box"];1963[label="xv211",fontsize=16,color="green",shape="box"];1964[label="xv211",fontsize=16,color="green",shape="box"];1965[label="xv211",fontsize=16,color="green",shape="box"];1966[label="xv211",fontsize=16,color="green",shape="box"];1967[label="xv211",fontsize=16,color="green",shape="box"];1968[label="xv211",fontsize=16,color="green",shape="box"];1969[label="xv211",fontsize=16,color="green",shape="box"];1970[label="xv211",fontsize=16,color="green",shape="box"];1971[label="xv211",fontsize=16,color="green",shape="box"];1972[label="xv211",fontsize=16,color="green",shape="box"];1973[label="xv211",fontsize=16,color="green",shape="box"];2524[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS (Succ xv2610) (Succ xv2620))",fontsize=16,color="black",shape="box"];2524 -> 2538[label="",style="solid", color="black", weight=3]; 2525[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS (Succ xv2610) Zero)",fontsize=16,color="black",shape="box"];2525 -> 2539[label="",style="solid", color="black", weight=3]; 2526[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS Zero (Succ xv2620))",fontsize=16,color="black",shape="box"];2526 -> 2540[label="",style="solid", color="black", weight=3]; 2527[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2527 -> 2541[label="",style="solid", color="black", weight=3]; 2726[label="Zero",fontsize=16,color="green",shape="box"];2727[label="Succ xv1910",fontsize=16,color="green",shape="box"];2728[label="Zero",fontsize=16,color="green",shape="box"];2725[label="primDivNatS (primMinusNatS xv273 xv274) (Succ xv275)",fontsize=16,color="burlywood",shape="triangle"];2837[label="xv273/Succ xv2730",fontsize=10,color="white",style="solid",shape="box"];2725 -> 2837[label="",style="solid", color="burlywood", weight=9]; 2837 -> 2750[label="",style="solid", color="burlywood", weight=3]; 2838[label="xv273/Zero",fontsize=10,color="white",style="solid",shape="box"];2725 -> 2838[label="",style="solid", color="burlywood", weight=9]; 2838 -> 2751[label="",style="solid", color="burlywood", weight=3]; 2729[label="Zero",fontsize=16,color="green",shape="box"];2730[label="Zero",fontsize=16,color="green",shape="box"];2731[label="Zero",fontsize=16,color="green",shape="box"];2547[label="xv1970",fontsize=16,color="green",shape="box"];2548[label="xv1980",fontsize=16,color="green",shape="box"];2549[label="xv1980",fontsize=16,color="green",shape="box"];2550[label="xv1970",fontsize=16,color="green",shape="box"];2546[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS xv266 xv267)",fontsize=16,color="burlywood",shape="triangle"];2839[label="xv266/Succ xv2660",fontsize=10,color="white",style="solid",shape="box"];2546 -> 2839[label="",style="solid", color="burlywood", weight=9]; 2839 -> 2587[label="",style="solid", color="burlywood", weight=3]; 2840[label="xv266/Zero",fontsize=10,color="white",style="solid",shape="box"];2546 -> 2840[label="",style="solid", color="burlywood", weight=9]; 2840 -> 2588[label="",style="solid", color="burlywood", weight=3]; 1803 -> 2633[label="",style="dashed", color="red", weight=0]; 1803[label="primModNatS (primMinusNatS (Succ xv1970) Zero) (Succ Zero)",fontsize=16,color="magenta"];1803 -> 2634[label="",style="dashed", color="magenta", weight=3]; 1803 -> 2635[label="",style="dashed", color="magenta", weight=3]; 1803 -> 2636[label="",style="dashed", color="magenta", weight=3]; 1804[label="Succ Zero",fontsize=16,color="green",shape="box"];1805 -> 2633[label="",style="dashed", color="red", weight=0]; 1805[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1805 -> 2637[label="",style="dashed", color="magenta", weight=3]; 1805 -> 2638[label="",style="dashed", color="magenta", weight=3]; 1805 -> 2639[label="",style="dashed", color="magenta", weight=3]; 1990 -> 1484[label="",style="dashed", color="red", weight=0]; 1990[label="(++) (Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : []) shows xv215 xv216",fontsize=16,color="magenta"];1990 -> 2006[label="",style="dashed", color="magenta", weight=3]; 1990 -> 2007[label="",style="dashed", color="magenta", weight=3]; 2538 -> 2471[label="",style="dashed", color="red", weight=0]; 2538[label="primDivNatS0 (Succ xv259) (Succ xv260) (primGEqNatS xv2610 xv2620)",fontsize=16,color="magenta"];2538 -> 2589[label="",style="dashed", color="magenta", weight=3]; 2538 -> 2590[label="",style="dashed", color="magenta", weight=3]; 2539[label="primDivNatS0 (Succ xv259) (Succ xv260) True",fontsize=16,color="black",shape="triangle"];2539 -> 2591[label="",style="solid", color="black", weight=3]; 2540[label="primDivNatS0 (Succ xv259) (Succ xv260) False",fontsize=16,color="black",shape="box"];2540 -> 2592[label="",style="solid", color="black", weight=3]; 2541 -> 2539[label="",style="dashed", color="red", weight=0]; 2541[label="primDivNatS0 (Succ xv259) (Succ xv260) True",fontsize=16,color="magenta"];2750[label="primDivNatS (primMinusNatS (Succ xv2730) xv274) (Succ xv275)",fontsize=16,color="burlywood",shape="box"];2841[label="xv274/Succ xv2740",fontsize=10,color="white",style="solid",shape="box"];2750 -> 2841[label="",style="solid", color="burlywood", weight=9]; 2841 -> 2752[label="",style="solid", color="burlywood", weight=3]; 2842[label="xv274/Zero",fontsize=10,color="white",style="solid",shape="box"];2750 -> 2842[label="",style="solid", color="burlywood", weight=9]; 2842 -> 2753[label="",style="solid", color="burlywood", weight=3]; 2751[label="primDivNatS (primMinusNatS Zero xv274) (Succ xv275)",fontsize=16,color="burlywood",shape="box"];2843[label="xv274/Succ xv2740",fontsize=10,color="white",style="solid",shape="box"];2751 -> 2843[label="",style="solid", color="burlywood", weight=9]; 2843 -> 2754[label="",style="solid", color="burlywood", weight=3]; 2844[label="xv274/Zero",fontsize=10,color="white",style="solid",shape="box"];2751 -> 2844[label="",style="solid", color="burlywood", weight=9]; 2844 -> 2755[label="",style="solid", color="burlywood", weight=3]; 2587[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS (Succ xv2660) xv267)",fontsize=16,color="burlywood",shape="box"];2845[label="xv267/Succ xv2670",fontsize=10,color="white",style="solid",shape="box"];2587 -> 2845[label="",style="solid", color="burlywood", weight=9]; 2845 -> 2597[label="",style="solid", color="burlywood", weight=3]; 2846[label="xv267/Zero",fontsize=10,color="white",style="solid",shape="box"];2587 -> 2846[label="",style="solid", color="burlywood", weight=9]; 2846 -> 2598[label="",style="solid", color="burlywood", weight=3]; 2588[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS Zero xv267)",fontsize=16,color="burlywood",shape="box"];2847[label="xv267/Succ xv2670",fontsize=10,color="white",style="solid",shape="box"];2588 -> 2847[label="",style="solid", color="burlywood", weight=9]; 2847 -> 2599[label="",style="solid", color="burlywood", weight=3]; 2848[label="xv267/Zero",fontsize=10,color="white",style="solid",shape="box"];2588 -> 2848[label="",style="solid", color="burlywood", weight=9]; 2848 -> 2600[label="",style="solid", color="burlywood", weight=3]; 2634[label="Zero",fontsize=16,color="green",shape="box"];2635[label="Zero",fontsize=16,color="green",shape="box"];2636[label="Succ xv1970",fontsize=16,color="green",shape="box"];2633[label="primModNatS (primMinusNatS xv269 xv270) (Succ xv271)",fontsize=16,color="burlywood",shape="triangle"];2849[label="xv269/Succ xv2690",fontsize=10,color="white",style="solid",shape="box"];2633 -> 2849[label="",style="solid", color="burlywood", weight=9]; 2849 -> 2664[label="",style="solid", color="burlywood", weight=3]; 2850[label="xv269/Zero",fontsize=10,color="white",style="solid",shape="box"];2633 -> 2850[label="",style="solid", color="burlywood", weight=9]; 2850 -> 2665[label="",style="solid", color="burlywood", weight=3]; 2637[label="Zero",fontsize=16,color="green",shape="box"];2638[label="Zero",fontsize=16,color="green",shape="box"];2639[label="Zero",fontsize=16,color="green",shape="box"];2006[label="Char (Succ xv212) : Char (Succ xv213) : Char (Succ xv214) : []",fontsize=16,color="green",shape="box"];2007[label="shows xv215 xv216",fontsize=16,color="black",shape="box"];2007 -> 2021[label="",style="solid", color="black", weight=3]; 2589[label="xv2610",fontsize=16,color="green",shape="box"];2590[label="xv2620",fontsize=16,color="green",shape="box"];2591[label="Succ (primDivNatS (primMinusNatS (Succ xv259) (Succ xv260)) (Succ (Succ xv260)))",fontsize=16,color="green",shape="box"];2591 -> 2601[label="",style="dashed", color="green", weight=3]; 2592[label="Zero",fontsize=16,color="green",shape="box"];2752[label="primDivNatS (primMinusNatS (Succ xv2730) (Succ xv2740)) (Succ xv275)",fontsize=16,color="black",shape="box"];2752 -> 2756[label="",style="solid", color="black", weight=3]; 2753[label="primDivNatS (primMinusNatS (Succ xv2730) Zero) (Succ xv275)",fontsize=16,color="black",shape="box"];2753 -> 2757[label="",style="solid", color="black", weight=3]; 2754[label="primDivNatS (primMinusNatS Zero (Succ xv2740)) (Succ xv275)",fontsize=16,color="black",shape="box"];2754 -> 2758[label="",style="solid", color="black", weight=3]; 2755[label="primDivNatS (primMinusNatS Zero Zero) (Succ xv275)",fontsize=16,color="black",shape="box"];2755 -> 2759[label="",style="solid", color="black", weight=3]; 2597[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS (Succ xv2660) (Succ xv2670))",fontsize=16,color="black",shape="box"];2597 -> 2608[label="",style="solid", color="black", weight=3]; 2598[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS (Succ xv2660) Zero)",fontsize=16,color="black",shape="box"];2598 -> 2609[label="",style="solid", color="black", weight=3]; 2599[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS Zero (Succ xv2670))",fontsize=16,color="black",shape="box"];2599 -> 2610[label="",style="solid", color="black", weight=3]; 2600[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2600 -> 2611[label="",style="solid", color="black", weight=3]; 2664[label="primModNatS (primMinusNatS (Succ xv2690) xv270) (Succ xv271)",fontsize=16,color="burlywood",shape="box"];2851[label="xv270/Succ xv2700",fontsize=10,color="white",style="solid",shape="box"];2664 -> 2851[label="",style="solid", color="burlywood", weight=9]; 2851 -> 2670[label="",style="solid", color="burlywood", weight=3]; 2852[label="xv270/Zero",fontsize=10,color="white",style="solid",shape="box"];2664 -> 2852[label="",style="solid", color="burlywood", weight=9]; 2852 -> 2671[label="",style="solid", color="burlywood", weight=3]; 2665[label="primModNatS (primMinusNatS Zero xv270) (Succ xv271)",fontsize=16,color="burlywood",shape="box"];2853[label="xv270/Succ xv2700",fontsize=10,color="white",style="solid",shape="box"];2665 -> 2853[label="",style="solid", color="burlywood", weight=9]; 2853 -> 2672[label="",style="solid", color="burlywood", weight=3]; 2854[label="xv270/Zero",fontsize=10,color="white",style="solid",shape="box"];2665 -> 2854[label="",style="solid", color="burlywood", weight=9]; 2854 -> 2673[label="",style="solid", color="burlywood", weight=3]; 2021[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="blue",shape="box"];2855[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2855[label="",style="solid", color="blue", weight=9]; 2855 -> 2037[label="",style="solid", color="blue", weight=3]; 2856[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2856[label="",style="solid", color="blue", weight=9]; 2856 -> 2038[label="",style="solid", color="blue", weight=3]; 2857[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2857[label="",style="solid", color="blue", weight=9]; 2857 -> 2039[label="",style="solid", color="blue", weight=3]; 2858[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2858[label="",style="solid", color="blue", weight=9]; 2858 -> 2040[label="",style="solid", color="blue", weight=3]; 2859[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2859[label="",style="solid", color="blue", weight=9]; 2859 -> 2041[label="",style="solid", color="blue", weight=3]; 2860[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2860[label="",style="solid", color="blue", weight=9]; 2860 -> 2042[label="",style="solid", color="blue", weight=3]; 2861[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2861[label="",style="solid", color="blue", weight=9]; 2861 -> 2043[label="",style="solid", color="blue", weight=3]; 2862[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2862[label="",style="solid", color="blue", weight=9]; 2862 -> 2044[label="",style="solid", color="blue", weight=3]; 2863[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2863[label="",style="solid", color="blue", weight=9]; 2863 -> 2045[label="",style="solid", color="blue", weight=3]; 2864[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2864[label="",style="solid", color="blue", weight=9]; 2864 -> 2046[label="",style="solid", color="blue", weight=3]; 2865[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2865[label="",style="solid", color="blue", weight=9]; 2865 -> 2047[label="",style="solid", color="blue", weight=3]; 2866[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2866[label="",style="solid", color="blue", weight=9]; 2866 -> 2048[label="",style="solid", color="blue", weight=3]; 2867[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2867[label="",style="solid", color="blue", weight=9]; 2867 -> 2049[label="",style="solid", color="blue", weight=3]; 2868[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2868[label="",style="solid", color="blue", weight=9]; 2868 -> 2050[label="",style="solid", color="blue", weight=3]; 2869[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2869[label="",style="solid", color="blue", weight=9]; 2869 -> 2051[label="",style="solid", color="blue", weight=3]; 2870[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2870[label="",style="solid", color="blue", weight=9]; 2870 -> 2052[label="",style="solid", color="blue", weight=3]; 2871[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2871[label="",style="solid", color="blue", weight=9]; 2871 -> 2053[label="",style="solid", color="blue", weight=3]; 2872[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];2021 -> 2872[label="",style="solid", color="blue", weight=9]; 2872 -> 2054[label="",style="solid", color="blue", weight=3]; 2601 -> 2725[label="",style="dashed", color="red", weight=0]; 2601[label="primDivNatS (primMinusNatS (Succ xv259) (Succ xv260)) (Succ (Succ xv260))",fontsize=16,color="magenta"];2601 -> 2732[label="",style="dashed", color="magenta", weight=3]; 2601 -> 2733[label="",style="dashed", color="magenta", weight=3]; 2601 -> 2734[label="",style="dashed", color="magenta", weight=3]; 2756 -> 2725[label="",style="dashed", color="red", weight=0]; 2756[label="primDivNatS (primMinusNatS xv2730 xv2740) (Succ xv275)",fontsize=16,color="magenta"];2756 -> 2760[label="",style="dashed", color="magenta", weight=3]; 2756 -> 2761[label="",style="dashed", color="magenta", weight=3]; 2757 -> 1679[label="",style="dashed", color="red", weight=0]; 2757[label="primDivNatS (Succ xv2730) (Succ xv275)",fontsize=16,color="magenta"];2757 -> 2762[label="",style="dashed", color="magenta", weight=3]; 2757 -> 2763[label="",style="dashed", color="magenta", weight=3]; 2758[label="primDivNatS Zero (Succ xv275)",fontsize=16,color="black",shape="triangle"];2758 -> 2764[label="",style="solid", color="black", weight=3]; 2759 -> 2758[label="",style="dashed", color="red", weight=0]; 2759[label="primDivNatS Zero (Succ xv275)",fontsize=16,color="magenta"];2608 -> 2546[label="",style="dashed", color="red", weight=0]; 2608[label="primModNatS0 (Succ xv264) (Succ xv265) (primGEqNatS xv2660 xv2670)",fontsize=16,color="magenta"];2608 -> 2617[label="",style="dashed", color="magenta", weight=3]; 2608 -> 2618[label="",style="dashed", color="magenta", weight=3]; 2609[label="primModNatS0 (Succ xv264) (Succ xv265) True",fontsize=16,color="black",shape="triangle"];2609 -> 2619[label="",style="solid", color="black", weight=3]; 2610[label="primModNatS0 (Succ xv264) (Succ xv265) False",fontsize=16,color="black",shape="box"];2610 -> 2620[label="",style="solid", color="black", weight=3]; 2611 -> 2609[label="",style="dashed", color="red", weight=0]; 2611[label="primModNatS0 (Succ xv264) (Succ xv265) True",fontsize=16,color="magenta"];2670[label="primModNatS (primMinusNatS (Succ xv2690) (Succ xv2700)) (Succ xv271)",fontsize=16,color="black",shape="box"];2670 -> 2680[label="",style="solid", color="black", weight=3]; 2671[label="primModNatS (primMinusNatS (Succ xv2690) Zero) (Succ xv271)",fontsize=16,color="black",shape="box"];2671 -> 2681[label="",style="solid", color="black", weight=3]; 2672[label="primModNatS (primMinusNatS Zero (Succ xv2700)) (Succ xv271)",fontsize=16,color="black",shape="box"];2672 -> 2682[label="",style="solid", color="black", weight=3]; 2673[label="primModNatS (primMinusNatS Zero Zero) (Succ xv271)",fontsize=16,color="black",shape="box"];2673 -> 2683[label="",style="solid", color="black", weight=3]; 2037[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2037 -> 2072[label="",style="solid", color="black", weight=3]; 2038[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2038 -> 2073[label="",style="solid", color="black", weight=3]; 2039[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2039 -> 2074[label="",style="solid", color="black", weight=3]; 2040[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2040 -> 2075[label="",style="solid", color="black", weight=3]; 2041[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2041 -> 2076[label="",style="solid", color="black", weight=3]; 2042[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="burlywood",shape="box"];2873[label="xv215/xv2150 :% xv2151",fontsize=10,color="white",style="solid",shape="box"];2042 -> 2873[label="",style="solid", color="burlywood", weight=9]; 2873 -> 2077[label="",style="solid", color="burlywood", weight=3]; 2043[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2043 -> 2078[label="",style="solid", color="black", weight=3]; 2044[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2044 -> 2079[label="",style="solid", color="black", weight=3]; 2045[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2045 -> 2080[label="",style="solid", color="black", weight=3]; 2046[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2046 -> 2081[label="",style="solid", color="black", weight=3]; 2047[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2047 -> 2082[label="",style="solid", color="black", weight=3]; 2048[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2048 -> 2083[label="",style="solid", color="black", weight=3]; 2049[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2049 -> 2084[label="",style="solid", color="black", weight=3]; 2050[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2050 -> 2085[label="",style="solid", color="black", weight=3]; 2051[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2051 -> 2086[label="",style="solid", color="black", weight=3]; 2052[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2052 -> 2087[label="",style="solid", color="black", weight=3]; 2053[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2053 -> 2088[label="",style="solid", color="black", weight=3]; 2054[label="showsPrec (Pos Zero) xv215 xv216",fontsize=16,color="black",shape="box"];2054 -> 2089[label="",style="solid", color="black", weight=3]; 2732[label="Succ xv260",fontsize=16,color="green",shape="box"];2733[label="Succ xv259",fontsize=16,color="green",shape="box"];2734[label="Succ xv260",fontsize=16,color="green",shape="box"];2760[label="xv2730",fontsize=16,color="green",shape="box"];2761[label="xv2740",fontsize=16,color="green",shape="box"];2762[label="xv2730",fontsize=16,color="green",shape="box"];2763[label="xv275",fontsize=16,color="green",shape="box"];2764[label="Zero",fontsize=16,color="green",shape="box"];2617[label="xv2660",fontsize=16,color="green",shape="box"];2618[label="xv2670",fontsize=16,color="green",shape="box"];2619 -> 2633[label="",style="dashed", color="red", weight=0]; 2619[label="primModNatS (primMinusNatS (Succ xv264) (Succ xv265)) (Succ (Succ xv265))",fontsize=16,color="magenta"];2619 -> 2646[label="",style="dashed", color="magenta", weight=3]; 2619 -> 2647[label="",style="dashed", color="magenta", weight=3]; 2619 -> 2648[label="",style="dashed", color="magenta", weight=3]; 2620[label="Succ (Succ xv264)",fontsize=16,color="green",shape="box"];2680 -> 2633[label="",style="dashed", color="red", weight=0]; 2680[label="primModNatS (primMinusNatS xv2690 xv2700) (Succ xv271)",fontsize=16,color="magenta"];2680 -> 2688[label="",style="dashed", color="magenta", weight=3]; 2680 -> 2689[label="",style="dashed", color="magenta", weight=3]; 2681 -> 1755[label="",style="dashed", color="red", weight=0]; 2681[label="primModNatS (Succ xv2690) (Succ xv271)",fontsize=16,color="magenta"];2681 -> 2690[label="",style="dashed", color="magenta", weight=3]; 2681 -> 2691[label="",style="dashed", color="magenta", weight=3]; 2682[label="primModNatS Zero (Succ xv271)",fontsize=16,color="black",shape="triangle"];2682 -> 2692[label="",style="solid", color="black", weight=3]; 2683 -> 2682[label="",style="dashed", color="red", weight=0]; 2683[label="primModNatS Zero (Succ xv271)",fontsize=16,color="magenta"];2072 -> 1484[label="",style="dashed", color="red", weight=0]; 2072[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2072 -> 2100[label="",style="dashed", color="magenta", weight=3]; 2072 -> 2101[label="",style="dashed", color="magenta", weight=3]; 2073 -> 1484[label="",style="dashed", color="red", weight=0]; 2073[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2073 -> 2102[label="",style="dashed", color="magenta", weight=3]; 2073 -> 2103[label="",style="dashed", color="magenta", weight=3]; 2074 -> 1484[label="",style="dashed", color="red", weight=0]; 2074[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2074 -> 2104[label="",style="dashed", color="magenta", weight=3]; 2074 -> 2105[label="",style="dashed", color="magenta", weight=3]; 2075 -> 1484[label="",style="dashed", color="red", weight=0]; 2075[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2075 -> 2106[label="",style="dashed", color="magenta", weight=3]; 2075 -> 2107[label="",style="dashed", color="magenta", weight=3]; 2076 -> 1484[label="",style="dashed", color="red", weight=0]; 2076[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2076 -> 2108[label="",style="dashed", color="magenta", weight=3]; 2076 -> 2109[label="",style="dashed", color="magenta", weight=3]; 2077[label="showsPrec (Pos Zero) (xv2150 :% xv2151) xv216",fontsize=16,color="black",shape="box"];2077 -> 2110[label="",style="solid", color="black", weight=3]; 2078 -> 1484[label="",style="dashed", color="red", weight=0]; 2078[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2078 -> 2111[label="",style="dashed", color="magenta", weight=3]; 2078 -> 2112[label="",style="dashed", color="magenta", weight=3]; 2079 -> 1484[label="",style="dashed", color="red", weight=0]; 2079[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2079 -> 2113[label="",style="dashed", color="magenta", weight=3]; 2079 -> 2114[label="",style="dashed", color="magenta", weight=3]; 2080 -> 1484[label="",style="dashed", color="red", weight=0]; 2080[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2080 -> 2115[label="",style="dashed", color="magenta", weight=3]; 2080 -> 2116[label="",style="dashed", color="magenta", weight=3]; 2081 -> 1484[label="",style="dashed", color="red", weight=0]; 2081[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2081 -> 2117[label="",style="dashed", color="magenta", weight=3]; 2081 -> 2118[label="",style="dashed", color="magenta", weight=3]; 2082 -> 1484[label="",style="dashed", color="red", weight=0]; 2082[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2082 -> 2119[label="",style="dashed", color="magenta", weight=3]; 2082 -> 2120[label="",style="dashed", color="magenta", weight=3]; 2083 -> 1484[label="",style="dashed", color="red", weight=0]; 2083[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2083 -> 2121[label="",style="dashed", color="magenta", weight=3]; 2083 -> 2122[label="",style="dashed", color="magenta", weight=3]; 2084 -> 1484[label="",style="dashed", color="red", weight=0]; 2084[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2084 -> 2123[label="",style="dashed", color="magenta", weight=3]; 2084 -> 2124[label="",style="dashed", color="magenta", weight=3]; 2085 -> 1484[label="",style="dashed", color="red", weight=0]; 2085[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2085 -> 2125[label="",style="dashed", color="magenta", weight=3]; 2085 -> 2126[label="",style="dashed", color="magenta", weight=3]; 2086 -> 1484[label="",style="dashed", color="red", weight=0]; 2086[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2086 -> 2127[label="",style="dashed", color="magenta", weight=3]; 2086 -> 2128[label="",style="dashed", color="magenta", weight=3]; 2087 -> 1484[label="",style="dashed", color="red", weight=0]; 2087[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2087 -> 2129[label="",style="dashed", color="magenta", weight=3]; 2087 -> 2130[label="",style="dashed", color="magenta", weight=3]; 2088 -> 1484[label="",style="dashed", color="red", weight=0]; 2088[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2088 -> 2131[label="",style="dashed", color="magenta", weight=3]; 2088 -> 2132[label="",style="dashed", color="magenta", weight=3]; 2089 -> 1484[label="",style="dashed", color="red", weight=0]; 2089[label="show xv215 ++ xv216",fontsize=16,color="magenta"];2089 -> 2133[label="",style="dashed", color="magenta", weight=3]; 2089 -> 2134[label="",style="dashed", color="magenta", weight=3]; 2646[label="Succ xv265",fontsize=16,color="green",shape="box"];2647[label="Succ xv265",fontsize=16,color="green",shape="box"];2648[label="Succ xv264",fontsize=16,color="green",shape="box"];2688[label="xv2700",fontsize=16,color="green",shape="box"];2689[label="xv2690",fontsize=16,color="green",shape="box"];2690[label="xv271",fontsize=16,color="green",shape="box"];2691[label="xv2690",fontsize=16,color="green",shape="box"];2692[label="Zero",fontsize=16,color="green",shape="box"];2100 -> 646[label="",style="dashed", color="red", weight=0]; 2100[label="show xv215",fontsize=16,color="magenta"];2100 -> 2145[label="",style="dashed", color="magenta", weight=3]; 2101[label="xv216",fontsize=16,color="green",shape="box"];2102 -> 647[label="",style="dashed", color="red", weight=0]; 2102[label="show xv215",fontsize=16,color="magenta"];2102 -> 2146[label="",style="dashed", color="magenta", weight=3]; 2103[label="xv216",fontsize=16,color="green",shape="box"];2104 -> 648[label="",style="dashed", color="red", weight=0]; 2104[label="show xv215",fontsize=16,color="magenta"];2104 -> 2147[label="",style="dashed", color="magenta", weight=3]; 2105[label="xv216",fontsize=16,color="green",shape="box"];2106 -> 649[label="",style="dashed", color="red", weight=0]; 2106[label="show xv215",fontsize=16,color="magenta"];2106 -> 2148[label="",style="dashed", color="magenta", weight=3]; 2107[label="xv216",fontsize=16,color="green",shape="box"];2108 -> 650[label="",style="dashed", color="red", weight=0]; 2108[label="show xv215",fontsize=16,color="magenta"];2108 -> 2149[label="",style="dashed", color="magenta", weight=3]; 2109[label="xv216",fontsize=16,color="green",shape="box"];2110 -> 1735[label="",style="dashed", color="red", weight=0]; 2110[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows xv2150) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows xv2151) xv216",fontsize=16,color="magenta"];2110 -> 2150[label="",style="dashed", color="magenta", weight=3]; 2110 -> 2151[label="",style="dashed", color="magenta", weight=3]; 2110 -> 2152[label="",style="dashed", color="magenta", weight=3]; 2110 -> 2153[label="",style="dashed", color="magenta", weight=3]; 2110 -> 2154[label="",style="dashed", color="magenta", weight=3]; 2111 -> 652[label="",style="dashed", color="red", weight=0]; 2111[label="show xv215",fontsize=16,color="magenta"];2111 -> 2155[label="",style="dashed", color="magenta", weight=3]; 2112[label="xv216",fontsize=16,color="green",shape="box"];2113 -> 653[label="",style="dashed", color="red", weight=0]; 2113[label="show xv215",fontsize=16,color="magenta"];2113 -> 2156[label="",style="dashed", color="magenta", weight=3]; 2114[label="xv216",fontsize=16,color="green",shape="box"];2115 -> 654[label="",style="dashed", color="red", weight=0]; 2115[label="show xv215",fontsize=16,color="magenta"];2115 -> 2157[label="",style="dashed", color="magenta", weight=3]; 2116[label="xv216",fontsize=16,color="green",shape="box"];2117 -> 655[label="",style="dashed", color="red", weight=0]; 2117[label="show xv215",fontsize=16,color="magenta"];2117 -> 2158[label="",style="dashed", color="magenta", weight=3]; 2118[label="xv216",fontsize=16,color="green",shape="box"];2119 -> 656[label="",style="dashed", color="red", weight=0]; 2119[label="show xv215",fontsize=16,color="magenta"];2119 -> 2159[label="",style="dashed", color="magenta", weight=3]; 2120[label="xv216",fontsize=16,color="green",shape="box"];2121 -> 657[label="",style="dashed", color="red", weight=0]; 2121[label="show xv215",fontsize=16,color="magenta"];2121 -> 2160[label="",style="dashed", color="magenta", weight=3]; 2122[label="xv216",fontsize=16,color="green",shape="box"];2123 -> 658[label="",style="dashed", color="red", weight=0]; 2123[label="show xv215",fontsize=16,color="magenta"];2123 -> 2161[label="",style="dashed", color="magenta", weight=3]; 2124[label="xv216",fontsize=16,color="green",shape="box"];2125 -> 659[label="",style="dashed", color="red", weight=0]; 2125[label="show xv215",fontsize=16,color="magenta"];2125 -> 2162[label="",style="dashed", color="magenta", weight=3]; 2126[label="xv216",fontsize=16,color="green",shape="box"];2127 -> 660[label="",style="dashed", color="red", weight=0]; 2127[label="show xv215",fontsize=16,color="magenta"];2127 -> 2163[label="",style="dashed", color="magenta", weight=3]; 2128[label="xv216",fontsize=16,color="green",shape="box"];2129 -> 661[label="",style="dashed", color="red", weight=0]; 2129[label="show xv215",fontsize=16,color="magenta"];2129 -> 2164[label="",style="dashed", color="magenta", weight=3]; 2130[label="xv216",fontsize=16,color="green",shape="box"];2131 -> 662[label="",style="dashed", color="red", weight=0]; 2131[label="show xv215",fontsize=16,color="magenta"];2131 -> 2165[label="",style="dashed", color="magenta", weight=3]; 2132[label="xv216",fontsize=16,color="green",shape="box"];2133 -> 663[label="",style="dashed", color="red", weight=0]; 2133[label="show xv215",fontsize=16,color="magenta"];2133 -> 2166[label="",style="dashed", color="magenta", weight=3]; 2134[label="xv216",fontsize=16,color="green",shape="box"];2145[label="xv215",fontsize=16,color="green",shape="box"];2146[label="xv215",fontsize=16,color="green",shape="box"];2147[label="xv215",fontsize=16,color="green",shape="box"];2148[label="xv215",fontsize=16,color="green",shape="box"];2149[label="xv215",fontsize=16,color="green",shape="box"];2150[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];2151[label="xv2151",fontsize=16,color="green",shape="box"];2152[label="xv2150",fontsize=16,color="green",shape="box"];2153[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];2154[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];2155[label="xv215",fontsize=16,color="green",shape="box"];2156[label="xv215",fontsize=16,color="green",shape="box"];2157[label="xv215",fontsize=16,color="green",shape="box"];2158[label="xv215",fontsize=16,color="green",shape="box"];2159[label="xv215",fontsize=16,color="green",shape="box"];2160[label="xv215",fontsize=16,color="green",shape="box"];2161[label="xv215",fontsize=16,color="green",shape="box"];2162[label="xv215",fontsize=16,color="green",shape="box"];2163[label="xv215",fontsize=16,color="green",shape="box"];2164[label="xv215",fontsize=16,color="green",shape="box"];2165[label="xv215",fontsize=16,color="green",shape="box"];2166[label="xv215",fontsize=16,color="green",shape="box"];} ---------------------------------------- (202) TRUE