/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 0 ms] (6) HASKELL (7) NumRed [SOUND, 0 ms] (8) HASKELL (9) Narrow [SOUND, 0 ms] (10) AND (11) QDP (12) DependencyGraphProof [EQUIVALENT, 2 ms] (13) QDP (14) QDPOrderProof [EQUIVALENT, 44 ms] (15) QDP (16) DependencyGraphProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) DependencyGraphProof [EQUIVALENT, 0 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 10 ms] (24) QDP (25) UsableRulesProof [EQUIVALENT, 0 ms] (26) QDP (27) QReductionProof [EQUIVALENT, 0 ms] (28) QDP (29) TransformationProof [EQUIVALENT, 59 ms] (30) QDP (31) TransformationProof [EQUIVALENT, 0 ms] (32) QDP (33) TransformationProof [EQUIVALENT, 0 ms] (34) QDP (35) TransformationProof [EQUIVALENT, 0 ms] (36) QDP (37) TransformationProof [EQUIVALENT, 0 ms] (38) QDP (39) TransformationProof [EQUIVALENT, 0 ms] (40) QDP (41) DependencyGraphProof [EQUIVALENT, 0 ms] (42) QDP (43) TransformationProof [EQUIVALENT, 0 ms] (44) QDP (45) DependencyGraphProof [EQUIVALENT, 0 ms] (46) QDP (47) TransformationProof [EQUIVALENT, 0 ms] (48) QDP (49) DependencyGraphProof [EQUIVALENT, 0 ms] (50) QDP (51) TransformationProof [EQUIVALENT, 0 ms] (52) QDP (53) DependencyGraphProof [EQUIVALENT, 0 ms] (54) QDP (55) TransformationProof [EQUIVALENT, 0 ms] (56) QDP (57) DependencyGraphProof [EQUIVALENT, 0 ms] (58) QDP (59) TransformationProof [EQUIVALENT, 0 ms] (60) QDP (61) TransformationProof [EQUIVALENT, 0 ms] (62) QDP (63) DependencyGraphProof [EQUIVALENT, 0 ms] (64) QDP (65) TransformationProof [EQUIVALENT, 0 ms] (66) QDP (67) DependencyGraphProof [EQUIVALENT, 0 ms] (68) QDP (69) TransformationProof [EQUIVALENT, 0 ms] (70) QDP (71) DependencyGraphProof [EQUIVALENT, 0 ms] (72) QDP (73) TransformationProof [EQUIVALENT, 0 ms] (74) QDP (75) DependencyGraphProof [EQUIVALENT, 0 ms] (76) QDP (77) TransformationProof [EQUIVALENT, 0 ms] (78) QDP (79) DependencyGraphProof [EQUIVALENT, 0 ms] (80) QDP (81) TransformationProof [EQUIVALENT, 0 ms] (82) QDP (83) DependencyGraphProof [EQUIVALENT, 0 ms] (84) QDP (85) TransformationProof [EQUIVALENT, 0 ms] (86) QDP (87) DependencyGraphProof [EQUIVALENT, 0 ms] (88) QDP (89) TransformationProof [EQUIVALENT, 0 ms] (90) QDP (91) DependencyGraphProof [EQUIVALENT, 0 ms] (92) QDP (93) TransformationProof [EQUIVALENT, 0 ms] (94) QDP (95) DependencyGraphProof [EQUIVALENT, 0 ms] (96) QDP (97) TransformationProof [EQUIVALENT, 0 ms] (98) QDP (99) DependencyGraphProof [EQUIVALENT, 0 ms] (100) QDP (101) TransformationProof [EQUIVALENT, 0 ms] (102) QDP (103) DependencyGraphProof [EQUIVALENT, 0 ms] (104) QDP (105) TransformationProof [EQUIVALENT, 0 ms] (106) QDP (107) DependencyGraphProof [EQUIVALENT, 0 ms] (108) QDP (109) TransformationProof [EQUIVALENT, 0 ms] (110) QDP (111) QDPSizeChangeProof [EQUIVALENT, 0 ms] (112) YES (113) QDP (114) DependencyGraphProof [EQUIVALENT, 0 ms] (115) QDP (116) TransformationProof [EQUIVALENT, 0 ms] (117) QDP (118) UsableRulesProof [EQUIVALENT, 0 ms] (119) QDP (120) QReductionProof [EQUIVALENT, 0 ms] (121) QDP (122) MNOCProof [EQUIVALENT, 0 ms] (123) QDP (124) InductionCalculusProof [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) MNOCProof [EQUIVALENT, 0 ms] (143) QDP (144) InductionCalculusProof [EQUIVALENT, 0 ms] (145) QDP (146) QDP (147) QDPSizeChangeProof [EQUIVALENT, 0 ms] (148) YES (149) QDP (150) DependencyGraphProof [EQUIVALENT, 0 ms] (151) QDP (152) QDPOrderProof [EQUIVALENT, 0 ms] (153) QDP (154) DependencyGraphProof [EQUIVALENT, 0 ms] (155) QDP (156) QDPSizeChangeProof [EQUIVALENT, 0 ms] (157) YES (158) Narrow [COMPLETE, 0 ms] (159) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) IFR (EQUIVALENT) If Reductions: The following If expression "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" is transformed to "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); primDivNatS0 x y False = Zero; " The following If expression "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" is transformed to "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); primModNatS0 x y False = Succ x; " 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; " ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="showsPrec",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="showsPrec ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="showsPrec ww3 ww4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 5[label="showsPrec ww3 ww4 ww5",fontsize=16,color="burlywood",shape="triangle"];1308[label="ww4/ww40 :% ww41",fontsize=10,color="white",style="solid",shape="box"];5 -> 1308[label="",style="solid", color="burlywood", weight=9]; 1308 -> 6[label="",style="solid", color="burlywood", weight=3]; 6[label="showsPrec ww3 (ww40 :% ww41) ww5",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7 -> 27[label="",style="dashed", color="red", weight=0]; 7[label="showParen (ww3 > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww40) . (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 ww41) ww5",fontsize=16,color="magenta"];7 -> 28[label="",style="dashed", color="magenta", weight=3]; 7 -> 29[label="",style="dashed", color="magenta", weight=3]; 7 -> 30[label="",style="dashed", color="magenta", weight=3]; 7 -> 31[label="",style="dashed", color="magenta", weight=3]; 7 -> 32[label="",style="dashed", color="magenta", weight=3]; 7 -> 33[label="",style="dashed", color="magenta", weight=3]; 7 -> 34[label="",style="dashed", color="magenta", weight=3]; 28[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"];29[label="ww40",fontsize=16,color="green",shape="box"];30[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"];31[label="ww5",fontsize=16,color="green",shape="box"];32[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"];33[label="ww41",fontsize=16,color="green",shape="box"];34[label="ww3",fontsize=16,color="green",shape="box"];27[label="showParen (ww20 > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) ww26",fontsize=16,color="black",shape="triangle"];27 -> 42[label="",style="solid", color="black", weight=3]; 42[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (ww20 > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww26",fontsize=16,color="black",shape="box"];42 -> 43[label="",style="solid", color="black", weight=3]; 43[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (compare ww20 (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3]; 44[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt ww20 (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1309[label="ww20/Pos ww200",fontsize=10,color="white",style="solid",shape="box"];44 -> 1309[label="",style="solid", color="burlywood", weight=9]; 1309 -> 45[label="",style="solid", color="burlywood", weight=3]; 1310[label="ww20/Neg ww200",fontsize=10,color="white",style="solid",shape="box"];44 -> 1310[label="",style="solid", color="burlywood", weight=9]; 1310 -> 46[label="",style="solid", color="burlywood", weight=3]; 45[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Pos ww200) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1311[label="ww200/Succ ww2000",fontsize=10,color="white",style="solid",shape="box"];45 -> 1311[label="",style="solid", color="burlywood", weight=9]; 1311 -> 47[label="",style="solid", color="burlywood", weight=3]; 1312[label="ww200/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 1312[label="",style="solid", color="burlywood", weight=9]; 1312 -> 48[label="",style="solid", color="burlywood", weight=3]; 46[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Neg ww200) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1313[label="ww200/Succ ww2000",fontsize=10,color="white",style="solid",shape="box"];46 -> 1313[label="",style="solid", color="burlywood", weight=9]; 1313 -> 49[label="",style="solid", color="burlywood", weight=3]; 1314[label="ww200/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 1314[label="",style="solid", color="burlywood", weight=9]; 1314 -> 50[label="",style="solid", color="burlywood", weight=3]; 47[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Pos (Succ ww2000)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];47 -> 51[label="",style="solid", color="black", weight=3]; 48[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3]; 49[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Neg (Succ ww2000)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];49 -> 53[label="",style="solid", color="black", weight=3]; 50[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Neg Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3]; 51[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww2000) (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww26",fontsize=16,color="black",shape="box"];51 -> 55[label="",style="solid", color="black", weight=3]; 52[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww26",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3]; 53[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="black",shape="triangle"];53 -> 57[label="",style="solid", color="black", weight=3]; 54 -> 53[label="",style="dashed", color="red", weight=0]; 54[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];55[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww2000 (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1315[label="ww2000/Succ ww20000",fontsize=10,color="white",style="solid",shape="box"];55 -> 1315[label="",style="solid", color="burlywood", weight=9]; 1315 -> 58[label="",style="solid", color="burlywood", weight=3]; 1316[label="ww2000/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 1316[label="",style="solid", color="burlywood", weight=9]; 1316 -> 59[label="",style="solid", color="burlywood", weight=3]; 56 -> 53[label="",style="dashed", color="red", weight=0]; 56[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];57[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) False ww26",fontsize=16,color="black",shape="triangle"];57 -> 60[label="",style="solid", color="black", weight=3]; 58[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww20000) (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))) == GT) ww26",fontsize=16,color="black",shape="box"];58 -> 61[label="",style="solid", color="black", weight=3]; 59[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))) == GT) ww26",fontsize=16,color="black",shape="box"];59 -> 62[label="",style="solid", color="black", weight=3]; 60[label="(shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="black",shape="triangle"];60 -> 63[label="",style="solid", color="black", weight=3]; 61[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww20000 (Succ (Succ (Succ (Succ (Succ Zero))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1317[label="ww20000/Succ ww200000",fontsize=10,color="white",style="solid",shape="box"];61 -> 1317[label="",style="solid", color="burlywood", weight=9]; 1317 -> 64[label="",style="solid", color="burlywood", weight=3]; 1318[label="ww20000/Zero",fontsize=10,color="white",style="solid",shape="box"];61 -> 1318[label="",style="solid", color="burlywood", weight=9]; 1318 -> 65[label="",style="solid", color="burlywood", weight=3]; 62 -> 53[label="",style="dashed", color="red", weight=0]; 62[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];63[label="shows ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];63 -> 66[label="",style="solid", color="black", weight=3]; 64[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww200000) (Succ (Succ (Succ (Succ (Succ Zero))))) == GT) ww26",fontsize=16,color="black",shape="box"];64 -> 67[label="",style="solid", color="black", weight=3]; 65[label="showParen0 ((shows ww21) . 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(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww200000 (Succ (Succ (Succ (Succ Zero)))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1337[label="ww200000/Succ ww2000000",fontsize=10,color="white",style="solid",shape="box"];67 -> 1337[label="",style="solid", color="burlywood", weight=9]; 1337 -> 87[label="",style="solid", color="burlywood", weight=3]; 1338[label="ww200000/Zero",fontsize=10,color="white",style="solid",shape="box"];67 -> 1338[label="",style="solid", color="burlywood", weight=9]; 1338 -> 88[label="",style="solid", color="burlywood", weight=3]; 68 -> 53[label="",style="dashed", color="red", weight=0]; 68[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];69[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];69 -> 89[label="",style="solid", color="black", weight=3]; 70[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="burlywood",shape="box"];1339[label="ww21/ww210 :% ww211",fontsize=10,color="white",style="solid",shape="box"];70 -> 1339[label="",style="solid", color="burlywood", weight=9]; 1339 -> 90[label="",style="solid", color="burlywood", weight=3]; 71[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];71 -> 91[label="",style="solid", color="black", weight=3]; 72[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];72 -> 92[label="",style="solid", color="black", weight=3]; 73[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];73 -> 93[label="",style="solid", color="black", weight=3]; 74[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];74 -> 94[label="",style="solid", color="black", weight=3]; 75[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];75 -> 95[label="",style="solid", color="black", weight=3]; 76[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];76 -> 96[label="",style="solid", color="black", weight=3]; 77[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];77 -> 97[label="",style="solid", color="black", weight=3]; 78[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];78 -> 98[label="",style="solid", color="black", weight=3]; 79[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];79 -> 99[label="",style="solid", color="black", weight=3]; 80[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];80 -> 100[label="",style="solid", color="black", weight=3]; 81[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];81 -> 101[label="",style="solid", color="black", weight=3]; 82[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];82 -> 102[label="",style="solid", color="black", weight=3]; 83[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];83 -> 103[label="",style="solid", color="black", weight=3]; 84[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];84 -> 104[label="",style="solid", color="black", weight=3]; 85[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];85 -> 105[label="",style="solid", color="black", weight=3]; 86[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];86 -> 106[label="",style="solid", color="black", weight=3]; 87[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww2000000) (Succ (Succ (Succ (Succ Zero)))) == GT) ww26",fontsize=16,color="black",shape="box"];87 -> 107[label="",style="solid", color="black", weight=3]; 88[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ (Succ (Succ (Succ Zero)))) == GT) ww26",fontsize=16,color="black",shape="box"];88 -> 108[label="",style="solid", color="black", weight=3]; 89 -> 224[label="",style="dashed", color="red", weight=0]; 89[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];89 -> 225[label="",style="dashed", color="magenta", weight=3]; 89 -> 226[label="",style="dashed", color="magenta", weight=3]; 90[label="showsPrec (Pos Zero) (ww210 :% ww211) ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];90 -> 110[label="",style="solid", color="black", weight=3]; 91 -> 224[label="",style="dashed", color="red", weight=0]; 91[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];91 -> 227[label="",style="dashed", color="magenta", weight=3]; 91 -> 228[label="",style="dashed", color="magenta", weight=3]; 92 -> 224[label="",style="dashed", color="red", weight=0]; 92[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];92 -> 229[label="",style="dashed", color="magenta", weight=3]; 92 -> 230[label="",style="dashed", color="magenta", weight=3]; 93 -> 224[label="",style="dashed", color="red", weight=0]; 93[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];93 -> 231[label="",style="dashed", color="magenta", weight=3]; 93 -> 232[label="",style="dashed", color="magenta", weight=3]; 94 -> 224[label="",style="dashed", color="red", weight=0]; 94[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];94 -> 233[label="",style="dashed", color="magenta", weight=3]; 94 -> 234[label="",style="dashed", color="magenta", weight=3]; 95 -> 224[label="",style="dashed", color="red", weight=0]; 95[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];95 -> 235[label="",style="dashed", color="magenta", weight=3]; 95 -> 236[label="",style="dashed", color="magenta", weight=3]; 96 -> 224[label="",style="dashed", color="red", weight=0]; 96[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];96 -> 237[label="",style="dashed", color="magenta", weight=3]; 96 -> 238[label="",style="dashed", color="magenta", weight=3]; 97 -> 224[label="",style="dashed", color="red", weight=0]; 97[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];97 -> 239[label="",style="dashed", color="magenta", weight=3]; 97 -> 240[label="",style="dashed", color="magenta", weight=3]; 98 -> 224[label="",style="dashed", color="red", weight=0]; 98[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];98 -> 241[label="",style="dashed", color="magenta", weight=3]; 98 -> 242[label="",style="dashed", color="magenta", weight=3]; 99 -> 224[label="",style="dashed", color="red", weight=0]; 99[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];99 -> 243[label="",style="dashed", color="magenta", weight=3]; 99 -> 244[label="",style="dashed", color="magenta", weight=3]; 100 -> 224[label="",style="dashed", color="red", weight=0]; 100[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];100 -> 245[label="",style="dashed", color="magenta", weight=3]; 100 -> 246[label="",style="dashed", color="magenta", weight=3]; 101 -> 224[label="",style="dashed", color="red", weight=0]; 101[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];101 -> 247[label="",style="dashed", color="magenta", weight=3]; 101 -> 248[label="",style="dashed", color="magenta", weight=3]; 102 -> 224[label="",style="dashed", color="red", weight=0]; 102[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];102 -> 249[label="",style="dashed", color="magenta", weight=3]; 102 -> 250[label="",style="dashed", color="magenta", weight=3]; 103 -> 224[label="",style="dashed", color="red", weight=0]; 103[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];103 -> 251[label="",style="dashed", color="magenta", weight=3]; 103 -> 252[label="",style="dashed", color="magenta", weight=3]; 104 -> 224[label="",style="dashed", color="red", weight=0]; 104[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];104 -> 253[label="",style="dashed", color="magenta", weight=3]; 104 -> 254[label="",style="dashed", color="magenta", weight=3]; 105 -> 224[label="",style="dashed", color="red", weight=0]; 105[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];105 -> 255[label="",style="dashed", color="magenta", weight=3]; 105 -> 256[label="",style="dashed", color="magenta", weight=3]; 106 -> 224[label="",style="dashed", color="red", weight=0]; 106[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];106 -> 257[label="",style="dashed", color="magenta", weight=3]; 106 -> 258[label="",style="dashed", color="magenta", weight=3]; 107[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww2000000 (Succ (Succ (Succ Zero))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1340[label="ww2000000/Succ ww20000000",fontsize=10,color="white",style="solid",shape="box"];107 -> 1340[label="",style="solid", color="burlywood", weight=9]; 1340 -> 127[label="",style="solid", color="burlywood", weight=3]; 1341[label="ww2000000/Zero",fontsize=10,color="white",style="solid",shape="box"];107 -> 1341[label="",style="solid", color="burlywood", weight=9]; 1341 -> 128[label="",style="solid", color="burlywood", weight=3]; 108 -> 53[label="",style="dashed", color="red", weight=0]; 108[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];225 -> 132[label="",style="dashed", color="red", weight=0]; 225[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];226[label="show ww21",fontsize=16,color="black",shape="triangle"];226 -> 284[label="",style="solid", color="black", weight=3]; 224[label="ww62 ++ ww60",fontsize=16,color="burlywood",shape="triangle"];1342[label="ww62/ww620 : ww621",fontsize=10,color="white",style="solid",shape="box"];224 -> 1342[label="",style="solid", color="burlywood", weight=9]; 1342 -> 285[label="",style="solid", color="burlywood", weight=3]; 1343[label="ww62/[]",fontsize=10,color="white",style="solid",shape="box"];224 -> 1343[label="",style="solid", color="burlywood", weight=9]; 1343 -> 286[label="",style="solid", color="burlywood", weight=3]; 110 -> 27[label="",style="dashed", color="red", weight=0]; 110[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww210) . (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 ww211) ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="magenta"];110 -> 129[label="",style="dashed", color="magenta", weight=3]; 110 -> 130[label="",style="dashed", color="magenta", weight=3]; 110 -> 131[label="",style="dashed", color="magenta", weight=3]; 110 -> 132[label="",style="dashed", color="magenta", weight=3]; 110 -> 133[label="",style="dashed", color="magenta", weight=3]; 110 -> 134[label="",style="dashed", color="magenta", weight=3]; 110 -> 135[label="",style="dashed", color="magenta", weight=3]; 227 -> 132[label="",style="dashed", color="red", weight=0]; 227[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];228[label="show ww21",fontsize=16,color="black",shape="triangle"];228 -> 287[label="",style="solid", color="black", weight=3]; 229 -> 132[label="",style="dashed", color="red", weight=0]; 229[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];230[label="show ww21",fontsize=16,color="black",shape="triangle"];230 -> 288[label="",style="solid", color="black", weight=3]; 231 -> 132[label="",style="dashed", color="red", weight=0]; 231[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];232[label="show ww21",fontsize=16,color="black",shape="triangle"];232 -> 289[label="",style="solid", color="black", weight=3]; 233 -> 132[label="",style="dashed", color="red", weight=0]; 233[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];234[label="show ww21",fontsize=16,color="black",shape="triangle"];234 -> 290[label="",style="solid", color="black", weight=3]; 235 -> 132[label="",style="dashed", color="red", weight=0]; 235[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];236[label="show ww21",fontsize=16,color="black",shape="triangle"];236 -> 291[label="",style="solid", color="black", weight=3]; 237 -> 132[label="",style="dashed", color="red", weight=0]; 237[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];238[label="show ww21",fontsize=16,color="black",shape="triangle"];238 -> 292[label="",style="solid", color="black", weight=3]; 239 -> 132[label="",style="dashed", color="red", weight=0]; 239[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];240[label="show ww21",fontsize=16,color="black",shape="triangle"];240 -> 293[label="",style="solid", color="black", weight=3]; 241 -> 132[label="",style="dashed", color="red", weight=0]; 241[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];242[label="show ww21",fontsize=16,color="black",shape="triangle"];242 -> 294[label="",style="solid", color="black", weight=3]; 243 -> 132[label="",style="dashed", color="red", weight=0]; 243[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];244[label="show ww21",fontsize=16,color="black",shape="triangle"];244 -> 295[label="",style="solid", color="black", weight=3]; 245 -> 132[label="",style="dashed", color="red", weight=0]; 245[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];246[label="show ww21",fontsize=16,color="black",shape="triangle"];246 -> 296[label="",style="solid", color="black", weight=3]; 247 -> 132[label="",style="dashed", color="red", weight=0]; 247[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];248[label="show ww21",fontsize=16,color="black",shape="triangle"];248 -> 297[label="",style="solid", color="black", weight=3]; 249 -> 132[label="",style="dashed", color="red", weight=0]; 249[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];250[label="show ww21",fontsize=16,color="black",shape="triangle"];250 -> 298[label="",style="solid", color="black", weight=3]; 251 -> 132[label="",style="dashed", color="red", weight=0]; 251[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];252[label="show ww21",fontsize=16,color="black",shape="triangle"];252 -> 299[label="",style="solid", color="black", weight=3]; 253 -> 132[label="",style="dashed", color="red", weight=0]; 253[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];254[label="show ww21",fontsize=16,color="black",shape="triangle"];254 -> 300[label="",style="solid", color="black", weight=3]; 255 -> 132[label="",style="dashed", color="red", weight=0]; 255[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];256[label="show ww21",fontsize=16,color="black",shape="triangle"];256 -> 301[label="",style="solid", color="black", weight=3]; 257 -> 132[label="",style="dashed", color="red", weight=0]; 257[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];258[label="show ww21",fontsize=16,color="black",shape="triangle"];258 -> 302[label="",style="solid", color="black", weight=3]; 127[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww20000000) (Succ (Succ (Succ Zero))) == GT) ww26",fontsize=16,color="black",shape="box"];127 -> 138[label="",style="solid", color="black", weight=3]; 128[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ (Succ (Succ Zero))) == GT) ww26",fontsize=16,color="black",shape="box"];128 -> 139[label="",style="solid", color="black", weight=3]; 132[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="black",shape="triangle"];132 -> 140[label="",style="solid", color="black", weight=3]; 284[label="error []",fontsize=16,color="red",shape="box"];285[label="(ww620 : ww621) ++ ww60",fontsize=16,color="black",shape="box"];285 -> 306[label="",style="solid", color="black", weight=3]; 286[label="[] ++ ww60",fontsize=16,color="black",shape="box"];286 -> 307[label="",style="solid", color="black", weight=3]; 129[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"];130[label="ww210",fontsize=16,color="green",shape="box"];131[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"];133[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"];134[label="ww211",fontsize=16,color="green",shape="box"];135[label="Pos Zero",fontsize=16,color="green",shape="box"];287[label="error []",fontsize=16,color="red",shape="box"];288[label="error []",fontsize=16,color="red",shape="box"];289[label="error []",fontsize=16,color="red",shape="box"];290[label="error []",fontsize=16,color="red",shape="box"];291[label="error []",fontsize=16,color="red",shape="box"];292[label="error []",fontsize=16,color="red",shape="box"];293[label="error []",fontsize=16,color="red",shape="box"];294[label="error []",fontsize=16,color="red",shape="box"];295[label="error []",fontsize=16,color="red",shape="box"];296[label="error []",fontsize=16,color="red",shape="box"];297[label="error []",fontsize=16,color="red",shape="box"];298[label="primShowInt ww21",fontsize=16,color="burlywood",shape="triangle"];1344[label="ww21/Pos ww210",fontsize=10,color="white",style="solid",shape="box"];298 -> 1344[label="",style="solid", color="burlywood", weight=9]; 1344 -> 308[label="",style="solid", color="burlywood", weight=3]; 1345[label="ww21/Neg ww210",fontsize=10,color="white",style="solid",shape="box"];298 -> 1345[label="",style="solid", color="burlywood", weight=9]; 1345 -> 309[label="",style="solid", color="burlywood", weight=3]; 299[label="error []",fontsize=16,color="red",shape="box"];300[label="error []",fontsize=16,color="red",shape="box"];301[label="error []",fontsize=16,color="red",shape="box"];302[label="error []",fontsize=16,color="red",shape="box"];138[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww20000000 (Succ (Succ Zero)) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1346[label="ww20000000/Succ ww200000000",fontsize=10,color="white",style="solid",shape="box"];138 -> 1346[label="",style="solid", color="burlywood", weight=9]; 1346 -> 144[label="",style="solid", color="burlywood", weight=3]; 1347[label="ww20000000/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 1347[label="",style="solid", color="burlywood", weight=9]; 1347 -> 145[label="",style="solid", color="burlywood", weight=3]; 139 -> 53[label="",style="dashed", color="red", weight=0]; 139[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];140[label="showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : []) (shows ww25 ww26)",fontsize=16,color="black",shape="box"];140 -> 146[label="",style="solid", color="black", weight=3]; 306[label="ww620 : ww621 ++ ww60",fontsize=16,color="green",shape="box"];306 -> 330[label="",style="dashed", color="green", weight=3]; 307[label="ww60",fontsize=16,color="green",shape="box"];308[label="primShowInt (Pos ww210)",fontsize=16,color="burlywood",shape="box"];1348[label="ww210/Succ ww2100",fontsize=10,color="white",style="solid",shape="box"];308 -> 1348[label="",style="solid", color="burlywood", weight=9]; 1348 -> 331[label="",style="solid", color="burlywood", weight=3]; 1349[label="ww210/Zero",fontsize=10,color="white",style="solid",shape="box"];308 -> 1349[label="",style="solid", color="burlywood", weight=9]; 1349 -> 332[label="",style="solid", color="burlywood", weight=3]; 309[label="primShowInt (Neg ww210)",fontsize=16,color="black",shape="box"];309 -> 333[label="",style="solid", color="black", weight=3]; 144[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww200000000) (Succ (Succ Zero)) == GT) ww26",fontsize=16,color="black",shape="box"];144 -> 157[label="",style="solid", color="black", weight=3]; 145[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ (Succ Zero)) == GT) ww26",fontsize=16,color="black",shape="box"];145 -> 158[label="",style="solid", color="black", weight=3]; 146 -> 224[label="",style="dashed", color="red", weight=0]; 146[label="(++) (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : []) shows ww25 ww26",fontsize=16,color="magenta"];146 -> 263[label="",style="dashed", color="magenta", weight=3]; 146 -> 264[label="",style="dashed", color="magenta", weight=3]; 330 -> 224[label="",style="dashed", color="red", weight=0]; 330[label="ww621 ++ ww60",fontsize=16,color="magenta"];330 -> 353[label="",style="dashed", color="magenta", weight=3]; 331[label="primShowInt (Pos (Succ ww2100))",fontsize=16,color="black",shape="box"];331 -> 354[label="",style="solid", color="black", weight=3]; 332[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];332 -> 355[label="",style="solid", color="black", weight=3]; 333[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 ww210)",fontsize=16,color="green",shape="box"];333 -> 356[label="",style="dashed", color="green", weight=3]; 157[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww200000000 (Succ Zero) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1350[label="ww200000000/Succ ww2000000000",fontsize=10,color="white",style="solid",shape="box"];157 -> 1350[label="",style="solid", color="burlywood", weight=9]; 1350 -> 181[label="",style="solid", color="burlywood", weight=3]; 1351[label="ww200000000/Zero",fontsize=10,color="white",style="solid",shape="box"];157 -> 1351[label="",style="solid", color="burlywood", weight=9]; 1351 -> 182[label="",style="solid", color="burlywood", weight=3]; 158 -> 53[label="",style="dashed", color="red", weight=0]; 158[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];263[label="shows ww25 ww26",fontsize=16,color="black",shape="box"];263 -> 303[label="",style="solid", color="black", weight=3]; 264[label="Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : []",fontsize=16,color="green",shape="box"];353[label="ww621",fontsize=16,color="green",shape="box"];354 -> 224[label="",style="dashed", color="red", weight=0]; 354[label="primShowInt (div Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];354 -> 400[label="",style="dashed", color="magenta", weight=3]; 354 -> 401[label="",style="dashed", color="magenta", weight=3]; 355[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"];356 -> 298[label="",style="dashed", color="red", weight=0]; 356[label="primShowInt (Pos ww210)",fontsize=16,color="magenta"];356 -> 402[label="",style="dashed", color="magenta", weight=3]; 181[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww2000000000) (Succ Zero) == GT) ww26",fontsize=16,color="black",shape="box"];181 -> 214[label="",style="solid", color="black", weight=3]; 182[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ Zero) == GT) ww26",fontsize=16,color="black",shape="box"];182 -> 215[label="",style="solid", color="black", weight=3]; 303[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="blue",shape="box"];1352[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1352[label="",style="solid", color="blue", weight=9]; 1352 -> 310[label="",style="solid", color="blue", weight=3]; 1353[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1353[label="",style="solid", color="blue", weight=9]; 1353 -> 311[label="",style="solid", color="blue", weight=3]; 1354[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1354[label="",style="solid", color="blue", weight=9]; 1354 -> 312[label="",style="solid", color="blue", weight=3]; 1355[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1355[label="",style="solid", color="blue", weight=9]; 1355 -> 313[label="",style="solid", color="blue", weight=3]; 1356[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1356[label="",style="solid", color="blue", weight=9]; 1356 -> 314[label="",style="solid", color="blue", weight=3]; 1357[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1357[label="",style="solid", color="blue", weight=9]; 1357 -> 315[label="",style="solid", color="blue", weight=3]; 1358[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1358[label="",style="solid", color="blue", weight=9]; 1358 -> 316[label="",style="solid", color="blue", weight=3]; 1359[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1359[label="",style="solid", color="blue", weight=9]; 1359 -> 317[label="",style="solid", color="blue", weight=3]; 1360[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1360[label="",style="solid", color="blue", weight=9]; 1360 -> 318[label="",style="solid", color="blue", weight=3]; 1361[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1361[label="",style="solid", color="blue", weight=9]; 1361 -> 319[label="",style="solid", color="blue", weight=3]; 1362[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1362[label="",style="solid", color="blue", weight=9]; 1362 -> 320[label="",style="solid", color="blue", weight=3]; 1363[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1363[label="",style="solid", color="blue", weight=9]; 1363 -> 321[label="",style="solid", color="blue", weight=3]; 1364[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1364[label="",style="solid", color="blue", weight=9]; 1364 -> 322[label="",style="solid", color="blue", weight=3]; 1365[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1365[label="",style="solid", color="blue", weight=9]; 1365 -> 323[label="",style="solid", color="blue", weight=3]; 1366[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1366[label="",style="solid", color="blue", weight=9]; 1366 -> 324[label="",style="solid", color="blue", weight=3]; 1367[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1367[label="",style="solid", color="blue", weight=9]; 1367 -> 325[label="",style="solid", color="blue", weight=3]; 1368[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1368[label="",style="solid", color="blue", weight=9]; 1368 -> 326[label="",style="solid", color="blue", weight=3]; 1369[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1369[label="",style="solid", color="blue", weight=9]; 1369 -> 327[label="",style="solid", color="blue", weight=3]; 400[label="toEnum (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];400 -> 443[label="",style="dashed", color="green", weight=3]; 401 -> 298[label="",style="dashed", color="red", weight=0]; 401[label="primShowInt (div Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];401 -> 444[label="",style="dashed", color="magenta", weight=3]; 402[label="Pos ww210",fontsize=16,color="green",shape="box"];214[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww2000000000 Zero == GT) ww26",fontsize=16,color="burlywood",shape="box"];1370[label="ww2000000000/Succ ww20000000000",fontsize=10,color="white",style="solid",shape="box"];214 -> 1370[label="",style="solid", color="burlywood", weight=9]; 1370 -> 221[label="",style="solid", color="burlywood", weight=3]; 1371[label="ww2000000000/Zero",fontsize=10,color="white",style="solid",shape="box"];214 -> 1371[label="",style="solid", color="burlywood", weight=9]; 1371 -> 222[label="",style="solid", color="burlywood", weight=3]; 215 -> 53[label="",style="dashed", color="red", weight=0]; 215[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];310[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];310 -> 334[label="",style="solid", color="black", weight=3]; 311[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="burlywood",shape="box"];1372[label="ww25/ww250 :% ww251",fontsize=10,color="white",style="solid",shape="box"];311 -> 1372[label="",style="solid", color="burlywood", weight=9]; 1372 -> 335[label="",style="solid", color="burlywood", weight=3]; 312[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];312 -> 336[label="",style="solid", color="black", weight=3]; 313[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];313 -> 337[label="",style="solid", color="black", weight=3]; 314[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];314 -> 338[label="",style="solid", color="black", weight=3]; 315[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];315 -> 339[label="",style="solid", color="black", weight=3]; 316[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];316 -> 340[label="",style="solid", color="black", weight=3]; 317[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];317 -> 341[label="",style="solid", color="black", weight=3]; 318[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];318 -> 342[label="",style="solid", color="black", weight=3]; 319[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];319 -> 343[label="",style="solid", color="black", weight=3]; 320[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];320 -> 344[label="",style="solid", color="black", weight=3]; 321[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];321 -> 345[label="",style="solid", color="black", weight=3]; 322[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];322 -> 346[label="",style="solid", color="black", weight=3]; 323[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];323 -> 347[label="",style="solid", color="black", weight=3]; 324[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];324 -> 348[label="",style="solid", color="black", weight=3]; 325[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];325 -> 349[label="",style="solid", color="black", weight=3]; 326[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];326 -> 350[label="",style="solid", color="black", weight=3]; 327[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];327 -> 351[label="",style="solid", color="black", weight=3]; 443[label="toEnum (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];443 -> 463[label="",style="solid", color="black", weight=3]; 444 -> 449[label="",style="dashed", color="red", weight=0]; 444[label="div Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];444 -> 450[label="",style="dashed", color="magenta", weight=3]; 444 -> 451[label="",style="dashed", color="magenta", weight=3]; 221[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww20000000000) Zero == GT) ww26",fontsize=16,color="black",shape="box"];221 -> 304[label="",style="solid", color="black", weight=3]; 222[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero Zero == GT) ww26",fontsize=16,color="black",shape="box"];222 -> 305[label="",style="solid", color="black", weight=3]; 334 -> 224[label="",style="dashed", color="red", weight=0]; 334[label="show ww25 ++ ww26",fontsize=16,color="magenta"];334 -> 357[label="",style="dashed", color="magenta", weight=3]; 334 -> 358[label="",style="dashed", color="magenta", weight=3]; 335[label="showsPrec (Pos Zero) (ww250 :% ww251) ww26",fontsize=16,color="black",shape="box"];335 -> 359[label="",style="solid", color="black", weight=3]; 336 -> 224[label="",style="dashed", color="red", weight=0]; 336[label="show ww25 ++ ww26",fontsize=16,color="magenta"];336 -> 360[label="",style="dashed", color="magenta", weight=3]; 336 -> 361[label="",style="dashed", color="magenta", weight=3]; 337 -> 224[label="",style="dashed", color="red", weight=0]; 337[label="show ww25 ++ ww26",fontsize=16,color="magenta"];337 -> 362[label="",style="dashed", color="magenta", weight=3]; 337 -> 363[label="",style="dashed", color="magenta", weight=3]; 338 -> 224[label="",style="dashed", color="red", weight=0]; 338[label="show ww25 ++ ww26",fontsize=16,color="magenta"];338 -> 364[label="",style="dashed", color="magenta", weight=3]; 338 -> 365[label="",style="dashed", color="magenta", weight=3]; 339 -> 224[label="",style="dashed", color="red", weight=0]; 339[label="show ww25 ++ ww26",fontsize=16,color="magenta"];339 -> 366[label="",style="dashed", color="magenta", weight=3]; 339 -> 367[label="",style="dashed", color="magenta", weight=3]; 340 -> 224[label="",style="dashed", color="red", weight=0]; 340[label="show ww25 ++ ww26",fontsize=16,color="magenta"];340 -> 368[label="",style="dashed", color="magenta", weight=3]; 340 -> 369[label="",style="dashed", color="magenta", weight=3]; 341 -> 224[label="",style="dashed", color="red", weight=0]; 341[label="show ww25 ++ ww26",fontsize=16,color="magenta"];341 -> 370[label="",style="dashed", color="magenta", weight=3]; 341 -> 371[label="",style="dashed", color="magenta", weight=3]; 342 -> 224[label="",style="dashed", color="red", weight=0]; 342[label="show ww25 ++ ww26",fontsize=16,color="magenta"];342 -> 372[label="",style="dashed", color="magenta", weight=3]; 342 -> 373[label="",style="dashed", color="magenta", weight=3]; 343 -> 224[label="",style="dashed", color="red", weight=0]; 343[label="show ww25 ++ ww26",fontsize=16,color="magenta"];343 -> 374[label="",style="dashed", color="magenta", weight=3]; 343 -> 375[label="",style="dashed", color="magenta", weight=3]; 344 -> 224[label="",style="dashed", color="red", weight=0]; 344[label="show ww25 ++ ww26",fontsize=16,color="magenta"];344 -> 376[label="",style="dashed", color="magenta", weight=3]; 344 -> 377[label="",style="dashed", color="magenta", weight=3]; 345 -> 224[label="",style="dashed", color="red", weight=0]; 345[label="show ww25 ++ ww26",fontsize=16,color="magenta"];345 -> 378[label="",style="dashed", color="magenta", weight=3]; 345 -> 379[label="",style="dashed", color="magenta", weight=3]; 346 -> 224[label="",style="dashed", color="red", weight=0]; 346[label="show ww25 ++ ww26",fontsize=16,color="magenta"];346 -> 380[label="",style="dashed", color="magenta", weight=3]; 346 -> 381[label="",style="dashed", color="magenta", weight=3]; 347 -> 224[label="",style="dashed", color="red", weight=0]; 347[label="show ww25 ++ ww26",fontsize=16,color="magenta"];347 -> 382[label="",style="dashed", color="magenta", weight=3]; 347 -> 383[label="",style="dashed", color="magenta", weight=3]; 348 -> 224[label="",style="dashed", color="red", weight=0]; 348[label="show ww25 ++ ww26",fontsize=16,color="magenta"];348 -> 384[label="",style="dashed", color="magenta", weight=3]; 348 -> 385[label="",style="dashed", color="magenta", weight=3]; 349 -> 224[label="",style="dashed", color="red", weight=0]; 349[label="show ww25 ++ ww26",fontsize=16,color="magenta"];349 -> 386[label="",style="dashed", color="magenta", weight=3]; 349 -> 387[label="",style="dashed", color="magenta", weight=3]; 350 -> 224[label="",style="dashed", color="red", weight=0]; 350[label="show ww25 ++ ww26",fontsize=16,color="magenta"];350 -> 388[label="",style="dashed", color="magenta", weight=3]; 350 -> 389[label="",style="dashed", color="magenta", weight=3]; 351 -> 224[label="",style="dashed", color="red", weight=0]; 351[label="show ww25 ++ ww26",fontsize=16,color="magenta"];351 -> 390[label="",style="dashed", color="magenta", weight=3]; 351 -> 391[label="",style="dashed", color="magenta", weight=3]; 463 -> 475[label="",style="dashed", color="red", weight=0]; 463[label="primIntToChar (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];463 -> 476[label="",style="dashed", color="magenta", weight=3]; 463 -> 477[label="",style="dashed", color="magenta", weight=3]; 450[label="ww2100",fontsize=16,color="green",shape="box"];451[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];449[label="div Pos (Succ ww84) Pos (Succ ww85)",fontsize=16,color="black",shape="triangle"];449 -> 461[label="",style="solid", color="black", weight=3]; 304[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (GT == GT) ww26",fontsize=16,color="black",shape="box"];304 -> 328[label="",style="solid", color="black", weight=3]; 305[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (EQ == GT) ww26",fontsize=16,color="black",shape="box"];305 -> 329[label="",style="solid", color="black", weight=3]; 357[label="ww26",fontsize=16,color="green",shape="box"];358 -> 226[label="",style="dashed", color="red", weight=0]; 358[label="show ww25",fontsize=16,color="magenta"];358 -> 403[label="",style="dashed", color="magenta", weight=3]; 359 -> 27[label="",style="dashed", color="red", weight=0]; 359[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww250) . (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 ww251) ww26",fontsize=16,color="magenta"];359 -> 404[label="",style="dashed", color="magenta", weight=3]; 359 -> 405[label="",style="dashed", color="magenta", weight=3]; 359 -> 406[label="",style="dashed", color="magenta", weight=3]; 359 -> 407[label="",style="dashed", color="magenta", weight=3]; 359 -> 408[label="",style="dashed", color="magenta", weight=3]; 359 -> 409[label="",style="dashed", color="magenta", weight=3]; 360[label="ww26",fontsize=16,color="green",shape="box"];361 -> 228[label="",style="dashed", color="red", weight=0]; 361[label="show ww25",fontsize=16,color="magenta"];361 -> 410[label="",style="dashed", color="magenta", weight=3]; 362[label="ww26",fontsize=16,color="green",shape="box"];363 -> 230[label="",style="dashed", color="red", weight=0]; 363[label="show ww25",fontsize=16,color="magenta"];363 -> 411[label="",style="dashed", color="magenta", weight=3]; 364[label="ww26",fontsize=16,color="green",shape="box"];365 -> 232[label="",style="dashed", color="red", weight=0]; 365[label="show ww25",fontsize=16,color="magenta"];365 -> 412[label="",style="dashed", color="magenta", weight=3]; 366[label="ww26",fontsize=16,color="green",shape="box"];367 -> 234[label="",style="dashed", color="red", weight=0]; 367[label="show ww25",fontsize=16,color="magenta"];367 -> 413[label="",style="dashed", color="magenta", weight=3]; 368[label="ww26",fontsize=16,color="green",shape="box"];369 -> 236[label="",style="dashed", color="red", weight=0]; 369[label="show ww25",fontsize=16,color="magenta"];369 -> 414[label="",style="dashed", color="magenta", weight=3]; 370[label="ww26",fontsize=16,color="green",shape="box"];371 -> 238[label="",style="dashed", color="red", weight=0]; 371[label="show ww25",fontsize=16,color="magenta"];371 -> 415[label="",style="dashed", color="magenta", weight=3]; 372[label="ww26",fontsize=16,color="green",shape="box"];373 -> 240[label="",style="dashed", color="red", weight=0]; 373[label="show ww25",fontsize=16,color="magenta"];373 -> 416[label="",style="dashed", color="magenta", weight=3]; 374[label="ww26",fontsize=16,color="green",shape="box"];375 -> 242[label="",style="dashed", color="red", weight=0]; 375[label="show ww25",fontsize=16,color="magenta"];375 -> 417[label="",style="dashed", color="magenta", weight=3]; 376[label="ww26",fontsize=16,color="green",shape="box"];377 -> 244[label="",style="dashed", color="red", weight=0]; 377[label="show ww25",fontsize=16,color="magenta"];377 -> 418[label="",style="dashed", color="magenta", weight=3]; 378[label="ww26",fontsize=16,color="green",shape="box"];379 -> 246[label="",style="dashed", color="red", weight=0]; 379[label="show ww25",fontsize=16,color="magenta"];379 -> 419[label="",style="dashed", color="magenta", weight=3]; 380[label="ww26",fontsize=16,color="green",shape="box"];381 -> 248[label="",style="dashed", color="red", weight=0]; 381[label="show ww25",fontsize=16,color="magenta"];381 -> 420[label="",style="dashed", color="magenta", weight=3]; 382[label="ww26",fontsize=16,color="green",shape="box"];383 -> 250[label="",style="dashed", color="red", weight=0]; 383[label="show ww25",fontsize=16,color="magenta"];383 -> 421[label="",style="dashed", color="magenta", weight=3]; 384[label="ww26",fontsize=16,color="green",shape="box"];385 -> 252[label="",style="dashed", color="red", weight=0]; 385[label="show ww25",fontsize=16,color="magenta"];385 -> 422[label="",style="dashed", color="magenta", weight=3]; 386[label="ww26",fontsize=16,color="green",shape="box"];387 -> 254[label="",style="dashed", color="red", weight=0]; 387[label="show ww25",fontsize=16,color="magenta"];387 -> 423[label="",style="dashed", color="magenta", weight=3]; 388[label="ww26",fontsize=16,color="green",shape="box"];389 -> 256[label="",style="dashed", color="red", weight=0]; 389[label="show ww25",fontsize=16,color="magenta"];389 -> 424[label="",style="dashed", color="magenta", weight=3]; 390[label="ww26",fontsize=16,color="green",shape="box"];391 -> 258[label="",style="dashed", color="red", weight=0]; 391[label="show ww25",fontsize=16,color="magenta"];391 -> 425[label="",style="dashed", color="magenta", weight=3]; 476[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];477[label="ww2100",fontsize=16,color="green",shape="box"];475[label="primIntToChar (mod Pos (Succ ww87) Pos (Succ ww88))",fontsize=16,color="black",shape="triangle"];475 -> 478[label="",style="solid", color="black", weight=3]; 461[label="primDivInt (Pos (Succ ww84)) (Pos (Succ ww85))",fontsize=16,color="black",shape="box"];461 -> 473[label="",style="solid", color="black", weight=3]; 328[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) True ww26",fontsize=16,color="black",shape="box"];328 -> 352[label="",style="solid", color="black", weight=3]; 329 -> 57[label="",style="dashed", color="red", weight=0]; 329[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) False ww26",fontsize=16,color="magenta"];403[label="ww25",fontsize=16,color="green",shape="box"];404[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"];405[label="ww250",fontsize=16,color="green",shape="box"];406[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"];407[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"];408[label="ww251",fontsize=16,color="green",shape="box"];409[label="Pos Zero",fontsize=16,color="green",shape="box"];410[label="ww25",fontsize=16,color="green",shape="box"];411[label="ww25",fontsize=16,color="green",shape="box"];412[label="ww25",fontsize=16,color="green",shape="box"];413[label="ww25",fontsize=16,color="green",shape="box"];414[label="ww25",fontsize=16,color="green",shape="box"];415[label="ww25",fontsize=16,color="green",shape="box"];416[label="ww25",fontsize=16,color="green",shape="box"];417[label="ww25",fontsize=16,color="green",shape="box"];418[label="ww25",fontsize=16,color="green",shape="box"];419[label="ww25",fontsize=16,color="green",shape="box"];420[label="ww25",fontsize=16,color="green",shape="box"];421[label="ww25",fontsize=16,color="green",shape="box"];422[label="ww25",fontsize=16,color="green",shape="box"];423[label="ww25",fontsize=16,color="green",shape="box"];424[label="ww25",fontsize=16,color="green",shape="box"];425[label="ww25",fontsize=16,color="green",shape="box"];478[label="primIntToChar (primModInt (Pos (Succ ww87)) (Pos (Succ ww88)))",fontsize=16,color="black",shape="box"];478 -> 481[label="",style="solid", color="black", weight=3]; 473[label="Pos (primDivNatS (Succ ww84) (Succ ww85))",fontsize=16,color="green",shape="box"];473 -> 479[label="",style="dashed", color="green", weight=3]; 352 -> 426[label="",style="dashed", color="red", weight=0]; 352[label="(showChar (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 Zero)))))))))))))))))))))))))))))))))))))))))) . ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) . showChar (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 Zero))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="magenta"];352 -> 427[label="",style="dashed", color="magenta", weight=3]; 352 -> 428[label="",style="dashed", color="magenta", weight=3]; 352 -> 429[label="",style="dashed", color="magenta", weight=3]; 352 -> 430[label="",style="dashed", color="magenta", weight=3]; 352 -> 431[label="",style="dashed", color="magenta", weight=3]; 352 -> 432[label="",style="dashed", color="magenta", weight=3]; 352 -> 433[label="",style="dashed", color="magenta", weight=3]; 352 -> 434[label="",style="dashed", color="magenta", weight=3]; 481[label="primIntToChar (Pos (primModNatS (Succ ww87) (Succ ww88)))",fontsize=16,color="black",shape="box"];481 -> 489[label="",style="solid", color="black", weight=3]; 479[label="primDivNatS (Succ ww84) (Succ ww85)",fontsize=16,color="black",shape="triangle"];479 -> 482[label="",style="solid", color="black", weight=3]; 427[label="ww26",fontsize=16,color="green",shape="box"];428[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 (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];429[label="ww23",fontsize=16,color="green",shape="box"];430[label="ww24",fontsize=16,color="green",shape="box"];431[label="ww22",fontsize=16,color="green",shape="box"];432[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 (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];433[label="ww21",fontsize=16,color="green",shape="box"];434[label="ww25",fontsize=16,color="green",shape="box"];426[label="(showChar (Char (Succ ww72))) . ((shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77) . showChar (Char (Succ ww78))",fontsize=16,color="black",shape="triangle"];426 -> 445[label="",style="solid", color="black", weight=3]; 489[label="Char (primModNatS (Succ ww87) (Succ ww88))",fontsize=16,color="green",shape="box"];489 -> 493[label="",style="dashed", color="green", weight=3]; 482[label="primDivNatS0 ww84 ww85 (primGEqNatS ww84 ww85)",fontsize=16,color="burlywood",shape="box"];1373[label="ww84/Succ ww840",fontsize=10,color="white",style="solid",shape="box"];482 -> 1373[label="",style="solid", color="burlywood", weight=9]; 1373 -> 490[label="",style="solid", color="burlywood", weight=3]; 1374[label="ww84/Zero",fontsize=10,color="white",style="solid",shape="box"];482 -> 1374[label="",style="solid", color="burlywood", weight=9]; 1374 -> 491[label="",style="solid", color="burlywood", weight=3]; 445[label="showChar (Char (Succ ww72)) (((shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77) . showChar (Char (Succ ww78)))",fontsize=16,color="black",shape="box"];445 -> 462[label="",style="solid", color="black", weight=3]; 493[label="primModNatS (Succ ww87) (Succ ww88)",fontsize=16,color="black",shape="triangle"];493 -> 498[label="",style="solid", color="black", weight=3]; 490[label="primDivNatS0 (Succ ww840) ww85 (primGEqNatS (Succ ww840) ww85)",fontsize=16,color="burlywood",shape="box"];1375[label="ww85/Succ ww850",fontsize=10,color="white",style="solid",shape="box"];490 -> 1375[label="",style="solid", color="burlywood", weight=9]; 1375 -> 494[label="",style="solid", color="burlywood", weight=3]; 1376[label="ww85/Zero",fontsize=10,color="white",style="solid",shape="box"];490 -> 1376[label="",style="solid", color="burlywood", weight=9]; 1376 -> 495[label="",style="solid", color="burlywood", weight=3]; 491[label="primDivNatS0 Zero ww85 (primGEqNatS Zero ww85)",fontsize=16,color="burlywood",shape="box"];1377[label="ww85/Succ ww850",fontsize=10,color="white",style="solid",shape="box"];491 -> 1377[label="",style="solid", color="burlywood", weight=9]; 1377 -> 496[label="",style="solid", color="burlywood", weight=3]; 1378[label="ww85/Zero",fontsize=10,color="white",style="solid",shape="box"];491 -> 1378[label="",style="solid", color="burlywood", weight=9]; 1378 -> 497[label="",style="solid", color="burlywood", weight=3]; 462[label="(:) Char (Succ ww72) ((shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77) . showChar (Char (Succ ww78))",fontsize=16,color="green",shape="box"];462 -> 474[label="",style="dashed", color="green", weight=3]; 498[label="primModNatS0 ww87 ww88 (primGEqNatS ww87 ww88)",fontsize=16,color="burlywood",shape="box"];1379[label="ww87/Succ ww870",fontsize=10,color="white",style="solid",shape="box"];498 -> 1379[label="",style="solid", color="burlywood", weight=9]; 1379 -> 503[label="",style="solid", color="burlywood", weight=3]; 1380[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];498 -> 1380[label="",style="solid", color="burlywood", weight=9]; 1380 -> 504[label="",style="solid", color="burlywood", weight=3]; 494[label="primDivNatS0 (Succ ww840) (Succ ww850) (primGEqNatS (Succ ww840) (Succ ww850))",fontsize=16,color="black",shape="box"];494 -> 499[label="",style="solid", color="black", weight=3]; 495[label="primDivNatS0 (Succ ww840) Zero (primGEqNatS (Succ ww840) Zero)",fontsize=16,color="black",shape="box"];495 -> 500[label="",style="solid", color="black", weight=3]; 496[label="primDivNatS0 Zero (Succ ww850) (primGEqNatS Zero (Succ ww850))",fontsize=16,color="black",shape="box"];496 -> 501[label="",style="solid", color="black", weight=3]; 497[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];497 -> 502[label="",style="solid", color="black", weight=3]; 474[label="((shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77) . showChar (Char (Succ ww78))",fontsize=16,color="black",shape="box"];474 -> 480[label="",style="solid", color="black", weight=3]; 503[label="primModNatS0 (Succ ww870) ww88 (primGEqNatS (Succ ww870) ww88)",fontsize=16,color="burlywood",shape="box"];1381[label="ww88/Succ ww880",fontsize=10,color="white",style="solid",shape="box"];503 -> 1381[label="",style="solid", color="burlywood", weight=9]; 1381 -> 510[label="",style="solid", color="burlywood", weight=3]; 1382[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];503 -> 1382[label="",style="solid", color="burlywood", weight=9]; 1382 -> 511[label="",style="solid", color="burlywood", weight=3]; 504[label="primModNatS0 Zero ww88 (primGEqNatS Zero ww88)",fontsize=16,color="burlywood",shape="box"];1383[label="ww88/Succ ww880",fontsize=10,color="white",style="solid",shape="box"];504 -> 1383[label="",style="solid", color="burlywood", weight=9]; 1383 -> 512[label="",style="solid", color="burlywood", weight=3]; 1384[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];504 -> 1384[label="",style="solid", color="burlywood", weight=9]; 1384 -> 513[label="",style="solid", color="burlywood", weight=3]; 499 -> 1024[label="",style="dashed", color="red", weight=0]; 499[label="primDivNatS0 (Succ ww840) (Succ ww850) (primGEqNatS ww840 ww850)",fontsize=16,color="magenta"];499 -> 1025[label="",style="dashed", color="magenta", weight=3]; 499 -> 1026[label="",style="dashed", color="magenta", weight=3]; 499 -> 1027[label="",style="dashed", color="magenta", weight=3]; 499 -> 1028[label="",style="dashed", color="magenta", weight=3]; 500[label="primDivNatS0 (Succ ww840) Zero True",fontsize=16,color="black",shape="box"];500 -> 507[label="",style="solid", color="black", weight=3]; 501[label="primDivNatS0 Zero (Succ ww850) False",fontsize=16,color="black",shape="box"];501 -> 508[label="",style="solid", color="black", weight=3]; 502[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];502 -> 509[label="",style="solid", color="black", weight=3]; 480 -> 60[label="",style="dashed", color="red", weight=0]; 480[label="(shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77",fontsize=16,color="magenta"];480 -> 483[label="",style="dashed", color="magenta", weight=3]; 480 -> 484[label="",style="dashed", color="magenta", weight=3]; 480 -> 485[label="",style="dashed", color="magenta", weight=3]; 480 -> 486[label="",style="dashed", color="magenta", weight=3]; 480 -> 487[label="",style="dashed", color="magenta", weight=3]; 480 -> 488[label="",style="dashed", color="magenta", weight=3]; 510[label="primModNatS0 (Succ ww870) (Succ ww880) (primGEqNatS (Succ ww870) (Succ ww880))",fontsize=16,color="black",shape="box"];510 -> 520[label="",style="solid", color="black", weight=3]; 511[label="primModNatS0 (Succ ww870) Zero (primGEqNatS (Succ ww870) Zero)",fontsize=16,color="black",shape="box"];511 -> 521[label="",style="solid", color="black", weight=3]; 512[label="primModNatS0 Zero (Succ ww880) (primGEqNatS Zero (Succ ww880))",fontsize=16,color="black",shape="box"];512 -> 522[label="",style="solid", color="black", weight=3]; 513[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];513 -> 523[label="",style="solid", color="black", weight=3]; 1025[label="ww850",fontsize=16,color="green",shape="box"];1026[label="ww840",fontsize=16,color="green",shape="box"];1027[label="ww840",fontsize=16,color="green",shape="box"];1028[label="ww850",fontsize=16,color="green",shape="box"];1024[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS ww133 ww134)",fontsize=16,color="burlywood",shape="triangle"];1385[label="ww133/Succ ww1330",fontsize=10,color="white",style="solid",shape="box"];1024 -> 1385[label="",style="solid", color="burlywood", weight=9]; 1385 -> 1065[label="",style="solid", color="burlywood", weight=3]; 1386[label="ww133/Zero",fontsize=10,color="white",style="solid",shape="box"];1024 -> 1386[label="",style="solid", color="burlywood", weight=9]; 1386 -> 1066[label="",style="solid", color="burlywood", weight=3]; 507[label="Succ (primDivNatS (primMinusNatS (Succ ww840) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];507 -> 518[label="",style="dashed", color="green", weight=3]; 508[label="Zero",fontsize=16,color="green",shape="box"];509[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];509 -> 519[label="",style="dashed", color="green", weight=3]; 483[label="ww76",fontsize=16,color="green",shape="box"];484[label="ww73",fontsize=16,color="green",shape="box"];485[label="ww74",fontsize=16,color="green",shape="box"];486[label="showChar (Char (Succ ww78)) ww79",fontsize=16,color="black",shape="box"];486 -> 492[label="",style="solid", color="black", weight=3]; 487[label="ww75",fontsize=16,color="green",shape="box"];488[label="ww77",fontsize=16,color="green",shape="box"];520 -> 1085[label="",style="dashed", color="red", weight=0]; 520[label="primModNatS0 (Succ ww870) (Succ ww880) (primGEqNatS ww870 ww880)",fontsize=16,color="magenta"];520 -> 1086[label="",style="dashed", color="magenta", weight=3]; 520 -> 1087[label="",style="dashed", color="magenta", weight=3]; 520 -> 1088[label="",style="dashed", color="magenta", weight=3]; 520 -> 1089[label="",style="dashed", color="magenta", weight=3]; 521[label="primModNatS0 (Succ ww870) Zero True",fontsize=16,color="black",shape="box"];521 -> 532[label="",style="solid", color="black", weight=3]; 522[label="primModNatS0 Zero (Succ ww880) False",fontsize=16,color="black",shape="box"];522 -> 533[label="",style="solid", color="black", weight=3]; 523[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];523 -> 534[label="",style="solid", color="black", weight=3]; 1065[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) ww134)",fontsize=16,color="burlywood",shape="box"];1387[label="ww134/Succ ww1340",fontsize=10,color="white",style="solid",shape="box"];1065 -> 1387[label="",style="solid", color="burlywood", weight=9]; 1387 -> 1077[label="",style="solid", color="burlywood", weight=3]; 1388[label="ww134/Zero",fontsize=10,color="white",style="solid",shape="box"];1065 -> 1388[label="",style="solid", color="burlywood", weight=9]; 1388 -> 1078[label="",style="solid", color="burlywood", weight=3]; 1066[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero ww134)",fontsize=16,color="burlywood",shape="box"];1389[label="ww134/Succ ww1340",fontsize=10,color="white",style="solid",shape="box"];1066 -> 1389[label="",style="solid", color="burlywood", weight=9]; 1389 -> 1079[label="",style="solid", color="burlywood", weight=3]; 1390[label="ww134/Zero",fontsize=10,color="white",style="solid",shape="box"];1066 -> 1390[label="",style="solid", color="burlywood", weight=9]; 1390 -> 1080[label="",style="solid", color="burlywood", weight=3]; 518 -> 1268[label="",style="dashed", color="red", weight=0]; 518[label="primDivNatS (primMinusNatS (Succ ww840) Zero) (Succ Zero)",fontsize=16,color="magenta"];518 -> 1269[label="",style="dashed", color="magenta", weight=3]; 518 -> 1270[label="",style="dashed", color="magenta", weight=3]; 518 -> 1271[label="",style="dashed", color="magenta", weight=3]; 519 -> 1268[label="",style="dashed", color="red", weight=0]; 519[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];519 -> 1272[label="",style="dashed", color="magenta", weight=3]; 519 -> 1273[label="",style="dashed", color="magenta", weight=3]; 519 -> 1274[label="",style="dashed", color="magenta", weight=3]; 492[label="(:) Char (Succ ww78) ww79",fontsize=16,color="green",shape="box"];1086[label="ww880",fontsize=16,color="green",shape="box"];1087[label="ww870",fontsize=16,color="green",shape="box"];1088[label="ww880",fontsize=16,color="green",shape="box"];1089[label="ww870",fontsize=16,color="green",shape="box"];1085[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS ww138 ww139)",fontsize=16,color="burlywood",shape="triangle"];1391[label="ww138/Succ ww1380",fontsize=10,color="white",style="solid",shape="box"];1085 -> 1391[label="",style="solid", color="burlywood", weight=9]; 1391 -> 1126[label="",style="solid", color="burlywood", weight=3]; 1392[label="ww138/Zero",fontsize=10,color="white",style="solid",shape="box"];1085 -> 1392[label="",style="solid", color="burlywood", weight=9]; 1392 -> 1127[label="",style="solid", color="burlywood", weight=3]; 532 -> 1172[label="",style="dashed", color="red", weight=0]; 532[label="primModNatS (primMinusNatS (Succ ww870) Zero) (Succ Zero)",fontsize=16,color="magenta"];532 -> 1173[label="",style="dashed", color="magenta", weight=3]; 532 -> 1174[label="",style="dashed", color="magenta", weight=3]; 532 -> 1175[label="",style="dashed", color="magenta", weight=3]; 533[label="Succ Zero",fontsize=16,color="green",shape="box"];534 -> 1172[label="",style="dashed", color="red", weight=0]; 534[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];534 -> 1176[label="",style="dashed", color="magenta", weight=3]; 534 -> 1177[label="",style="dashed", color="magenta", weight=3]; 534 -> 1178[label="",style="dashed", color="magenta", weight=3]; 1077[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) (Succ ww1340))",fontsize=16,color="black",shape="box"];1077 -> 1128[label="",style="solid", color="black", weight=3]; 1078[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) Zero)",fontsize=16,color="black",shape="box"];1078 -> 1129[label="",style="solid", color="black", weight=3]; 1079[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero (Succ ww1340))",fontsize=16,color="black",shape="box"];1079 -> 1130[label="",style="solid", color="black", weight=3]; 1080[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1080 -> 1131[label="",style="solid", color="black", weight=3]; 1269[label="Succ ww840",fontsize=16,color="green",shape="box"];1270[label="Zero",fontsize=16,color="green",shape="box"];1271[label="Zero",fontsize=16,color="green",shape="box"];1268[label="primDivNatS (primMinusNatS ww145 ww146) (Succ ww147)",fontsize=16,color="burlywood",shape="triangle"];1393[label="ww145/Succ ww1450",fontsize=10,color="white",style="solid",shape="box"];1268 -> 1393[label="",style="solid", color="burlywood", weight=9]; 1393 -> 1293[label="",style="solid", color="burlywood", weight=3]; 1394[label="ww145/Zero",fontsize=10,color="white",style="solid",shape="box"];1268 -> 1394[label="",style="solid", color="burlywood", weight=9]; 1394 -> 1294[label="",style="solid", color="burlywood", weight=3]; 1272[label="Zero",fontsize=16,color="green",shape="box"];1273[label="Zero",fontsize=16,color="green",shape="box"];1274[label="Zero",fontsize=16,color="green",shape="box"];1126[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) ww139)",fontsize=16,color="burlywood",shape="box"];1395[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1126 -> 1395[label="",style="solid", color="burlywood", weight=9]; 1395 -> 1136[label="",style="solid", color="burlywood", weight=3]; 1396[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1126 -> 1396[label="",style="solid", color="burlywood", weight=9]; 1396 -> 1137[label="",style="solid", color="burlywood", weight=3]; 1127[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero ww139)",fontsize=16,color="burlywood",shape="box"];1397[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1127 -> 1397[label="",style="solid", color="burlywood", weight=9]; 1397 -> 1138[label="",style="solid", color="burlywood", weight=3]; 1398[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1127 -> 1398[label="",style="solid", color="burlywood", weight=9]; 1398 -> 1139[label="",style="solid", color="burlywood", weight=3]; 1173[label="Succ ww870",fontsize=16,color="green",shape="box"];1174[label="Zero",fontsize=16,color="green",shape="box"];1175[label="Zero",fontsize=16,color="green",shape="box"];1172[label="primModNatS (primMinusNatS ww141 ww142) (Succ ww143)",fontsize=16,color="burlywood",shape="triangle"];1399[label="ww141/Succ ww1410",fontsize=10,color="white",style="solid",shape="box"];1172 -> 1399[label="",style="solid", color="burlywood", weight=9]; 1399 -> 1203[label="",style="solid", color="burlywood", weight=3]; 1400[label="ww141/Zero",fontsize=10,color="white",style="solid",shape="box"];1172 -> 1400[label="",style="solid", color="burlywood", weight=9]; 1400 -> 1204[label="",style="solid", color="burlywood", weight=3]; 1176[label="Zero",fontsize=16,color="green",shape="box"];1177[label="Zero",fontsize=16,color="green",shape="box"];1178[label="Zero",fontsize=16,color="green",shape="box"];1128 -> 1024[label="",style="dashed", color="red", weight=0]; 1128[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS ww1330 ww1340)",fontsize=16,color="magenta"];1128 -> 1140[label="",style="dashed", color="magenta", weight=3]; 1128 -> 1141[label="",style="dashed", color="magenta", weight=3]; 1129[label="primDivNatS0 (Succ ww131) (Succ ww132) True",fontsize=16,color="black",shape="triangle"];1129 -> 1142[label="",style="solid", color="black", weight=3]; 1130[label="primDivNatS0 (Succ ww131) (Succ ww132) False",fontsize=16,color="black",shape="box"];1130 -> 1143[label="",style="solid", color="black", weight=3]; 1131 -> 1129[label="",style="dashed", color="red", weight=0]; 1131[label="primDivNatS0 (Succ ww131) (Succ ww132) True",fontsize=16,color="magenta"];1293[label="primDivNatS (primMinusNatS (Succ ww1450) ww146) (Succ ww147)",fontsize=16,color="burlywood",shape="box"];1401[label="ww146/Succ ww1460",fontsize=10,color="white",style="solid",shape="box"];1293 -> 1401[label="",style="solid", color="burlywood", weight=9]; 1401 -> 1295[label="",style="solid", color="burlywood", weight=3]; 1402[label="ww146/Zero",fontsize=10,color="white",style="solid",shape="box"];1293 -> 1402[label="",style="solid", color="burlywood", weight=9]; 1402 -> 1296[label="",style="solid", color="burlywood", weight=3]; 1294[label="primDivNatS (primMinusNatS Zero ww146) (Succ ww147)",fontsize=16,color="burlywood",shape="box"];1403[label="ww146/Succ ww1460",fontsize=10,color="white",style="solid",shape="box"];1294 -> 1403[label="",style="solid", color="burlywood", weight=9]; 1403 -> 1297[label="",style="solid", color="burlywood", weight=3]; 1404[label="ww146/Zero",fontsize=10,color="white",style="solid",shape="box"];1294 -> 1404[label="",style="solid", color="burlywood", weight=9]; 1404 -> 1298[label="",style="solid", color="burlywood", weight=3]; 1136[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) (Succ ww1390))",fontsize=16,color="black",shape="box"];1136 -> 1150[label="",style="solid", color="black", weight=3]; 1137[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) Zero)",fontsize=16,color="black",shape="box"];1137 -> 1151[label="",style="solid", color="black", weight=3]; 1138[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero (Succ ww1390))",fontsize=16,color="black",shape="box"];1138 -> 1152[label="",style="solid", color="black", weight=3]; 1139[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1139 -> 1153[label="",style="solid", color="black", weight=3]; 1203[label="primModNatS (primMinusNatS (Succ ww1410) ww142) (Succ ww143)",fontsize=16,color="burlywood",shape="box"];1405[label="ww142/Succ ww1420",fontsize=10,color="white",style="solid",shape="box"];1203 -> 1405[label="",style="solid", color="burlywood", weight=9]; 1405 -> 1209[label="",style="solid", color="burlywood", weight=3]; 1406[label="ww142/Zero",fontsize=10,color="white",style="solid",shape="box"];1203 -> 1406[label="",style="solid", color="burlywood", weight=9]; 1406 -> 1210[label="",style="solid", color="burlywood", weight=3]; 1204[label="primModNatS (primMinusNatS Zero ww142) (Succ ww143)",fontsize=16,color="burlywood",shape="box"];1407[label="ww142/Succ ww1420",fontsize=10,color="white",style="solid",shape="box"];1204 -> 1407[label="",style="solid", color="burlywood", weight=9]; 1407 -> 1211[label="",style="solid", color="burlywood", weight=3]; 1408[label="ww142/Zero",fontsize=10,color="white",style="solid",shape="box"];1204 -> 1408[label="",style="solid", color="burlywood", weight=9]; 1408 -> 1212[label="",style="solid", color="burlywood", weight=3]; 1140[label="ww1330",fontsize=16,color="green",shape="box"];1141[label="ww1340",fontsize=16,color="green",shape="box"];1142[label="Succ (primDivNatS (primMinusNatS (Succ ww131) (Succ ww132)) (Succ (Succ ww132)))",fontsize=16,color="green",shape="box"];1142 -> 1154[label="",style="dashed", color="green", weight=3]; 1143[label="Zero",fontsize=16,color="green",shape="box"];1295[label="primDivNatS (primMinusNatS (Succ ww1450) (Succ ww1460)) (Succ ww147)",fontsize=16,color="black",shape="box"];1295 -> 1299[label="",style="solid", color="black", weight=3]; 1296[label="primDivNatS (primMinusNatS (Succ ww1450) Zero) (Succ ww147)",fontsize=16,color="black",shape="box"];1296 -> 1300[label="",style="solid", color="black", weight=3]; 1297[label="primDivNatS (primMinusNatS Zero (Succ ww1460)) (Succ ww147)",fontsize=16,color="black",shape="box"];1297 -> 1301[label="",style="solid", color="black", weight=3]; 1298[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww147)",fontsize=16,color="black",shape="box"];1298 -> 1302[label="",style="solid", color="black", weight=3]; 1150 -> 1085[label="",style="dashed", color="red", weight=0]; 1150[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS ww1380 ww1390)",fontsize=16,color="magenta"];1150 -> 1159[label="",style="dashed", color="magenta", weight=3]; 1150 -> 1160[label="",style="dashed", color="magenta", weight=3]; 1151[label="primModNatS0 (Succ ww136) (Succ ww137) True",fontsize=16,color="black",shape="triangle"];1151 -> 1161[label="",style="solid", color="black", weight=3]; 1152[label="primModNatS0 (Succ ww136) (Succ ww137) False",fontsize=16,color="black",shape="box"];1152 -> 1162[label="",style="solid", color="black", weight=3]; 1153 -> 1151[label="",style="dashed", color="red", weight=0]; 1153[label="primModNatS0 (Succ ww136) (Succ ww137) True",fontsize=16,color="magenta"];1209[label="primModNatS (primMinusNatS (Succ ww1410) (Succ ww1420)) (Succ ww143)",fontsize=16,color="black",shape="box"];1209 -> 1217[label="",style="solid", color="black", weight=3]; 1210[label="primModNatS (primMinusNatS (Succ ww1410) Zero) (Succ ww143)",fontsize=16,color="black",shape="box"];1210 -> 1218[label="",style="solid", color="black", weight=3]; 1211[label="primModNatS (primMinusNatS Zero (Succ ww1420)) (Succ ww143)",fontsize=16,color="black",shape="box"];1211 -> 1219[label="",style="solid", color="black", weight=3]; 1212[label="primModNatS (primMinusNatS Zero Zero) (Succ ww143)",fontsize=16,color="black",shape="box"];1212 -> 1220[label="",style="solid", color="black", weight=3]; 1154 -> 1268[label="",style="dashed", color="red", weight=0]; 1154[label="primDivNatS (primMinusNatS (Succ ww131) (Succ ww132)) (Succ (Succ ww132))",fontsize=16,color="magenta"];1154 -> 1275[label="",style="dashed", color="magenta", weight=3]; 1154 -> 1276[label="",style="dashed", color="magenta", weight=3]; 1154 -> 1277[label="",style="dashed", color="magenta", weight=3]; 1299 -> 1268[label="",style="dashed", color="red", weight=0]; 1299[label="primDivNatS (primMinusNatS ww1450 ww1460) (Succ ww147)",fontsize=16,color="magenta"];1299 -> 1303[label="",style="dashed", color="magenta", weight=3]; 1299 -> 1304[label="",style="dashed", color="magenta", weight=3]; 1300 -> 479[label="",style="dashed", color="red", weight=0]; 1300[label="primDivNatS (Succ ww1450) (Succ ww147)",fontsize=16,color="magenta"];1300 -> 1305[label="",style="dashed", color="magenta", weight=3]; 1300 -> 1306[label="",style="dashed", color="magenta", weight=3]; 1301[label="primDivNatS Zero (Succ ww147)",fontsize=16,color="black",shape="triangle"];1301 -> 1307[label="",style="solid", color="black", weight=3]; 1302 -> 1301[label="",style="dashed", color="red", weight=0]; 1302[label="primDivNatS Zero (Succ ww147)",fontsize=16,color="magenta"];1159[label="ww1380",fontsize=16,color="green",shape="box"];1160[label="ww1390",fontsize=16,color="green",shape="box"];1161 -> 1172[label="",style="dashed", color="red", weight=0]; 1161[label="primModNatS (primMinusNatS (Succ ww136) (Succ ww137)) (Succ (Succ ww137))",fontsize=16,color="magenta"];1161 -> 1185[label="",style="dashed", color="magenta", weight=3]; 1161 -> 1186[label="",style="dashed", color="magenta", weight=3]; 1161 -> 1187[label="",style="dashed", color="magenta", weight=3]; 1162[label="Succ (Succ ww136)",fontsize=16,color="green",shape="box"];1217 -> 1172[label="",style="dashed", color="red", weight=0]; 1217[label="primModNatS (primMinusNatS ww1410 ww1420) (Succ ww143)",fontsize=16,color="magenta"];1217 -> 1227[label="",style="dashed", color="magenta", weight=3]; 1217 -> 1228[label="",style="dashed", color="magenta", weight=3]; 1218 -> 493[label="",style="dashed", color="red", weight=0]; 1218[label="primModNatS (Succ ww1410) (Succ ww143)",fontsize=16,color="magenta"];1218 -> 1229[label="",style="dashed", color="magenta", weight=3]; 1218 -> 1230[label="",style="dashed", color="magenta", weight=3]; 1219[label="primModNatS Zero (Succ ww143)",fontsize=16,color="black",shape="triangle"];1219 -> 1231[label="",style="solid", color="black", weight=3]; 1220 -> 1219[label="",style="dashed", color="red", weight=0]; 1220[label="primModNatS Zero (Succ ww143)",fontsize=16,color="magenta"];1275[label="Succ ww131",fontsize=16,color="green",shape="box"];1276[label="Succ ww132",fontsize=16,color="green",shape="box"];1277[label="Succ ww132",fontsize=16,color="green",shape="box"];1303[label="ww1450",fontsize=16,color="green",shape="box"];1304[label="ww1460",fontsize=16,color="green",shape="box"];1305[label="ww1450",fontsize=16,color="green",shape="box"];1306[label="ww147",fontsize=16,color="green",shape="box"];1307[label="Zero",fontsize=16,color="green",shape="box"];1185[label="Succ ww136",fontsize=16,color="green",shape="box"];1186[label="Succ ww137",fontsize=16,color="green",shape="box"];1187[label="Succ ww137",fontsize=16,color="green",shape="box"];1227[label="ww1410",fontsize=16,color="green",shape="box"];1228[label="ww1420",fontsize=16,color="green",shape="box"];1229[label="ww143",fontsize=16,color="green",shape="box"];1230[label="ww1410",fontsize=16,color="green",shape="box"];1231[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (10) Complex Obligation (AND) ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(ww131, ww132, Zero, Zero) -> new_primDivNatS00(ww131, ww132) new_primDivNatS00(ww131, ww132) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) new_primDivNatS(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS(ww1450, ww1460, ww147) new_primDivNatS1(Succ(ww840), Zero) -> new_primDivNatS(Succ(ww840), Zero, Zero) new_primDivNatS0(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) new_primDivNatS0(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) new_primDivNatS1(Succ(ww840), Succ(ww850)) -> new_primDivNatS0(ww840, ww850, ww840, ww850) new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) new_primDivNatS(Succ(ww1450), Zero, ww147) -> new_primDivNatS1(ww1450, ww147) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (12) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(ww131, ww132) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) new_primDivNatS(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS(ww1450, ww1460, ww147) new_primDivNatS(Succ(ww1450), Zero, ww147) -> new_primDivNatS1(ww1450, ww147) new_primDivNatS1(Succ(ww840), Zero) -> new_primDivNatS(Succ(ww840), Zero, Zero) new_primDivNatS1(Succ(ww840), Succ(ww850)) -> new_primDivNatS0(ww840, ww850, ww840, ww850) new_primDivNatS0(ww131, ww132, Zero, Zero) -> new_primDivNatS00(ww131, ww132) new_primDivNatS0(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) new_primDivNatS0(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (14) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primDivNatS(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS(ww1450, ww1460, ww147) new_primDivNatS1(Succ(ww840), Zero) -> new_primDivNatS(Succ(ww840), Zero, Zero) new_primDivNatS1(Succ(ww840), Succ(ww850)) -> new_primDivNatS0(ww840, ww850, ww840, ww850) 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 ---------------------------------------- (15) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(ww131, ww132) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) new_primDivNatS(Succ(ww1450), Zero, ww147) -> new_primDivNatS1(ww1450, ww147) new_primDivNatS0(ww131, ww132, Zero, Zero) -> new_primDivNatS00(ww131, ww132) new_primDivNatS0(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) new_primDivNatS0(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (16) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) 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(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Succ(Succ(Succ(Zero)))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Succ(Succ(Succ(Succ(Zero))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Succ(Zero)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(ww20000000000))))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))), ww21, ww22, ww23, ww24, ww25, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))), ww26, cg, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Succ(Succ(Zero))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt(ww72, ww73, ww74, ww75, ww76, ww77, ww78, ww79, h, ba) -> new_pt0(ww73, ww74, ww75, ww76, ww77, :(Char(Succ(ww78)), ww79), h, ba) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), :%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), :%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen(Neg(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) The TRS R consists of the following rules: new_showParen1(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(ww20000000000))))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt3(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))), ww21, ww22, ww23, ww24, ww25, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))), ww26, cg, bd) new_show6(ww21, bh) -> error([]) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show(ww21, bb, bc) -> error([]) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_show10(ww21) -> error([]) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show11(ww21) -> new_primShowInt0(ww21) new_showParen1(Pos(Succ(Succ(Zero))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_show8(ww21) -> error([]) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt3(ww72, ww73, ww74, ww75, ww76, ww77, ww78, ww79, h, ba) -> :(Char(Succ(ww72)), new_pt4(ww73, ww74, ww75, ww76, ww77, :(Char(Succ(ww78)), ww79), h, ba)) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_show13(ww21) -> error([]) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_psPs0([], ww60) -> ww60 new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_show5(ww21) -> error([]) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_show14(ww21, ce, cf) -> error([]) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_show2(ww21, bg) -> error([]) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_show1(ww21) -> error([]) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_show3(ww21) -> error([]) new_primModNatS4(ww143) -> Zero new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show4(ww21) -> error([]) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_showParen1(Neg(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_show0(ww21) -> error([]) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen1(Pos(Succ(Zero)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show12(ww21) -> error([]) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show7(ww21, ca, cb, cc) -> error([]) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_show9(ww21, cd) -> error([]) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_show15(ww21) -> error([]) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_primDivNatS4(ww147) -> Zero The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_pt3(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 67 less nodes. ---------------------------------------- (22) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) The TRS R consists of the following rules: new_showParen1(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(ww20000000000))))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt3(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))), ww21, ww22, ww23, ww24, ww25, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))), ww26, cg, bd) new_show6(ww21, bh) -> error([]) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show(ww21, bb, bc) -> error([]) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_show10(ww21) -> error([]) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show11(ww21) -> new_primShowInt0(ww21) new_showParen1(Pos(Succ(Succ(Zero))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_show8(ww21) -> error([]) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt3(ww72, ww73, ww74, ww75, ww76, ww77, ww78, ww79, h, ba) -> :(Char(Succ(ww72)), new_pt4(ww73, ww74, ww75, ww76, ww77, :(Char(Succ(ww78)), ww79), h, ba)) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_show13(ww21) -> error([]) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_psPs0([], ww60) -> ww60 new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_show5(ww21) -> error([]) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_show14(ww21, ce, cf) -> error([]) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_show2(ww21, bg) -> error([]) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_show1(ww21) -> error([]) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_show3(ww21) -> error([]) new_primModNatS4(ww143) -> Zero new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show4(ww21) -> error([]) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_showParen1(Neg(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_show0(ww21) -> error([]) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen1(Pos(Succ(Zero)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show12(ww21) -> error([]) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show7(ww21, ca, cb, cc) -> error([]) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_show9(ww21, cd) -> error([]) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_show15(ww21) -> error([]) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_primDivNatS4(ww147) -> Zero The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_pt3(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (23) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) we obtained the following new rules [LPAR04]: (new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6),new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6)) ---------------------------------------- (24) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) The TRS R consists of the following rules: new_showParen1(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(ww20000000000))))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt3(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))), ww21, ww22, ww23, ww24, ww25, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))), ww26, cg, bd) new_show6(ww21, bh) -> error([]) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show(ww21, bb, bc) -> error([]) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_show10(ww21) -> error([]) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show11(ww21) -> new_primShowInt0(ww21) new_showParen1(Pos(Succ(Succ(Zero))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_show8(ww21) -> error([]) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt3(ww72, ww73, ww74, ww75, ww76, ww77, ww78, ww79, h, ba) -> :(Char(Succ(ww72)), new_pt4(ww73, ww74, ww75, ww76, ww77, :(Char(Succ(ww78)), ww79), h, ba)) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_show13(ww21) -> error([]) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_psPs0([], ww60) -> ww60 new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_show5(ww21) -> error([]) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_show14(ww21, ce, cf) -> error([]) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_show2(ww21, bg) -> error([]) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_show1(ww21) -> error([]) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_show3(ww21) -> error([]) new_primModNatS4(ww143) -> Zero new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show4(ww21) -> error([]) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_showParen1(Neg(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_show0(ww21) -> error([]) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen1(Pos(Succ(Zero)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show12(ww21) -> error([]) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show7(ww21, ca, cb, cc) -> error([]) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_show9(ww21, cd) -> error([]) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_show15(ww21) -> error([]) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_primDivNatS4(ww147) -> Zero The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_pt3(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (25) 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. ---------------------------------------- (26) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_pt3(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (27) 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_pt3(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) ---------------------------------------- (28) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (29) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) at position [6] we obtained the following new rules [LPAR04]: (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, be)), be, be),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, be)), be, be)) ---------------------------------------- (30) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, be)), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (31) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, be)), be, be) at position [6] we obtained the following new rules [LPAR04]: (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), new_psPs0(:(Char(Succ(ww23)), :(Char(Succ(ww24)), [])), new_showsPrec(ww25, ww26, be))), be, be),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), new_psPs0(:(Char(Succ(ww23)), :(Char(Succ(ww24)), [])), new_showsPrec(ww25, ww26, be))), be, be)) ---------------------------------------- (32) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), new_psPs0(:(Char(Succ(ww23)), :(Char(Succ(ww24)), [])), new_showsPrec(ww25, ww26, be))), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (33) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), new_psPs0(:(Char(Succ(ww23)), :(Char(Succ(ww24)), [])), new_showsPrec(ww25, ww26, be))), be, be) at position [6,1] we obtained the following new rules [LPAR04]: (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), new_psPs0(:(Char(Succ(ww24)), []), new_showsPrec(ww25, ww26, be)))), be, be),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), new_psPs0(:(Char(Succ(ww24)), []), new_showsPrec(ww25, ww26, be)))), be, be)) ---------------------------------------- (34) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), new_psPs0(:(Char(Succ(ww24)), []), new_showsPrec(ww25, ww26, be)))), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (35) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), new_psPs0(:(Char(Succ(ww24)), []), new_showsPrec(ww25, ww26, be)))), be, be) at position [6,1,1] we obtained the following new rules [LPAR04]: (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_psPs0([], new_showsPrec(ww25, ww26, be))))), be, be),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_psPs0([], new_showsPrec(ww25, ww26, be))))), be, be)) ---------------------------------------- (36) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_psPs0([], new_showsPrec(ww25, ww26, be))))), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (37) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_psPs0([], new_showsPrec(ww25, ww26, be))))), be, be) at position [6,1,1,1] we obtained the following new rules [LPAR04]: (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be)) ---------------------------------------- (38) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (39) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_Char, ty_Char) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Char),new_showParen00(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, z2, ty_Char, ty_Char) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Char)) ---------------------------------------- (40) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(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, z2, ty_Char, ty_Char) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Char) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (41) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (42) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (43) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_HugsException, ty_HugsException) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_HugsException),new_showParen00(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, z2, ty_HugsException, ty_HugsException) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_HugsException)) ---------------------------------------- (44) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(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, z2, ty_HugsException, ty_HugsException) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_HugsException) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (45) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (46) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (47) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(app(ty_@2, x6), x7)),new_showParen00(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, z2, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(app(ty_@2, x6), x7))) ---------------------------------------- (48) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(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, z2, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(app(ty_@2, x6), x7)) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (49) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (50) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (51) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_Double, ty_Double) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Double),new_showParen00(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, z2, ty_Double, ty_Double) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Double)) ---------------------------------------- (52) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(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, z2, ty_Double, ty_Double) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Double) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (53) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (54) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (55) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_@0, ty_@0) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_@0),new_showParen00(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, z2, ty_@0, ty_@0) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_@0)) ---------------------------------------- (56) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(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, z2, ty_@0, ty_@0) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_@0) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (57) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (58) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (59) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, be), app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) we obtained the following new rules [LPAR04]: (new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8),new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8)) ---------------------------------------- (60) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (61) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(ty_IO, x6)),new_showParen00(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, z2, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(ty_IO, x6))) ---------------------------------------- (62) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(ty_IO, x6)) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (63) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (64) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (65) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_Int, ty_Int) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Int),new_showParen00(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, z2, ty_Int, ty_Int) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Int)) ---------------------------------------- (66) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, ty_Int, ty_Int) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Int) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (67) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (68) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (69) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(app(app(ty_@3, x6), x7), x8)),new_showParen00(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, z2, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(app(app(ty_@3, x6), x7), x8))) ---------------------------------------- (70) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(app(app(ty_@3, x6), x7), x8)) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) 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_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (73) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(app(ty_Either, x6), x7)),new_showParen00(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, z2, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(app(ty_Either, x6), x7))) ---------------------------------------- (74) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(app(ty_Either, x6), x7)) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) 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 1 less node. ---------------------------------------- (76) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (77) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_Float, ty_Float) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Float),new_showParen00(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, z2, ty_Float, ty_Float) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Float)) ---------------------------------------- (78) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, ty_Float, ty_Float) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Float) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (79) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (80) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (81) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_Integer, ty_Integer) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Integer),new_showParen00(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, z2, ty_Integer, ty_Integer) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Integer)) ---------------------------------------- (82) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, ty_Integer, ty_Integer) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Integer) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (83) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (84) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (85) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(ty_Maybe, x6)),new_showParen00(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, z2, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(ty_Maybe, x6))) ---------------------------------------- (86) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(ty_Maybe, x6)) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (87) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (88) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (89) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_Ordering, ty_Ordering) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Ordering),new_showParen00(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, z2, ty_Ordering, ty_Ordering) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Ordering)) ---------------------------------------- (90) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, ty_Ordering, ty_Ordering) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Ordering) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (91) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (92) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (93) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_Bool, ty_Bool) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Bool),new_showParen00(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, z2, ty_Bool, ty_Bool) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Bool)) ---------------------------------------- (94) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, ty_Bool, ty_Bool) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_Bool) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (95) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (96) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (97) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_IOErrorKind),new_showParen00(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, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_IOErrorKind)) ---------------------------------------- (98) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_IOErrorKind) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (99) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (100) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (101) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, ty_IOError, ty_IOError) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_IOError),new_showParen00(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, z2, ty_IOError, ty_IOError) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_IOError)) ---------------------------------------- (102) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, ty_IOError, ty_IOError) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, ty_IOError) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (103) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (104) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (105) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bd) we obtained the following new rules [LPAR04]: (new_showParen00(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, z2, app(ty_[], x6), app(ty_[], x6)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(ty_[], x6)),new_showParen00(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, z2, app(ty_[], x6), app(ty_[], x6)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(ty_[], x6))) ---------------------------------------- (106) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(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, z2, app(ty_[], x6), app(ty_[], x6)) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, z2, app(ty_[], x6)) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (107) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (108) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (109) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, :(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), new_showsPrec(ww25, ww26, be)))), be, be) we obtained the following new rules [LPAR04]: (new_showParen00(:%(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, z2, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(Pos(Zero), 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, z2, x7)))), x7, x7),new_showParen00(:%(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, z2, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(Pos(Zero), 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, z2, x7)))), x7, x7)) ---------------------------------------- (110) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) new_showParen00(:%(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, z2, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(Pos(Zero), 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, z2, x7)))), x7, x7) The TRS R consists of the following rules: new_pt2(ww22, ww23, ww24, ww25, ww26, bd) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bd)) new_showsPrec(ww25, ww26, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show7(ww25, de, df, dg), ww26) new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show15(ww25), ww26) new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show4(ww25), ww26) new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show13(ww25), ww26) new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show5(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show14(ww25, ea, eb), ww26) new_showsPrec(ww25, ww26, app(ty_[], dd)) -> new_psPs0(new_show6(ww25, dd), ww26) new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show11(ww25), ww26) new_showsPrec(ww25, ww26, app(ty_IO, dh)) -> new_psPs0(new_show9(ww25, dh), ww26) new_showsPrec(ww25, ww26, app(ty_Maybe, dc)) -> new_psPs0(new_show2(ww25, dc), ww26) new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bf)) -> new_showParen1(Pos(Zero), ww250, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww251, ww26, bf, bf) new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show0(ww25), ww26) new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show1(ww25), ww26) new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show10(ww25), ww26) new_showsPrec(ww25, ww26, app(app(ty_Either, da), db)) -> new_psPs0(new_show(ww25, da, db), ww26) new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show8(ww25), ww26) new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show12(ww25), ww26) new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) new_psPs0([], ww60) -> ww60 new_show12(ww21) -> error([]) new_show8(ww21) -> error([]) new_show(ww21, bb, bc) -> error([]) new_show10(ww21) -> error([]) new_show1(ww21) -> error([]) new_show0(ww21) -> error([]) new_pt4(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, be), bd) -> new_showParen1(Pos(Zero), ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, new_pt2(ww22, ww23, ww24, ww25, ww26, be), be, be) new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) -> new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, cg, bd) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bd) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bh), bd) -> new_psPs0(new_show6(ww21, bh), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bd) -> new_psPs0(new_show15(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bd) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bd) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bd) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bd) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bd) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bd) -> new_psPs0(new_show10(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, bb), bc), bd) -> new_psPs0(new_show(ww21, bb, bc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, ce), cf), bd) -> new_psPs0(new_show14(ww21, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bd) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bd) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, cd), bd) -> new_psPs0(new_show9(ww21, cd), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, bg), bd) -> new_psPs0(new_show2(ww21, bg), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, ca), cb), cc), bd) -> new_psPs0(new_show7(ww21, ca, cb, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_pt4(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bd) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bd)) new_show13(ww21) -> error([]) new_show7(ww21, ca, cb, cc) -> error([]) new_show2(ww21, bg) -> error([]) new_show9(ww21, cd) -> error([]) new_show11(ww21) -> new_primShowInt0(ww21) new_primShowInt0(Neg(ww210)) -> :(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(ww210))) new_primShowInt0(Pos(Succ(ww2100))) -> new_psPs0(new_primShowInt0(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww2100, 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_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) new_primModNatS02(ww136, ww137, Zero, Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS01(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS02(ww870, ww880, ww870, ww880) new_primModNatS02(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS01(ww136, ww137) new_primModNatS02(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS02(ww136, ww137, ww1380, ww1390) new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) new_primModNatS02(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) new_primModNatS4(ww143) -> Zero new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_show14(ww21, ce, cf) -> error([]) new_show3(ww21) -> error([]) new_show4(ww21) -> error([]) new_show5(ww21) -> error([]) new_show15(ww21) -> error([]) new_show6(ww21, bh) -> error([]) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primShowInt0(Pos(Succ(x0))) new_primModNatS02(x0, x1, Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) new_show9(x0, x1) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_show14(x0, x1, x2) new_primDivNatS01(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primModNatS02(x0, x1, Succ(x2), Succ(x3)) new_show(x0, x1, x2) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_Bool) new_showsPrec(x0, x1, ty_@0) new_primModNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primModNatS2(Zero, Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1) new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) new_primShowInt0(Pos(Zero)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_show1(x0) new_psPs0(:(x0, x1), x2) new_primModNatS3(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0), x1) new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) new_showsPrec(x0, x1, ty_Float) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) new_show12(x0) new_show8(x0) new_div(x0, x1) new_primModNatS3(Zero, Zero, x0) new_primModNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS02(x0, x1, Zero, Zero) new_show6(x0, x1) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show15(x0) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) new_pt4(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) new_showsPrec(x0, x1, ty_HugsException) new_show2(x0, x1) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_primModNatS3(Succ(x0), Zero, x1) new_primModNatS2(Zero, Succ(x0)) new_show5(x0) new_showsPrec(x0, x1, ty_Integer) new_primDivNatS4(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_pt4(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_primModNatS02(x0, x1, Succ(x2), Zero) new_primModNatS4(x0) new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) new_primIntToChar(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, ty_Int) new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1)) new_show4(x0) new_psPs0([], x0) new_pt4(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_pt4(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_pt4(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(x0, x1, ty_IOErrorKind) new_pt4(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_pt2(x0, x1, x2, x3, x4, x5) new_show0(x0) new_primDivNatS3(Succ(x0), Zero) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) new_show7(x0, x1, x2, x3) new_pt4(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show13(x0) new_show3(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, ty_Char) new_pt4(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_pt4(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) new_pt4(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show10(x0) new_showsPrec(x0, x1, ty_Double) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (111) 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_showParen(Pos(Zero), 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, z6, z6) -> new_showParen00(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, z6, z6) The graph contains the following edges 2 >= 1, 3 >= 2, 4 > 2, 5 >= 2, 4 >= 3, 3 >= 4, 4 > 4, 5 >= 4, 6 >= 5, 7 >= 6, 8 >= 7, 9 >= 7, 8 >= 8, 9 >= 8 *new_showParen00(:%(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))))))))))))))))))))))))))))))), :%(x5, x6), z2, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(Pos(Zero), x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z2, x8, x8) The graph contains the following edges 5 > 2, 2 >= 3, 3 > 3, 4 >= 3, 3 >= 4, 2 >= 5, 3 > 5, 4 >= 5, 5 > 6, 6 >= 7, 7 > 8, 8 > 8, 7 > 9, 8 > 9 *new_showParen00(:%(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, z2, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(Pos(Zero), 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, z2, x7)))), x7, x7) The graph contains the following edges 1 > 2, 2 >= 3, 3 > 3, 4 >= 3, 3 >= 4, 2 >= 5, 3 > 5, 4 >= 5, 1 > 6, 7 > 8, 8 > 8, 7 > 9, 8 > 9 ---------------------------------------- (112) YES ---------------------------------------- (113) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Neg(ww210)) -> new_primShowInt(Pos(ww210)) new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS4(ww147) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_div(x0, x1) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (114) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (115) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS4(ww147) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_div(x0, x1) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (116) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ---------------------------------------- (117) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_div(ww84, ww85) -> Pos(new_primDivNatS3(ww84, ww85)) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS4(ww147) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_div(x0, x1) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (118) 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. ---------------------------------------- (119) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_div(x0, x1) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (120) 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) ---------------------------------------- (121) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (122) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (123) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (124) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, 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_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), new_primShowInt(Pos(Succ(x1))) -> new_primShowInt(Pos(new_primDivNatS3(x1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) which results in the following constraint: (1) (new_primShowInt(Pos(new_primDivNatS3(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_primDivNatS3(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_primDivNatS3(x0, x2)=Succ(x1) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS3(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_primDivNatS3(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_primDivNatS3(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_primDivNatS3(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_primDivNatS3(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_primDivNatS3(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_primDivNatS3(Succ(x12), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ==> new_primShowInt(Pos(Succ(Succ(x12))))_>=_new_primShowInt(Pos(new_primDivNatS3(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_primDivNatS3(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_primDivNatS3(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_primDivNatS3(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(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) *(new_primShowInt(Pos(Succ(Succ(Succ(x10)))))_>=_new_primShowInt(Pos(new_primDivNatS3(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. ---------------------------------------- (125) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (126) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS3(ww2100, 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))) ---------------------------------------- (127) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) 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 1 less node. ---------------------------------------- (129) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (130) 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))) ---------------------------------------- (131) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (132) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (133) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (134) 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))) ---------------------------------------- (135) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) 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 1 less node. ---------------------------------------- (137) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (138) 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))) ---------------------------------------- (139) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) 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 1 less node. ---------------------------------------- (141) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (142) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (143) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (144) 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. ---------------------------------------- (145) 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_primDivNatS3(Succ(ww840), Succ(ww850)) -> new_primDivNatS02(ww840, ww850, ww840, ww850) new_primDivNatS3(Zero, Succ(ww850)) -> Zero new_primDivNatS02(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS02(ww131, ww132, ww1330, ww1340) new_primDivNatS02(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Zero) -> new_primDivNatS01(ww131, ww132) new_primDivNatS02(ww131, ww132, Zero, Succ(ww1340)) -> Zero new_primDivNatS01(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS3(ww1450, ww147) new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS4(ww147) new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS4(ww147) new_primDivNatS4(ww147) -> Zero new_primDivNatS3(Succ(ww840), Zero) -> Succ(new_primDivNatS2(Succ(ww840), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS02(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1, Zero, Zero) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS4(x0) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS02(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (146) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(ww620, ww621), ww60) -> new_psPs(ww621, ww60) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (147) 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(:(ww620, ww621), ww60) -> new_psPs(ww621, ww60) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (148) YES ---------------------------------------- (149) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(ww1410), Zero, ww143) -> new_primModNatS1(ww1410, ww143) new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero) new_primModNatS00(ww136, ww137) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS0(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS(ww1410, ww1420, ww143) new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) new_primModNatS1(Succ(ww870), Succ(ww880)) -> new_primModNatS0(ww870, ww880, ww870, ww880) new_primModNatS0(ww136, ww137, Zero, Zero) -> new_primModNatS00(ww136, ww137) new_primModNatS1(Succ(ww870), Zero) -> new_primModNatS(Succ(ww870), Zero, Zero) R is empty. Q is empty. 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 1 less node. ---------------------------------------- (151) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS1(Succ(ww870), Succ(ww880)) -> new_primModNatS0(ww870, ww880, ww870, ww880) new_primModNatS0(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS(ww1410, ww1420, ww143) new_primModNatS(Succ(ww1410), Zero, ww143) -> new_primModNatS1(ww1410, ww143) new_primModNatS1(Succ(ww870), Zero) -> new_primModNatS(Succ(ww870), Zero, Zero) new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) new_primModNatS0(ww136, ww137, Zero, Zero) -> new_primModNatS00(ww136, ww137) new_primModNatS00(ww136, ww137) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (152) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primModNatS1(Succ(ww870), Succ(ww880)) -> new_primModNatS0(ww870, ww880, ww870, ww880) new_primModNatS(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS(ww1410, ww1420, ww143) new_primModNatS1(Succ(ww870), Zero) -> new_primModNatS(Succ(ww870), 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 ---------------------------------------- (153) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) new_primModNatS(Succ(ww1410), Zero, ww143) -> new_primModNatS1(ww1410, ww143) new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) new_primModNatS0(ww136, ww137, Zero, Zero) -> new_primModNatS00(ww136, ww137) new_primModNatS00(ww136, ww137) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) R is empty. Q is empty. 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 4 less nodes. ---------------------------------------- (155) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (156) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (157) YES ---------------------------------------- (158) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="showsPrec",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="showsPrec ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="showsPrec ww3 ww4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 5[label="showsPrec ww3 ww4 ww5",fontsize=16,color="burlywood",shape="triangle"];1308[label="ww4/ww40 :% ww41",fontsize=10,color="white",style="solid",shape="box"];5 -> 1308[label="",style="solid", color="burlywood", weight=9]; 1308 -> 6[label="",style="solid", color="burlywood", weight=3]; 6[label="showsPrec ww3 (ww40 :% ww41) ww5",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7 -> 27[label="",style="dashed", color="red", weight=0]; 7[label="showParen (ww3 > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww40) . (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 ww41) ww5",fontsize=16,color="magenta"];7 -> 28[label="",style="dashed", color="magenta", weight=3]; 7 -> 29[label="",style="dashed", color="magenta", weight=3]; 7 -> 30[label="",style="dashed", color="magenta", weight=3]; 7 -> 31[label="",style="dashed", color="magenta", weight=3]; 7 -> 32[label="",style="dashed", color="magenta", weight=3]; 7 -> 33[label="",style="dashed", color="magenta", weight=3]; 7 -> 34[label="",style="dashed", color="magenta", weight=3]; 28[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"];29[label="ww40",fontsize=16,color="green",shape="box"];30[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"];31[label="ww5",fontsize=16,color="green",shape="box"];32[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"];33[label="ww41",fontsize=16,color="green",shape="box"];34[label="ww3",fontsize=16,color="green",shape="box"];27[label="showParen (ww20 > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) ww26",fontsize=16,color="black",shape="triangle"];27 -> 42[label="",style="solid", color="black", weight=3]; 42[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (ww20 > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww26",fontsize=16,color="black",shape="box"];42 -> 43[label="",style="solid", color="black", weight=3]; 43[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (compare ww20 (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3]; 44[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt ww20 (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1309[label="ww20/Pos ww200",fontsize=10,color="white",style="solid",shape="box"];44 -> 1309[label="",style="solid", color="burlywood", weight=9]; 1309 -> 45[label="",style="solid", color="burlywood", weight=3]; 1310[label="ww20/Neg ww200",fontsize=10,color="white",style="solid",shape="box"];44 -> 1310[label="",style="solid", color="burlywood", weight=9]; 1310 -> 46[label="",style="solid", color="burlywood", weight=3]; 45[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Pos ww200) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1311[label="ww200/Succ ww2000",fontsize=10,color="white",style="solid",shape="box"];45 -> 1311[label="",style="solid", color="burlywood", weight=9]; 1311 -> 47[label="",style="solid", color="burlywood", weight=3]; 1312[label="ww200/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 1312[label="",style="solid", color="burlywood", weight=9]; 1312 -> 48[label="",style="solid", color="burlywood", weight=3]; 46[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Neg ww200) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1313[label="ww200/Succ ww2000",fontsize=10,color="white",style="solid",shape="box"];46 -> 1313[label="",style="solid", color="burlywood", weight=9]; 1313 -> 49[label="",style="solid", color="burlywood", weight=3]; 1314[label="ww200/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 1314[label="",style="solid", color="burlywood", weight=9]; 1314 -> 50[label="",style="solid", color="burlywood", weight=3]; 47[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Pos (Succ ww2000)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];47 -> 51[label="",style="solid", color="black", weight=3]; 48[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3]; 49[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Neg (Succ ww2000)) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];49 -> 53[label="",style="solid", color="black", weight=3]; 50[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpInt (Neg Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww26",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3]; 51[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww2000) (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww26",fontsize=16,color="black",shape="box"];51 -> 55[label="",style="solid", color="black", weight=3]; 52[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww26",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3]; 53[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="black",shape="triangle"];53 -> 57[label="",style="solid", color="black", weight=3]; 54 -> 53[label="",style="dashed", color="red", weight=0]; 54[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];55[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww2000 (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1315[label="ww2000/Succ ww20000",fontsize=10,color="white",style="solid",shape="box"];55 -> 1315[label="",style="solid", color="burlywood", weight=9]; 1315 -> 58[label="",style="solid", color="burlywood", weight=3]; 1316[label="ww2000/Zero",fontsize=10,color="white",style="solid",shape="box"];55 -> 1316[label="",style="solid", color="burlywood", weight=9]; 1316 -> 59[label="",style="solid", color="burlywood", weight=3]; 56 -> 53[label="",style="dashed", color="red", weight=0]; 56[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];57[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) False ww26",fontsize=16,color="black",shape="triangle"];57 -> 60[label="",style="solid", color="black", weight=3]; 58[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww20000) (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))) == GT) ww26",fontsize=16,color="black",shape="box"];58 -> 61[label="",style="solid", color="black", weight=3]; 59[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))) == GT) ww26",fontsize=16,color="black",shape="box"];59 -> 62[label="",style="solid", color="black", weight=3]; 60[label="(shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="black",shape="triangle"];60 -> 63[label="",style="solid", color="black", weight=3]; 61[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww20000 (Succ (Succ (Succ (Succ (Succ Zero))))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1317[label="ww20000/Succ ww200000",fontsize=10,color="white",style="solid",shape="box"];61 -> 1317[label="",style="solid", color="burlywood", weight=9]; 1317 -> 64[label="",style="solid", color="burlywood", weight=3]; 1318[label="ww20000/Zero",fontsize=10,color="white",style="solid",shape="box"];61 -> 1318[label="",style="solid", color="burlywood", weight=9]; 1318 -> 65[label="",style="solid", color="burlywood", weight=3]; 62 -> 53[label="",style="dashed", color="red", weight=0]; 62[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];63[label="shows ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];63 -> 66[label="",style="solid", color="black", weight=3]; 64[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww200000) (Succ (Succ (Succ (Succ (Succ Zero))))) == GT) ww26",fontsize=16,color="black",shape="box"];64 -> 67[label="",style="solid", color="black", weight=3]; 65[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ Zero))))) == GT) ww26",fontsize=16,color="black",shape="box"];65 -> 68[label="",style="solid", color="black", weight=3]; 66[label="showsPrec (Pos Zero) ww21 ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="blue",shape="box"];1319[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1319[label="",style="solid", color="blue", weight=9]; 1319 -> 69[label="",style="solid", color="blue", weight=3]; 1320[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1320[label="",style="solid", color="blue", weight=9]; 1320 -> 70[label="",style="solid", color="blue", weight=3]; 1321[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1321[label="",style="solid", color="blue", weight=9]; 1321 -> 71[label="",style="solid", color="blue", weight=3]; 1322[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1322[label="",style="solid", color="blue", weight=9]; 1322 -> 72[label="",style="solid", color="blue", weight=3]; 1323[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1323[label="",style="solid", color="blue", weight=9]; 1323 -> 73[label="",style="solid", color="blue", weight=3]; 1324[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1324[label="",style="solid", color="blue", weight=9]; 1324 -> 74[label="",style="solid", color="blue", weight=3]; 1325[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1325[label="",style="solid", color="blue", weight=9]; 1325 -> 75[label="",style="solid", color="blue", weight=3]; 1326[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1326[label="",style="solid", color="blue", weight=9]; 1326 -> 76[label="",style="solid", color="blue", weight=3]; 1327[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1327[label="",style="solid", color="blue", weight=9]; 1327 -> 77[label="",style="solid", color="blue", weight=3]; 1328[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1328[label="",style="solid", color="blue", weight=9]; 1328 -> 78[label="",style="solid", color="blue", weight=3]; 1329[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1329[label="",style="solid", color="blue", weight=9]; 1329 -> 79[label="",style="solid", color="blue", weight=3]; 1330[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1330[label="",style="solid", color="blue", weight=9]; 1330 -> 80[label="",style="solid", color="blue", weight=3]; 1331[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1331[label="",style="solid", color="blue", weight=9]; 1331 -> 81[label="",style="solid", color="blue", weight=3]; 1332[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1332[label="",style="solid", color="blue", weight=9]; 1332 -> 82[label="",style="solid", color="blue", weight=3]; 1333[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1333[label="",style="solid", color="blue", weight=9]; 1333 -> 83[label="",style="solid", color="blue", weight=3]; 1334[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1334[label="",style="solid", color="blue", weight=9]; 1334 -> 84[label="",style="solid", color="blue", weight=3]; 1335[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1335[label="",style="solid", color="blue", weight=9]; 1335 -> 85[label="",style="solid", color="blue", weight=3]; 1336[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];66 -> 1336[label="",style="solid", color="blue", weight=9]; 1336 -> 86[label="",style="solid", color="blue", weight=3]; 67[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww200000 (Succ (Succ (Succ (Succ Zero)))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1337[label="ww200000/Succ ww2000000",fontsize=10,color="white",style="solid",shape="box"];67 -> 1337[label="",style="solid", color="burlywood", weight=9]; 1337 -> 87[label="",style="solid", color="burlywood", weight=3]; 1338[label="ww200000/Zero",fontsize=10,color="white",style="solid",shape="box"];67 -> 1338[label="",style="solid", color="burlywood", weight=9]; 1338 -> 88[label="",style="solid", color="burlywood", weight=3]; 68 -> 53[label="",style="dashed", color="red", weight=0]; 68[label="showParen0 ((shows ww21) . 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(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww2000000) (Succ (Succ (Succ (Succ Zero)))) == GT) ww26",fontsize=16,color="black",shape="box"];87 -> 107[label="",style="solid", color="black", weight=3]; 88[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero (Succ (Succ (Succ (Succ Zero)))) == GT) ww26",fontsize=16,color="black",shape="box"];88 -> 108[label="",style="solid", color="black", weight=3]; 89 -> 224[label="",style="dashed", color="red", weight=0]; 89[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];89 -> 225[label="",style="dashed", color="magenta", weight=3]; 89 -> 226[label="",style="dashed", color="magenta", weight=3]; 90[label="showsPrec (Pos Zero) (ww210 :% ww211) ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];90 -> 110[label="",style="solid", color="black", weight=3]; 91 -> 224[label="",style="dashed", color="red", weight=0]; 91[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];91 -> 227[label="",style="dashed", color="magenta", weight=3]; 91 -> 228[label="",style="dashed", color="magenta", weight=3]; 92 -> 224[label="",style="dashed", color="red", weight=0]; 92[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];92 -> 229[label="",style="dashed", color="magenta", weight=3]; 92 -> 230[label="",style="dashed", color="magenta", weight=3]; 93 -> 224[label="",style="dashed", color="red", weight=0]; 93[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];93 -> 231[label="",style="dashed", color="magenta", weight=3]; 93 -> 232[label="",style="dashed", color="magenta", weight=3]; 94 -> 224[label="",style="dashed", color="red", weight=0]; 94[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];94 -> 233[label="",style="dashed", color="magenta", weight=3]; 94 -> 234[label="",style="dashed", color="magenta", weight=3]; 95 -> 224[label="",style="dashed", color="red", weight=0]; 95[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];95 -> 235[label="",style="dashed", color="magenta", weight=3]; 95 -> 236[label="",style="dashed", color="magenta", weight=3]; 96 -> 224[label="",style="dashed", color="red", weight=0]; 96[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];96 -> 237[label="",style="dashed", color="magenta", weight=3]; 96 -> 238[label="",style="dashed", color="magenta", weight=3]; 97 -> 224[label="",style="dashed", color="red", weight=0]; 97[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];97 -> 239[label="",style="dashed", color="magenta", weight=3]; 97 -> 240[label="",style="dashed", color="magenta", weight=3]; 98 -> 224[label="",style="dashed", color="red", weight=0]; 98[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];98 -> 241[label="",style="dashed", color="magenta", weight=3]; 98 -> 242[label="",style="dashed", color="magenta", weight=3]; 99 -> 224[label="",style="dashed", color="red", weight=0]; 99[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];99 -> 243[label="",style="dashed", color="magenta", weight=3]; 99 -> 244[label="",style="dashed", color="magenta", weight=3]; 100 -> 224[label="",style="dashed", color="red", weight=0]; 100[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];100 -> 245[label="",style="dashed", color="magenta", weight=3]; 100 -> 246[label="",style="dashed", color="magenta", weight=3]; 101 -> 224[label="",style="dashed", color="red", weight=0]; 101[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];101 -> 247[label="",style="dashed", color="magenta", weight=3]; 101 -> 248[label="",style="dashed", color="magenta", weight=3]; 102 -> 224[label="",style="dashed", color="red", weight=0]; 102[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];102 -> 249[label="",style="dashed", color="magenta", weight=3]; 102 -> 250[label="",style="dashed", color="magenta", weight=3]; 103 -> 224[label="",style="dashed", color="red", weight=0]; 103[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];103 -> 251[label="",style="dashed", color="magenta", weight=3]; 103 -> 252[label="",style="dashed", color="magenta", weight=3]; 104 -> 224[label="",style="dashed", color="red", weight=0]; 104[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];104 -> 253[label="",style="dashed", color="magenta", weight=3]; 104 -> 254[label="",style="dashed", color="magenta", weight=3]; 105 -> 224[label="",style="dashed", color="red", weight=0]; 105[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];105 -> 255[label="",style="dashed", color="magenta", weight=3]; 105 -> 256[label="",style="dashed", color="magenta", weight=3]; 106 -> 224[label="",style="dashed", color="red", weight=0]; 106[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];106 -> 257[label="",style="dashed", color="magenta", weight=3]; 106 -> 258[label="",style="dashed", color="magenta", weight=3]; 107[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww2000000 (Succ (Succ (Succ Zero))) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1340[label="ww2000000/Succ ww20000000",fontsize=10,color="white",style="solid",shape="box"];107 -> 1340[label="",style="solid", color="burlywood", weight=9]; 1340 -> 127[label="",style="solid", color="burlywood", weight=3]; 1341[label="ww2000000/Zero",fontsize=10,color="white",style="solid",shape="box"];107 -> 1341[label="",style="solid", color="burlywood", weight=9]; 1341 -> 128[label="",style="solid", color="burlywood", weight=3]; 108 -> 53[label="",style="dashed", color="red", weight=0]; 108[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];225 -> 132[label="",style="dashed", color="red", weight=0]; 225[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];226[label="show ww21",fontsize=16,color="black",shape="triangle"];226 -> 284[label="",style="solid", color="black", weight=3]; 224[label="ww62 ++ ww60",fontsize=16,color="burlywood",shape="triangle"];1342[label="ww62/ww620 : ww621",fontsize=10,color="white",style="solid",shape="box"];224 -> 1342[label="",style="solid", color="burlywood", weight=9]; 1342 -> 285[label="",style="solid", color="burlywood", weight=3]; 1343[label="ww62/[]",fontsize=10,color="white",style="solid",shape="box"];224 -> 1343[label="",style="solid", color="burlywood", weight=9]; 1343 -> 286[label="",style="solid", color="burlywood", weight=3]; 110 -> 27[label="",style="dashed", color="red", weight=0]; 110[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww210) . (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 ww211) ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="magenta"];110 -> 129[label="",style="dashed", color="magenta", weight=3]; 110 -> 130[label="",style="dashed", color="magenta", weight=3]; 110 -> 131[label="",style="dashed", color="magenta", weight=3]; 110 -> 132[label="",style="dashed", color="magenta", weight=3]; 110 -> 133[label="",style="dashed", color="magenta", weight=3]; 110 -> 134[label="",style="dashed", color="magenta", weight=3]; 110 -> 135[label="",style="dashed", color="magenta", weight=3]; 227 -> 132[label="",style="dashed", color="red", weight=0]; 227[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];228[label="show ww21",fontsize=16,color="black",shape="triangle"];228 -> 287[label="",style="solid", color="black", weight=3]; 229 -> 132[label="",style="dashed", color="red", weight=0]; 229[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];230[label="show ww21",fontsize=16,color="black",shape="triangle"];230 -> 288[label="",style="solid", color="black", weight=3]; 231 -> 132[label="",style="dashed", color="red", weight=0]; 231[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];232[label="show ww21",fontsize=16,color="black",shape="triangle"];232 -> 289[label="",style="solid", color="black", weight=3]; 233 -> 132[label="",style="dashed", color="red", weight=0]; 233[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];234[label="show ww21",fontsize=16,color="black",shape="triangle"];234 -> 290[label="",style="solid", color="black", weight=3]; 235 -> 132[label="",style="dashed", color="red", weight=0]; 235[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];236[label="show ww21",fontsize=16,color="black",shape="triangle"];236 -> 291[label="",style="solid", color="black", weight=3]; 237 -> 132[label="",style="dashed", color="red", weight=0]; 237[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];238[label="show ww21",fontsize=16,color="black",shape="triangle"];238 -> 292[label="",style="solid", color="black", weight=3]; 239 -> 132[label="",style="dashed", color="red", weight=0]; 239[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];240[label="show ww21",fontsize=16,color="black",shape="triangle"];240 -> 293[label="",style="solid", color="black", weight=3]; 241 -> 132[label="",style="dashed", color="red", weight=0]; 241[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];242[label="show ww21",fontsize=16,color="black",shape="triangle"];242 -> 294[label="",style="solid", color="black", weight=3]; 243 -> 132[label="",style="dashed", color="red", weight=0]; 243[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];244[label="show ww21",fontsize=16,color="black",shape="triangle"];244 -> 295[label="",style="solid", color="black", weight=3]; 245 -> 132[label="",style="dashed", color="red", weight=0]; 245[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];246[label="show ww21",fontsize=16,color="black",shape="triangle"];246 -> 296[label="",style="solid", color="black", weight=3]; 247 -> 132[label="",style="dashed", color="red", weight=0]; 247[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];248[label="show ww21",fontsize=16,color="black",shape="triangle"];248 -> 297[label="",style="solid", color="black", weight=3]; 249 -> 132[label="",style="dashed", color="red", weight=0]; 249[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];250[label="show ww21",fontsize=16,color="black",shape="triangle"];250 -> 298[label="",style="solid", color="black", weight=3]; 251 -> 132[label="",style="dashed", color="red", weight=0]; 251[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];252[label="show ww21",fontsize=16,color="black",shape="triangle"];252 -> 299[label="",style="solid", color="black", weight=3]; 253 -> 132[label="",style="dashed", color="red", weight=0]; 253[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];254[label="show ww21",fontsize=16,color="black",shape="triangle"];254 -> 300[label="",style="solid", color="black", weight=3]; 255 -> 132[label="",style="dashed", color="red", weight=0]; 255[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];256[label="show ww21",fontsize=16,color="black",shape="triangle"];256 -> 301[label="",style="solid", color="black", weight=3]; 257 -> 132[label="",style="dashed", color="red", weight=0]; 257[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];258[label="show ww21",fontsize=16,color="black",shape="triangle"];258 -> 302[label="",style="solid", color="black", weight=3]; 127[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww20000000) (Succ (Succ (Succ Zero))) == GT) ww26",fontsize=16,color="black",shape="box"];127 -> 138[label="",style="solid", color="black", weight=3]; 128[label="showParen0 ((shows ww21) . 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(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww200000000) (Succ (Succ Zero)) == GT) ww26",fontsize=16,color="black",shape="box"];144 -> 157[label="",style="solid", color="black", weight=3]; 145[label="showParen0 ((shows ww21) . 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(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww200000000 (Succ Zero) == GT) ww26",fontsize=16,color="burlywood",shape="box"];1350[label="ww200000000/Succ ww2000000000",fontsize=10,color="white",style="solid",shape="box"];157 -> 1350[label="",style="solid", color="burlywood", weight=9]; 1350 -> 181[label="",style="solid", color="burlywood", weight=3]; 1351[label="ww200000000/Zero",fontsize=10,color="white",style="solid",shape="box"];157 -> 1351[label="",style="solid", color="burlywood", weight=9]; 1351 -> 182[label="",style="solid", color="burlywood", weight=3]; 158 -> 53[label="",style="dashed", color="red", weight=0]; 158[label="showParen0 ((shows ww21) . 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(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww2000000000) (Succ Zero) == GT) ww26",fontsize=16,color="black",shape="box"];181 -> 214[label="",style="solid", color="black", weight=3]; 182[label="showParen0 ((shows ww21) . 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1355[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1355[label="",style="solid", color="blue", weight=9]; 1355 -> 313[label="",style="solid", color="blue", weight=3]; 1356[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1356[label="",style="solid", color="blue", weight=9]; 1356 -> 314[label="",style="solid", color="blue", weight=3]; 1357[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1357[label="",style="solid", color="blue", weight=9]; 1357 -> 315[label="",style="solid", color="blue", weight=3]; 1358[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1358[label="",style="solid", color="blue", weight=9]; 1358 -> 316[label="",style="solid", color="blue", weight=3]; 1359[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1359[label="",style="solid", color="blue", weight=9]; 1359 -> 317[label="",style="solid", color="blue", weight=3]; 1360[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1360[label="",style="solid", color="blue", weight=9]; 1360 -> 318[label="",style="solid", color="blue", weight=3]; 1361[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1361[label="",style="solid", color="blue", weight=9]; 1361 -> 319[label="",style="solid", color="blue", weight=3]; 1362[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1362[label="",style="solid", color="blue", weight=9]; 1362 -> 320[label="",style="solid", color="blue", weight=3]; 1363[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1363[label="",style="solid", color="blue", weight=9]; 1363 -> 321[label="",style="solid", color="blue", weight=3]; 1364[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1364[label="",style="solid", color="blue", weight=9]; 1364 -> 322[label="",style="solid", color="blue", weight=3]; 1365[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1365[label="",style="solid", color="blue", weight=9]; 1365 -> 323[label="",style="solid", color="blue", weight=3]; 1366[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1366[label="",style="solid", color="blue", weight=9]; 1366 -> 324[label="",style="solid", color="blue", weight=3]; 1367[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1367[label="",style="solid", color="blue", weight=9]; 1367 -> 325[label="",style="solid", color="blue", weight=3]; 1368[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1368[label="",style="solid", color="blue", weight=9]; 1368 -> 326[label="",style="solid", color="blue", weight=3]; 1369[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1369[label="",style="solid", color="blue", weight=9]; 1369 -> 327[label="",style="solid", color="blue", weight=3]; 400[label="toEnum (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];400 -> 443[label="",style="dashed", color="green", weight=3]; 401 -> 298[label="",style="dashed", color="red", weight=0]; 401[label="primShowInt (div Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];401 -> 444[label="",style="dashed", color="magenta", weight=3]; 402[label="Pos ww210",fontsize=16,color="green",shape="box"];214[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat ww2000000000 Zero == GT) ww26",fontsize=16,color="burlywood",shape="box"];1370[label="ww2000000000/Succ ww20000000000",fontsize=10,color="white",style="solid",shape="box"];214 -> 1370[label="",style="solid", color="burlywood", weight=9]; 1370 -> 221[label="",style="solid", color="burlywood", weight=3]; 1371[label="ww2000000000/Zero",fontsize=10,color="white",style="solid",shape="box"];214 -> 1371[label="",style="solid", color="burlywood", weight=9]; 1371 -> 222[label="",style="solid", color="burlywood", weight=3]; 215 -> 53[label="",style="dashed", color="red", weight=0]; 215[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];310[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];310 -> 334[label="",style="solid", color="black", weight=3]; 311[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="burlywood",shape="box"];1372[label="ww25/ww250 :% ww251",fontsize=10,color="white",style="solid",shape="box"];311 -> 1372[label="",style="solid", color="burlywood", weight=9]; 1372 -> 335[label="",style="solid", color="burlywood", weight=3]; 312[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];312 -> 336[label="",style="solid", color="black", weight=3]; 313[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];313 -> 337[label="",style="solid", color="black", weight=3]; 314[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];314 -> 338[label="",style="solid", color="black", weight=3]; 315[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];315 -> 339[label="",style="solid", color="black", weight=3]; 316[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];316 -> 340[label="",style="solid", color="black", weight=3]; 317[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];317 -> 341[label="",style="solid", color="black", weight=3]; 318[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];318 -> 342[label="",style="solid", color="black", weight=3]; 319[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];319 -> 343[label="",style="solid", color="black", weight=3]; 320[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];320 -> 344[label="",style="solid", color="black", weight=3]; 321[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];321 -> 345[label="",style="solid", color="black", weight=3]; 322[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];322 -> 346[label="",style="solid", color="black", weight=3]; 323[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];323 -> 347[label="",style="solid", color="black", weight=3]; 324[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];324 -> 348[label="",style="solid", color="black", weight=3]; 325[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];325 -> 349[label="",style="solid", color="black", weight=3]; 326[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];326 -> 350[label="",style="solid", color="black", weight=3]; 327[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="black",shape="box"];327 -> 351[label="",style="solid", color="black", weight=3]; 443[label="toEnum (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];443 -> 463[label="",style="solid", color="black", weight=3]; 444 -> 449[label="",style="dashed", color="red", weight=0]; 444[label="div Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];444 -> 450[label="",style="dashed", color="magenta", weight=3]; 444 -> 451[label="",style="dashed", color="magenta", weight=3]; 221[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat (Succ ww20000000000) Zero == GT) ww26",fontsize=16,color="black",shape="box"];221 -> 304[label="",style="solid", color="black", weight=3]; 222[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (primCmpNat Zero Zero == GT) ww26",fontsize=16,color="black",shape="box"];222 -> 305[label="",style="solid", color="black", weight=3]; 334 -> 224[label="",style="dashed", color="red", weight=0]; 334[label="show ww25 ++ ww26",fontsize=16,color="magenta"];334 -> 357[label="",style="dashed", color="magenta", weight=3]; 334 -> 358[label="",style="dashed", color="magenta", weight=3]; 335[label="showsPrec (Pos Zero) (ww250 :% ww251) ww26",fontsize=16,color="black",shape="box"];335 -> 359[label="",style="solid", color="black", weight=3]; 336 -> 224[label="",style="dashed", color="red", weight=0]; 336[label="show ww25 ++ ww26",fontsize=16,color="magenta"];336 -> 360[label="",style="dashed", color="magenta", weight=3]; 336 -> 361[label="",style="dashed", color="magenta", weight=3]; 337 -> 224[label="",style="dashed", color="red", weight=0]; 337[label="show ww25 ++ ww26",fontsize=16,color="magenta"];337 -> 362[label="",style="dashed", color="magenta", weight=3]; 337 -> 363[label="",style="dashed", color="magenta", weight=3]; 338 -> 224[label="",style="dashed", color="red", weight=0]; 338[label="show ww25 ++ ww26",fontsize=16,color="magenta"];338 -> 364[label="",style="dashed", color="magenta", weight=3]; 338 -> 365[label="",style="dashed", color="magenta", weight=3]; 339 -> 224[label="",style="dashed", color="red", weight=0]; 339[label="show ww25 ++ ww26",fontsize=16,color="magenta"];339 -> 366[label="",style="dashed", color="magenta", weight=3]; 339 -> 367[label="",style="dashed", color="magenta", weight=3]; 340 -> 224[label="",style="dashed", color="red", weight=0]; 340[label="show ww25 ++ ww26",fontsize=16,color="magenta"];340 -> 368[label="",style="dashed", color="magenta", weight=3]; 340 -> 369[label="",style="dashed", color="magenta", weight=3]; 341 -> 224[label="",style="dashed", color="red", weight=0]; 341[label="show ww25 ++ ww26",fontsize=16,color="magenta"];341 -> 370[label="",style="dashed", color="magenta", weight=3]; 341 -> 371[label="",style="dashed", color="magenta", weight=3]; 342 -> 224[label="",style="dashed", color="red", weight=0]; 342[label="show ww25 ++ ww26",fontsize=16,color="magenta"];342 -> 372[label="",style="dashed", color="magenta", weight=3]; 342 -> 373[label="",style="dashed", color="magenta", weight=3]; 343 -> 224[label="",style="dashed", color="red", weight=0]; 343[label="show ww25 ++ ww26",fontsize=16,color="magenta"];343 -> 374[label="",style="dashed", color="magenta", weight=3]; 343 -> 375[label="",style="dashed", color="magenta", weight=3]; 344 -> 224[label="",style="dashed", color="red", weight=0]; 344[label="show ww25 ++ ww26",fontsize=16,color="magenta"];344 -> 376[label="",style="dashed", color="magenta", weight=3]; 344 -> 377[label="",style="dashed", color="magenta", weight=3]; 345 -> 224[label="",style="dashed", color="red", weight=0]; 345[label="show ww25 ++ ww26",fontsize=16,color="magenta"];345 -> 378[label="",style="dashed", color="magenta", weight=3]; 345 -> 379[label="",style="dashed", color="magenta", weight=3]; 346 -> 224[label="",style="dashed", color="red", weight=0]; 346[label="show ww25 ++ ww26",fontsize=16,color="magenta"];346 -> 380[label="",style="dashed", color="magenta", weight=3]; 346 -> 381[label="",style="dashed", color="magenta", weight=3]; 347 -> 224[label="",style="dashed", color="red", weight=0]; 347[label="show ww25 ++ ww26",fontsize=16,color="magenta"];347 -> 382[label="",style="dashed", color="magenta", weight=3]; 347 -> 383[label="",style="dashed", color="magenta", weight=3]; 348 -> 224[label="",style="dashed", color="red", weight=0]; 348[label="show ww25 ++ ww26",fontsize=16,color="magenta"];348 -> 384[label="",style="dashed", color="magenta", weight=3]; 348 -> 385[label="",style="dashed", color="magenta", weight=3]; 349 -> 224[label="",style="dashed", color="red", weight=0]; 349[label="show ww25 ++ ww26",fontsize=16,color="magenta"];349 -> 386[label="",style="dashed", color="magenta", weight=3]; 349 -> 387[label="",style="dashed", color="magenta", weight=3]; 350 -> 224[label="",style="dashed", color="red", weight=0]; 350[label="show ww25 ++ ww26",fontsize=16,color="magenta"];350 -> 388[label="",style="dashed", color="magenta", weight=3]; 350 -> 389[label="",style="dashed", color="magenta", weight=3]; 351 -> 224[label="",style="dashed", color="red", weight=0]; 351[label="show ww25 ++ ww26",fontsize=16,color="magenta"];351 -> 390[label="",style="dashed", color="magenta", weight=3]; 351 -> 391[label="",style="dashed", color="magenta", weight=3]; 463 -> 475[label="",style="dashed", color="red", weight=0]; 463[label="primIntToChar (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];463 -> 476[label="",style="dashed", color="magenta", weight=3]; 463 -> 477[label="",style="dashed", color="magenta", weight=3]; 450[label="ww2100",fontsize=16,color="green",shape="box"];451[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];449[label="div Pos (Succ ww84) Pos (Succ ww85)",fontsize=16,color="black",shape="triangle"];449 -> 461[label="",style="solid", color="black", weight=3]; 304[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (GT == GT) ww26",fontsize=16,color="black",shape="box"];304 -> 328[label="",style="solid", color="black", weight=3]; 305[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (EQ == GT) ww26",fontsize=16,color="black",shape="box"];305 -> 329[label="",style="solid", color="black", weight=3]; 357[label="ww26",fontsize=16,color="green",shape="box"];358 -> 226[label="",style="dashed", color="red", weight=0]; 358[label="show ww25",fontsize=16,color="magenta"];358 -> 403[label="",style="dashed", color="magenta", weight=3]; 359 -> 27[label="",style="dashed", color="red", weight=0]; 359[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww250) . (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 ww251) ww26",fontsize=16,color="magenta"];359 -> 404[label="",style="dashed", color="magenta", weight=3]; 359 -> 405[label="",style="dashed", color="magenta", weight=3]; 359 -> 406[label="",style="dashed", color="magenta", weight=3]; 359 -> 407[label="",style="dashed", color="magenta", weight=3]; 359 -> 408[label="",style="dashed", color="magenta", weight=3]; 359 -> 409[label="",style="dashed", color="magenta", weight=3]; 360[label="ww26",fontsize=16,color="green",shape="box"];361 -> 228[label="",style="dashed", color="red", weight=0]; 361[label="show ww25",fontsize=16,color="magenta"];361 -> 410[label="",style="dashed", color="magenta", weight=3]; 362[label="ww26",fontsize=16,color="green",shape="box"];363 -> 230[label="",style="dashed", color="red", weight=0]; 363[label="show ww25",fontsize=16,color="magenta"];363 -> 411[label="",style="dashed", color="magenta", weight=3]; 364[label="ww26",fontsize=16,color="green",shape="box"];365 -> 232[label="",style="dashed", color="red", weight=0]; 365[label="show ww25",fontsize=16,color="magenta"];365 -> 412[label="",style="dashed", color="magenta", weight=3]; 366[label="ww26",fontsize=16,color="green",shape="box"];367 -> 234[label="",style="dashed", color="red", weight=0]; 367[label="show ww25",fontsize=16,color="magenta"];367 -> 413[label="",style="dashed", color="magenta", weight=3]; 368[label="ww26",fontsize=16,color="green",shape="box"];369 -> 236[label="",style="dashed", color="red", weight=0]; 369[label="show ww25",fontsize=16,color="magenta"];369 -> 414[label="",style="dashed", color="magenta", weight=3]; 370[label="ww26",fontsize=16,color="green",shape="box"];371 -> 238[label="",style="dashed", color="red", weight=0]; 371[label="show ww25",fontsize=16,color="magenta"];371 -> 415[label="",style="dashed", color="magenta", weight=3]; 372[label="ww26",fontsize=16,color="green",shape="box"];373 -> 240[label="",style="dashed", color="red", weight=0]; 373[label="show ww25",fontsize=16,color="magenta"];373 -> 416[label="",style="dashed", color="magenta", weight=3]; 374[label="ww26",fontsize=16,color="green",shape="box"];375 -> 242[label="",style="dashed", color="red", weight=0]; 375[label="show ww25",fontsize=16,color="magenta"];375 -> 417[label="",style="dashed", color="magenta", weight=3]; 376[label="ww26",fontsize=16,color="green",shape="box"];377 -> 244[label="",style="dashed", color="red", weight=0]; 377[label="show ww25",fontsize=16,color="magenta"];377 -> 418[label="",style="dashed", color="magenta", weight=3]; 378[label="ww26",fontsize=16,color="green",shape="box"];379 -> 246[label="",style="dashed", color="red", weight=0]; 379[label="show ww25",fontsize=16,color="magenta"];379 -> 419[label="",style="dashed", color="magenta", weight=3]; 380[label="ww26",fontsize=16,color="green",shape="box"];381 -> 248[label="",style="dashed", color="red", weight=0]; 381[label="show ww25",fontsize=16,color="magenta"];381 -> 420[label="",style="dashed", color="magenta", weight=3]; 382[label="ww26",fontsize=16,color="green",shape="box"];383 -> 250[label="",style="dashed", color="red", weight=0]; 383[label="show ww25",fontsize=16,color="magenta"];383 -> 421[label="",style="dashed", color="magenta", weight=3]; 384[label="ww26",fontsize=16,color="green",shape="box"];385 -> 252[label="",style="dashed", color="red", weight=0]; 385[label="show ww25",fontsize=16,color="magenta"];385 -> 422[label="",style="dashed", color="magenta", weight=3]; 386[label="ww26",fontsize=16,color="green",shape="box"];387 -> 254[label="",style="dashed", color="red", weight=0]; 387[label="show ww25",fontsize=16,color="magenta"];387 -> 423[label="",style="dashed", color="magenta", weight=3]; 388[label="ww26",fontsize=16,color="green",shape="box"];389 -> 256[label="",style="dashed", color="red", weight=0]; 389[label="show ww25",fontsize=16,color="magenta"];389 -> 424[label="",style="dashed", color="magenta", weight=3]; 390[label="ww26",fontsize=16,color="green",shape="box"];391 -> 258[label="",style="dashed", color="red", weight=0]; 391[label="show ww25",fontsize=16,color="magenta"];391 -> 425[label="",style="dashed", color="magenta", weight=3]; 476[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];477[label="ww2100",fontsize=16,color="green",shape="box"];475[label="primIntToChar (mod Pos (Succ ww87) Pos (Succ ww88))",fontsize=16,color="black",shape="triangle"];475 -> 478[label="",style="solid", color="black", weight=3]; 461[label="primDivInt (Pos (Succ ww84)) (Pos (Succ ww85))",fontsize=16,color="black",shape="box"];461 -> 473[label="",style="solid", color="black", weight=3]; 328[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) True ww26",fontsize=16,color="black",shape="box"];328 -> 352[label="",style="solid", color="black", weight=3]; 329 -> 57[label="",style="dashed", color="red", weight=0]; 329[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) False ww26",fontsize=16,color="magenta"];403[label="ww25",fontsize=16,color="green",shape="box"];404[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"];405[label="ww250",fontsize=16,color="green",shape="box"];406[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"];407[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"];408[label="ww251",fontsize=16,color="green",shape="box"];409[label="Pos Zero",fontsize=16,color="green",shape="box"];410[label="ww25",fontsize=16,color="green",shape="box"];411[label="ww25",fontsize=16,color="green",shape="box"];412[label="ww25",fontsize=16,color="green",shape="box"];413[label="ww25",fontsize=16,color="green",shape="box"];414[label="ww25",fontsize=16,color="green",shape="box"];415[label="ww25",fontsize=16,color="green",shape="box"];416[label="ww25",fontsize=16,color="green",shape="box"];417[label="ww25",fontsize=16,color="green",shape="box"];418[label="ww25",fontsize=16,color="green",shape="box"];419[label="ww25",fontsize=16,color="green",shape="box"];420[label="ww25",fontsize=16,color="green",shape="box"];421[label="ww25",fontsize=16,color="green",shape="box"];422[label="ww25",fontsize=16,color="green",shape="box"];423[label="ww25",fontsize=16,color="green",shape="box"];424[label="ww25",fontsize=16,color="green",shape="box"];425[label="ww25",fontsize=16,color="green",shape="box"];478[label="primIntToChar (primModInt (Pos (Succ ww87)) (Pos (Succ ww88)))",fontsize=16,color="black",shape="box"];478 -> 481[label="",style="solid", color="black", weight=3]; 473[label="Pos (primDivNatS (Succ ww84) (Succ ww85))",fontsize=16,color="green",shape="box"];473 -> 479[label="",style="dashed", color="green", weight=3]; 352 -> 426[label="",style="dashed", color="red", weight=0]; 352[label="(showChar (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 Zero)))))))))))))))))))))))))))))))))))))))))) . ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) . showChar (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 Zero))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="magenta"];352 -> 427[label="",style="dashed", color="magenta", weight=3]; 352 -> 428[label="",style="dashed", color="magenta", weight=3]; 352 -> 429[label="",style="dashed", color="magenta", weight=3]; 352 -> 430[label="",style="dashed", color="magenta", weight=3]; 352 -> 431[label="",style="dashed", color="magenta", weight=3]; 352 -> 432[label="",style="dashed", color="magenta", weight=3]; 352 -> 433[label="",style="dashed", color="magenta", weight=3]; 352 -> 434[label="",style="dashed", color="magenta", weight=3]; 481[label="primIntToChar (Pos (primModNatS (Succ ww87) (Succ ww88)))",fontsize=16,color="black",shape="box"];481 -> 489[label="",style="solid", color="black", weight=3]; 479[label="primDivNatS (Succ ww84) (Succ ww85)",fontsize=16,color="black",shape="triangle"];479 -> 482[label="",style="solid", color="black", weight=3]; 427[label="ww26",fontsize=16,color="green",shape="box"];428[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 (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];429[label="ww23",fontsize=16,color="green",shape="box"];430[label="ww24",fontsize=16,color="green",shape="box"];431[label="ww22",fontsize=16,color="green",shape="box"];432[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 (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];433[label="ww21",fontsize=16,color="green",shape="box"];434[label="ww25",fontsize=16,color="green",shape="box"];426[label="(showChar (Char (Succ ww72))) . ((shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77) . showChar (Char (Succ ww78))",fontsize=16,color="black",shape="triangle"];426 -> 445[label="",style="solid", color="black", weight=3]; 489[label="Char (primModNatS (Succ ww87) (Succ ww88))",fontsize=16,color="green",shape="box"];489 -> 493[label="",style="dashed", color="green", weight=3]; 482[label="primDivNatS0 ww84 ww85 (primGEqNatS ww84 ww85)",fontsize=16,color="burlywood",shape="box"];1373[label="ww84/Succ ww840",fontsize=10,color="white",style="solid",shape="box"];482 -> 1373[label="",style="solid", color="burlywood", weight=9]; 1373 -> 490[label="",style="solid", color="burlywood", weight=3]; 1374[label="ww84/Zero",fontsize=10,color="white",style="solid",shape="box"];482 -> 1374[label="",style="solid", color="burlywood", weight=9]; 1374 -> 491[label="",style="solid", color="burlywood", weight=3]; 445[label="showChar (Char (Succ ww72)) (((shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77) . showChar (Char (Succ ww78)))",fontsize=16,color="black",shape="box"];445 -> 462[label="",style="solid", color="black", weight=3]; 493[label="primModNatS (Succ ww87) (Succ ww88)",fontsize=16,color="black",shape="triangle"];493 -> 498[label="",style="solid", color="black", weight=3]; 490[label="primDivNatS0 (Succ ww840) ww85 (primGEqNatS (Succ ww840) ww85)",fontsize=16,color="burlywood",shape="box"];1375[label="ww85/Succ ww850",fontsize=10,color="white",style="solid",shape="box"];490 -> 1375[label="",style="solid", color="burlywood", weight=9]; 1375 -> 494[label="",style="solid", color="burlywood", weight=3]; 1376[label="ww85/Zero",fontsize=10,color="white",style="solid",shape="box"];490 -> 1376[label="",style="solid", color="burlywood", weight=9]; 1376 -> 495[label="",style="solid", color="burlywood", weight=3]; 491[label="primDivNatS0 Zero ww85 (primGEqNatS Zero ww85)",fontsize=16,color="burlywood",shape="box"];1377[label="ww85/Succ ww850",fontsize=10,color="white",style="solid",shape="box"];491 -> 1377[label="",style="solid", color="burlywood", weight=9]; 1377 -> 496[label="",style="solid", color="burlywood", weight=3]; 1378[label="ww85/Zero",fontsize=10,color="white",style="solid",shape="box"];491 -> 1378[label="",style="solid", color="burlywood", weight=9]; 1378 -> 497[label="",style="solid", color="burlywood", weight=3]; 462[label="(:) Char (Succ ww72) ((shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77) . showChar (Char (Succ ww78))",fontsize=16,color="green",shape="box"];462 -> 474[label="",style="dashed", color="green", weight=3]; 498[label="primModNatS0 ww87 ww88 (primGEqNatS ww87 ww88)",fontsize=16,color="burlywood",shape="box"];1379[label="ww87/Succ ww870",fontsize=10,color="white",style="solid",shape="box"];498 -> 1379[label="",style="solid", color="burlywood", weight=9]; 1379 -> 503[label="",style="solid", color="burlywood", weight=3]; 1380[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];498 -> 1380[label="",style="solid", color="burlywood", weight=9]; 1380 -> 504[label="",style="solid", color="burlywood", weight=3]; 494[label="primDivNatS0 (Succ ww840) (Succ ww850) (primGEqNatS (Succ ww840) (Succ ww850))",fontsize=16,color="black",shape="box"];494 -> 499[label="",style="solid", color="black", weight=3]; 495[label="primDivNatS0 (Succ ww840) Zero (primGEqNatS (Succ ww840) Zero)",fontsize=16,color="black",shape="box"];495 -> 500[label="",style="solid", color="black", weight=3]; 496[label="primDivNatS0 Zero (Succ ww850) (primGEqNatS Zero (Succ ww850))",fontsize=16,color="black",shape="box"];496 -> 501[label="",style="solid", color="black", weight=3]; 497[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];497 -> 502[label="",style="solid", color="black", weight=3]; 474[label="((shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77) . showChar (Char (Succ ww78))",fontsize=16,color="black",shape="box"];474 -> 480[label="",style="solid", color="black", weight=3]; 503[label="primModNatS0 (Succ ww870) ww88 (primGEqNatS (Succ ww870) ww88)",fontsize=16,color="burlywood",shape="box"];1381[label="ww88/Succ ww880",fontsize=10,color="white",style="solid",shape="box"];503 -> 1381[label="",style="solid", color="burlywood", weight=9]; 1381 -> 510[label="",style="solid", color="burlywood", weight=3]; 1382[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];503 -> 1382[label="",style="solid", color="burlywood", weight=9]; 1382 -> 511[label="",style="solid", color="burlywood", weight=3]; 504[label="primModNatS0 Zero ww88 (primGEqNatS Zero ww88)",fontsize=16,color="burlywood",shape="box"];1383[label="ww88/Succ ww880",fontsize=10,color="white",style="solid",shape="box"];504 -> 1383[label="",style="solid", color="burlywood", weight=9]; 1383 -> 512[label="",style="solid", color="burlywood", weight=3]; 1384[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];504 -> 1384[label="",style="solid", color="burlywood", weight=9]; 1384 -> 513[label="",style="solid", color="burlywood", weight=3]; 499 -> 1024[label="",style="dashed", color="red", weight=0]; 499[label="primDivNatS0 (Succ ww840) (Succ ww850) (primGEqNatS ww840 ww850)",fontsize=16,color="magenta"];499 -> 1025[label="",style="dashed", color="magenta", weight=3]; 499 -> 1026[label="",style="dashed", color="magenta", weight=3]; 499 -> 1027[label="",style="dashed", color="magenta", weight=3]; 499 -> 1028[label="",style="dashed", color="magenta", weight=3]; 500[label="primDivNatS0 (Succ ww840) Zero True",fontsize=16,color="black",shape="box"];500 -> 507[label="",style="solid", color="black", weight=3]; 501[label="primDivNatS0 Zero (Succ ww850) False",fontsize=16,color="black",shape="box"];501 -> 508[label="",style="solid", color="black", weight=3]; 502[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];502 -> 509[label="",style="solid", color="black", weight=3]; 480 -> 60[label="",style="dashed", color="red", weight=0]; 480[label="(shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77",fontsize=16,color="magenta"];480 -> 483[label="",style="dashed", color="magenta", weight=3]; 480 -> 484[label="",style="dashed", color="magenta", weight=3]; 480 -> 485[label="",style="dashed", color="magenta", weight=3]; 480 -> 486[label="",style="dashed", color="magenta", weight=3]; 480 -> 487[label="",style="dashed", color="magenta", weight=3]; 480 -> 488[label="",style="dashed", color="magenta", weight=3]; 510[label="primModNatS0 (Succ ww870) (Succ ww880) (primGEqNatS (Succ ww870) (Succ ww880))",fontsize=16,color="black",shape="box"];510 -> 520[label="",style="solid", color="black", weight=3]; 511[label="primModNatS0 (Succ ww870) Zero (primGEqNatS (Succ ww870) Zero)",fontsize=16,color="black",shape="box"];511 -> 521[label="",style="solid", color="black", weight=3]; 512[label="primModNatS0 Zero (Succ ww880) (primGEqNatS Zero (Succ ww880))",fontsize=16,color="black",shape="box"];512 -> 522[label="",style="solid", color="black", weight=3]; 513[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];513 -> 523[label="",style="solid", color="black", weight=3]; 1025[label="ww850",fontsize=16,color="green",shape="box"];1026[label="ww840",fontsize=16,color="green",shape="box"];1027[label="ww840",fontsize=16,color="green",shape="box"];1028[label="ww850",fontsize=16,color="green",shape="box"];1024[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS ww133 ww134)",fontsize=16,color="burlywood",shape="triangle"];1385[label="ww133/Succ ww1330",fontsize=10,color="white",style="solid",shape="box"];1024 -> 1385[label="",style="solid", color="burlywood", weight=9]; 1385 -> 1065[label="",style="solid", color="burlywood", weight=3]; 1386[label="ww133/Zero",fontsize=10,color="white",style="solid",shape="box"];1024 -> 1386[label="",style="solid", color="burlywood", weight=9]; 1386 -> 1066[label="",style="solid", color="burlywood", weight=3]; 507[label="Succ (primDivNatS (primMinusNatS (Succ ww840) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];507 -> 518[label="",style="dashed", color="green", weight=3]; 508[label="Zero",fontsize=16,color="green",shape="box"];509[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];509 -> 519[label="",style="dashed", color="green", weight=3]; 483[label="ww76",fontsize=16,color="green",shape="box"];484[label="ww73",fontsize=16,color="green",shape="box"];485[label="ww74",fontsize=16,color="green",shape="box"];486[label="showChar (Char (Succ ww78)) ww79",fontsize=16,color="black",shape="box"];486 -> 492[label="",style="solid", color="black", weight=3]; 487[label="ww75",fontsize=16,color="green",shape="box"];488[label="ww77",fontsize=16,color="green",shape="box"];520 -> 1085[label="",style="dashed", color="red", weight=0]; 520[label="primModNatS0 (Succ ww870) (Succ ww880) (primGEqNatS ww870 ww880)",fontsize=16,color="magenta"];520 -> 1086[label="",style="dashed", color="magenta", weight=3]; 520 -> 1087[label="",style="dashed", color="magenta", weight=3]; 520 -> 1088[label="",style="dashed", color="magenta", weight=3]; 520 -> 1089[label="",style="dashed", color="magenta", weight=3]; 521[label="primModNatS0 (Succ ww870) Zero True",fontsize=16,color="black",shape="box"];521 -> 532[label="",style="solid", color="black", weight=3]; 522[label="primModNatS0 Zero (Succ ww880) False",fontsize=16,color="black",shape="box"];522 -> 533[label="",style="solid", color="black", weight=3]; 523[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];523 -> 534[label="",style="solid", color="black", weight=3]; 1065[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) ww134)",fontsize=16,color="burlywood",shape="box"];1387[label="ww134/Succ ww1340",fontsize=10,color="white",style="solid",shape="box"];1065 -> 1387[label="",style="solid", color="burlywood", weight=9]; 1387 -> 1077[label="",style="solid", color="burlywood", weight=3]; 1388[label="ww134/Zero",fontsize=10,color="white",style="solid",shape="box"];1065 -> 1388[label="",style="solid", color="burlywood", weight=9]; 1388 -> 1078[label="",style="solid", color="burlywood", weight=3]; 1066[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero ww134)",fontsize=16,color="burlywood",shape="box"];1389[label="ww134/Succ ww1340",fontsize=10,color="white",style="solid",shape="box"];1066 -> 1389[label="",style="solid", color="burlywood", weight=9]; 1389 -> 1079[label="",style="solid", color="burlywood", weight=3]; 1390[label="ww134/Zero",fontsize=10,color="white",style="solid",shape="box"];1066 -> 1390[label="",style="solid", color="burlywood", weight=9]; 1390 -> 1080[label="",style="solid", color="burlywood", weight=3]; 518 -> 1268[label="",style="dashed", color="red", weight=0]; 518[label="primDivNatS (primMinusNatS (Succ ww840) Zero) (Succ Zero)",fontsize=16,color="magenta"];518 -> 1269[label="",style="dashed", color="magenta", weight=3]; 518 -> 1270[label="",style="dashed", color="magenta", weight=3]; 518 -> 1271[label="",style="dashed", color="magenta", weight=3]; 519 -> 1268[label="",style="dashed", color="red", weight=0]; 519[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];519 -> 1272[label="",style="dashed", color="magenta", weight=3]; 519 -> 1273[label="",style="dashed", color="magenta", weight=3]; 519 -> 1274[label="",style="dashed", color="magenta", weight=3]; 492[label="(:) Char (Succ ww78) ww79",fontsize=16,color="green",shape="box"];1086[label="ww880",fontsize=16,color="green",shape="box"];1087[label="ww870",fontsize=16,color="green",shape="box"];1088[label="ww880",fontsize=16,color="green",shape="box"];1089[label="ww870",fontsize=16,color="green",shape="box"];1085[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS ww138 ww139)",fontsize=16,color="burlywood",shape="triangle"];1391[label="ww138/Succ ww1380",fontsize=10,color="white",style="solid",shape="box"];1085 -> 1391[label="",style="solid", color="burlywood", weight=9]; 1391 -> 1126[label="",style="solid", color="burlywood", weight=3]; 1392[label="ww138/Zero",fontsize=10,color="white",style="solid",shape="box"];1085 -> 1392[label="",style="solid", color="burlywood", weight=9]; 1392 -> 1127[label="",style="solid", color="burlywood", weight=3]; 532 -> 1172[label="",style="dashed", color="red", weight=0]; 532[label="primModNatS (primMinusNatS (Succ ww870) Zero) (Succ Zero)",fontsize=16,color="magenta"];532 -> 1173[label="",style="dashed", color="magenta", weight=3]; 532 -> 1174[label="",style="dashed", color="magenta", weight=3]; 532 -> 1175[label="",style="dashed", color="magenta", weight=3]; 533[label="Succ Zero",fontsize=16,color="green",shape="box"];534 -> 1172[label="",style="dashed", color="red", weight=0]; 534[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];534 -> 1176[label="",style="dashed", color="magenta", weight=3]; 534 -> 1177[label="",style="dashed", color="magenta", weight=3]; 534 -> 1178[label="",style="dashed", color="magenta", weight=3]; 1077[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) (Succ ww1340))",fontsize=16,color="black",shape="box"];1077 -> 1128[label="",style="solid", color="black", weight=3]; 1078[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) Zero)",fontsize=16,color="black",shape="box"];1078 -> 1129[label="",style="solid", color="black", weight=3]; 1079[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero (Succ ww1340))",fontsize=16,color="black",shape="box"];1079 -> 1130[label="",style="solid", color="black", weight=3]; 1080[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1080 -> 1131[label="",style="solid", color="black", weight=3]; 1269[label="Succ ww840",fontsize=16,color="green",shape="box"];1270[label="Zero",fontsize=16,color="green",shape="box"];1271[label="Zero",fontsize=16,color="green",shape="box"];1268[label="primDivNatS (primMinusNatS ww145 ww146) (Succ ww147)",fontsize=16,color="burlywood",shape="triangle"];1393[label="ww145/Succ ww1450",fontsize=10,color="white",style="solid",shape="box"];1268 -> 1393[label="",style="solid", color="burlywood", weight=9]; 1393 -> 1293[label="",style="solid", color="burlywood", weight=3]; 1394[label="ww145/Zero",fontsize=10,color="white",style="solid",shape="box"];1268 -> 1394[label="",style="solid", color="burlywood", weight=9]; 1394 -> 1294[label="",style="solid", color="burlywood", weight=3]; 1272[label="Zero",fontsize=16,color="green",shape="box"];1273[label="Zero",fontsize=16,color="green",shape="box"];1274[label="Zero",fontsize=16,color="green",shape="box"];1126[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) ww139)",fontsize=16,color="burlywood",shape="box"];1395[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1126 -> 1395[label="",style="solid", color="burlywood", weight=9]; 1395 -> 1136[label="",style="solid", color="burlywood", weight=3]; 1396[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1126 -> 1396[label="",style="solid", color="burlywood", weight=9]; 1396 -> 1137[label="",style="solid", color="burlywood", weight=3]; 1127[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero ww139)",fontsize=16,color="burlywood",shape="box"];1397[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1127 -> 1397[label="",style="solid", color="burlywood", weight=9]; 1397 -> 1138[label="",style="solid", color="burlywood", weight=3]; 1398[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1127 -> 1398[label="",style="solid", color="burlywood", weight=9]; 1398 -> 1139[label="",style="solid", color="burlywood", weight=3]; 1173[label="Succ ww870",fontsize=16,color="green",shape="box"];1174[label="Zero",fontsize=16,color="green",shape="box"];1175[label="Zero",fontsize=16,color="green",shape="box"];1172[label="primModNatS (primMinusNatS ww141 ww142) (Succ ww143)",fontsize=16,color="burlywood",shape="triangle"];1399[label="ww141/Succ ww1410",fontsize=10,color="white",style="solid",shape="box"];1172 -> 1399[label="",style="solid", color="burlywood", weight=9]; 1399 -> 1203[label="",style="solid", color="burlywood", weight=3]; 1400[label="ww141/Zero",fontsize=10,color="white",style="solid",shape="box"];1172 -> 1400[label="",style="solid", color="burlywood", weight=9]; 1400 -> 1204[label="",style="solid", color="burlywood", weight=3]; 1176[label="Zero",fontsize=16,color="green",shape="box"];1177[label="Zero",fontsize=16,color="green",shape="box"];1178[label="Zero",fontsize=16,color="green",shape="box"];1128 -> 1024[label="",style="dashed", color="red", weight=0]; 1128[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS ww1330 ww1340)",fontsize=16,color="magenta"];1128 -> 1140[label="",style="dashed", color="magenta", weight=3]; 1128 -> 1141[label="",style="dashed", color="magenta", weight=3]; 1129[label="primDivNatS0 (Succ ww131) (Succ ww132) True",fontsize=16,color="black",shape="triangle"];1129 -> 1142[label="",style="solid", color="black", weight=3]; 1130[label="primDivNatS0 (Succ ww131) (Succ ww132) False",fontsize=16,color="black",shape="box"];1130 -> 1143[label="",style="solid", color="black", weight=3]; 1131 -> 1129[label="",style="dashed", color="red", weight=0]; 1131[label="primDivNatS0 (Succ ww131) (Succ ww132) True",fontsize=16,color="magenta"];1293[label="primDivNatS (primMinusNatS (Succ ww1450) ww146) (Succ ww147)",fontsize=16,color="burlywood",shape="box"];1401[label="ww146/Succ ww1460",fontsize=10,color="white",style="solid",shape="box"];1293 -> 1401[label="",style="solid", color="burlywood", weight=9]; 1401 -> 1295[label="",style="solid", color="burlywood", weight=3]; 1402[label="ww146/Zero",fontsize=10,color="white",style="solid",shape="box"];1293 -> 1402[label="",style="solid", color="burlywood", weight=9]; 1402 -> 1296[label="",style="solid", color="burlywood", weight=3]; 1294[label="primDivNatS (primMinusNatS Zero ww146) (Succ ww147)",fontsize=16,color="burlywood",shape="box"];1403[label="ww146/Succ ww1460",fontsize=10,color="white",style="solid",shape="box"];1294 -> 1403[label="",style="solid", color="burlywood", weight=9]; 1403 -> 1297[label="",style="solid", color="burlywood", weight=3]; 1404[label="ww146/Zero",fontsize=10,color="white",style="solid",shape="box"];1294 -> 1404[label="",style="solid", color="burlywood", weight=9]; 1404 -> 1298[label="",style="solid", color="burlywood", weight=3]; 1136[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) (Succ ww1390))",fontsize=16,color="black",shape="box"];1136 -> 1150[label="",style="solid", color="black", weight=3]; 1137[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) Zero)",fontsize=16,color="black",shape="box"];1137 -> 1151[label="",style="solid", color="black", weight=3]; 1138[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero (Succ ww1390))",fontsize=16,color="black",shape="box"];1138 -> 1152[label="",style="solid", color="black", weight=3]; 1139[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1139 -> 1153[label="",style="solid", color="black", weight=3]; 1203[label="primModNatS (primMinusNatS (Succ ww1410) ww142) (Succ ww143)",fontsize=16,color="burlywood",shape="box"];1405[label="ww142/Succ ww1420",fontsize=10,color="white",style="solid",shape="box"];1203 -> 1405[label="",style="solid", color="burlywood", weight=9]; 1405 -> 1209[label="",style="solid", color="burlywood", weight=3]; 1406[label="ww142/Zero",fontsize=10,color="white",style="solid",shape="box"];1203 -> 1406[label="",style="solid", color="burlywood", weight=9]; 1406 -> 1210[label="",style="solid", color="burlywood", weight=3]; 1204[label="primModNatS (primMinusNatS Zero ww142) (Succ ww143)",fontsize=16,color="burlywood",shape="box"];1407[label="ww142/Succ ww1420",fontsize=10,color="white",style="solid",shape="box"];1204 -> 1407[label="",style="solid", color="burlywood", weight=9]; 1407 -> 1211[label="",style="solid", color="burlywood", weight=3]; 1408[label="ww142/Zero",fontsize=10,color="white",style="solid",shape="box"];1204 -> 1408[label="",style="solid", color="burlywood", weight=9]; 1408 -> 1212[label="",style="solid", color="burlywood", weight=3]; 1140[label="ww1330",fontsize=16,color="green",shape="box"];1141[label="ww1340",fontsize=16,color="green",shape="box"];1142[label="Succ (primDivNatS (primMinusNatS (Succ ww131) (Succ ww132)) (Succ (Succ ww132)))",fontsize=16,color="green",shape="box"];1142 -> 1154[label="",style="dashed", color="green", weight=3]; 1143[label="Zero",fontsize=16,color="green",shape="box"];1295[label="primDivNatS (primMinusNatS (Succ ww1450) (Succ ww1460)) (Succ ww147)",fontsize=16,color="black",shape="box"];1295 -> 1299[label="",style="solid", color="black", weight=3]; 1296[label="primDivNatS (primMinusNatS (Succ ww1450) Zero) (Succ ww147)",fontsize=16,color="black",shape="box"];1296 -> 1300[label="",style="solid", color="black", weight=3]; 1297[label="primDivNatS (primMinusNatS Zero (Succ ww1460)) (Succ ww147)",fontsize=16,color="black",shape="box"];1297 -> 1301[label="",style="solid", color="black", weight=3]; 1298[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww147)",fontsize=16,color="black",shape="box"];1298 -> 1302[label="",style="solid", color="black", weight=3]; 1150 -> 1085[label="",style="dashed", color="red", weight=0]; 1150[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS ww1380 ww1390)",fontsize=16,color="magenta"];1150 -> 1159[label="",style="dashed", color="magenta", weight=3]; 1150 -> 1160[label="",style="dashed", color="magenta", weight=3]; 1151[label="primModNatS0 (Succ ww136) (Succ ww137) True",fontsize=16,color="black",shape="triangle"];1151 -> 1161[label="",style="solid", color="black", weight=3]; 1152[label="primModNatS0 (Succ ww136) (Succ ww137) False",fontsize=16,color="black",shape="box"];1152 -> 1162[label="",style="solid", color="black", weight=3]; 1153 -> 1151[label="",style="dashed", color="red", weight=0]; 1153[label="primModNatS0 (Succ ww136) (Succ ww137) True",fontsize=16,color="magenta"];1209[label="primModNatS (primMinusNatS (Succ ww1410) (Succ ww1420)) (Succ ww143)",fontsize=16,color="black",shape="box"];1209 -> 1217[label="",style="solid", color="black", weight=3]; 1210[label="primModNatS (primMinusNatS (Succ ww1410) Zero) (Succ ww143)",fontsize=16,color="black",shape="box"];1210 -> 1218[label="",style="solid", color="black", weight=3]; 1211[label="primModNatS (primMinusNatS Zero (Succ ww1420)) (Succ ww143)",fontsize=16,color="black",shape="box"];1211 -> 1219[label="",style="solid", color="black", weight=3]; 1212[label="primModNatS (primMinusNatS Zero Zero) (Succ ww143)",fontsize=16,color="black",shape="box"];1212 -> 1220[label="",style="solid", color="black", weight=3]; 1154 -> 1268[label="",style="dashed", color="red", weight=0]; 1154[label="primDivNatS (primMinusNatS (Succ ww131) (Succ ww132)) (Succ (Succ ww132))",fontsize=16,color="magenta"];1154 -> 1275[label="",style="dashed", color="magenta", weight=3]; 1154 -> 1276[label="",style="dashed", color="magenta", weight=3]; 1154 -> 1277[label="",style="dashed", color="magenta", weight=3]; 1299 -> 1268[label="",style="dashed", color="red", weight=0]; 1299[label="primDivNatS (primMinusNatS ww1450 ww1460) (Succ ww147)",fontsize=16,color="magenta"];1299 -> 1303[label="",style="dashed", color="magenta", weight=3]; 1299 -> 1304[label="",style="dashed", color="magenta", weight=3]; 1300 -> 479[label="",style="dashed", color="red", weight=0]; 1300[label="primDivNatS (Succ ww1450) (Succ ww147)",fontsize=16,color="magenta"];1300 -> 1305[label="",style="dashed", color="magenta", weight=3]; 1300 -> 1306[label="",style="dashed", color="magenta", weight=3]; 1301[label="primDivNatS Zero (Succ ww147)",fontsize=16,color="black",shape="triangle"];1301 -> 1307[label="",style="solid", color="black", weight=3]; 1302 -> 1301[label="",style="dashed", color="red", weight=0]; 1302[label="primDivNatS Zero (Succ ww147)",fontsize=16,color="magenta"];1159[label="ww1380",fontsize=16,color="green",shape="box"];1160[label="ww1390",fontsize=16,color="green",shape="box"];1161 -> 1172[label="",style="dashed", color="red", weight=0]; 1161[label="primModNatS (primMinusNatS (Succ ww136) (Succ ww137)) (Succ (Succ ww137))",fontsize=16,color="magenta"];1161 -> 1185[label="",style="dashed", color="magenta", weight=3]; 1161 -> 1186[label="",style="dashed", color="magenta", weight=3]; 1161 -> 1187[label="",style="dashed", color="magenta", weight=3]; 1162[label="Succ (Succ ww136)",fontsize=16,color="green",shape="box"];1217 -> 1172[label="",style="dashed", color="red", weight=0]; 1217[label="primModNatS (primMinusNatS ww1410 ww1420) (Succ ww143)",fontsize=16,color="magenta"];1217 -> 1227[label="",style="dashed", color="magenta", weight=3]; 1217 -> 1228[label="",style="dashed", color="magenta", weight=3]; 1218 -> 493[label="",style="dashed", color="red", weight=0]; 1218[label="primModNatS (Succ ww1410) (Succ ww143)",fontsize=16,color="magenta"];1218 -> 1229[label="",style="dashed", color="magenta", weight=3]; 1218 -> 1230[label="",style="dashed", color="magenta", weight=3]; 1219[label="primModNatS Zero (Succ ww143)",fontsize=16,color="black",shape="triangle"];1219 -> 1231[label="",style="solid", color="black", weight=3]; 1220 -> 1219[label="",style="dashed", color="red", weight=0]; 1220[label="primModNatS Zero (Succ ww143)",fontsize=16,color="magenta"];1275[label="Succ ww131",fontsize=16,color="green",shape="box"];1276[label="Succ ww132",fontsize=16,color="green",shape="box"];1277[label="Succ ww132",fontsize=16,color="green",shape="box"];1303[label="ww1450",fontsize=16,color="green",shape="box"];1304[label="ww1460",fontsize=16,color="green",shape="box"];1305[label="ww1450",fontsize=16,color="green",shape="box"];1306[label="ww147",fontsize=16,color="green",shape="box"];1307[label="Zero",fontsize=16,color="green",shape="box"];1185[label="Succ ww136",fontsize=16,color="green",shape="box"];1186[label="Succ ww137",fontsize=16,color="green",shape="box"];1187[label="Succ ww137",fontsize=16,color="green",shape="box"];1227[label="ww1410",fontsize=16,color="green",shape="box"];1228[label="ww1420",fontsize=16,color="green",shape="box"];1229[label="ww143",fontsize=16,color="green",shape="box"];1230[label="ww1410",fontsize=16,color="green",shape="box"];1231[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (159) TRUE