31.25/16.38 MAYBE 33.79/17.02 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 33.79/17.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 33.79/17.02 33.79/17.02 33.79/17.02 H-Termination with start terms of the given HASKELL could not be shown: 33.79/17.02 33.79/17.02 (0) HASKELL 33.79/17.02 (1) IFR [EQUIVALENT, 0 ms] 33.79/17.02 (2) HASKELL 33.79/17.02 (3) BR [EQUIVALENT, 0 ms] 33.79/17.02 (4) HASKELL 33.79/17.02 (5) COR [EQUIVALENT, 0 ms] 33.79/17.02 (6) HASKELL 33.79/17.02 (7) NumRed [SOUND, 0 ms] 33.79/17.02 (8) HASKELL 33.79/17.02 (9) Narrow [SOUND, 0 ms] 33.79/17.02 (10) AND 33.79/17.02 (11) QDP 33.79/17.02 (12) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (13) QDP 33.79/17.02 (14) QDPOrderProof [EQUIVALENT, 0 ms] 33.79/17.02 (15) QDP 33.79/17.02 (16) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (17) QDP 33.79/17.02 (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.79/17.02 (19) YES 33.79/17.02 (20) QDP 33.79/17.02 (21) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (22) QDP 33.79/17.02 (23) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (24) QDP 33.79/17.02 (25) UsableRulesProof [EQUIVALENT, 0 ms] 33.79/17.02 (26) QDP 33.79/17.02 (27) QReductionProof [EQUIVALENT, 0 ms] 33.79/17.02 (28) QDP 33.79/17.02 (29) MNOCProof [EQUIVALENT, 0 ms] 33.79/17.02 (30) QDP 33.79/17.02 (31) InductionCalculusProof [EQUIVALENT, 0 ms] 33.79/17.02 (32) QDP 33.79/17.02 (33) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (34) QDP 33.79/17.02 (35) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (36) QDP 33.79/17.02 (37) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (38) QDP 33.79/17.02 (39) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (40) QDP 33.79/17.02 (41) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (42) QDP 33.79/17.02 (43) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (44) QDP 33.79/17.02 (45) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (46) QDP 33.79/17.02 (47) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (48) QDP 33.79/17.02 (49) MNOCProof [EQUIVALENT, 0 ms] 33.79/17.02 (50) QDP 33.79/17.02 (51) InductionCalculusProof [EQUIVALENT, 0 ms] 33.79/17.02 (52) QDP 33.79/17.02 (53) QDP 33.79/17.02 (54) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (55) QDP 33.79/17.02 (56) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (57) QDP 33.79/17.02 (58) UsableRulesProof [EQUIVALENT, 0 ms] 33.79/17.02 (59) QDP 33.79/17.02 (60) QReductionProof [EQUIVALENT, 0 ms] 33.79/17.02 (61) QDP 33.79/17.02 (62) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (63) QDP 33.79/17.02 (64) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (65) QDP 33.79/17.02 (66) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (67) QDP 33.79/17.02 (68) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (69) QDP 33.79/17.02 (70) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (71) QDP 33.79/17.02 (72) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (73) QDP 33.79/17.02 (74) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (75) QDP 33.79/17.02 (76) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (77) QDP 33.79/17.02 (78) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (79) QDP 33.79/17.02 (80) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (81) QDP 33.79/17.02 (82) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (83) QDP 33.79/17.02 (84) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (85) QDP 33.79/17.02 (86) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (87) QDP 33.79/17.02 (88) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (89) QDP 33.79/17.02 (90) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (91) QDP 33.79/17.02 (92) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (93) QDP 33.79/17.02 (94) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (95) QDP 33.79/17.02 (96) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (97) QDP 33.79/17.02 (98) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (99) QDP 33.79/17.02 (100) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (101) QDP 33.79/17.02 (102) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (103) QDP 33.79/17.02 (104) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (105) QDP 33.79/17.02 (106) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (107) QDP 33.79/17.02 (108) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (109) QDP 33.79/17.02 (110) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (111) QDP 33.79/17.02 (112) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (113) QDP 33.79/17.02 (114) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (115) QDP 33.79/17.02 (116) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (117) QDP 33.79/17.02 (118) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (119) QDP 33.79/17.02 (120) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (121) QDP 33.79/17.02 (122) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (123) QDP 33.79/17.02 (124) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (125) QDP 33.79/17.02 (126) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (127) QDP 33.79/17.02 (128) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (129) QDP 33.79/17.02 (130) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (131) QDP 33.79/17.02 (132) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (133) QDP 33.79/17.02 (134) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (135) QDP 33.79/17.02 (136) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (137) QDP 33.79/17.02 (138) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (139) QDP 33.79/17.02 (140) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (141) QDP 33.79/17.02 (142) TransformationProof [EQUIVALENT, 0 ms] 33.79/17.02 (143) QDP 33.79/17.02 (144) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.79/17.02 (145) YES 33.79/17.02 (146) QDP 33.79/17.02 (147) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.79/17.02 (148) YES 33.79/17.02 (149) QDP 33.79/17.02 (150) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (151) QDP 33.79/17.02 (152) QDPOrderProof [EQUIVALENT, 0 ms] 33.79/17.02 (153) QDP 33.79/17.02 (154) DependencyGraphProof [EQUIVALENT, 0 ms] 33.79/17.02 (155) QDP 33.79/17.02 (156) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.79/17.02 (157) YES 33.79/17.02 (158) Narrow [COMPLETE, 0 ms] 33.79/17.02 (159) TRUE 33.79/17.02 33.79/17.02 33.79/17.02 ---------------------------------------- 33.79/17.02 33.79/17.02 (0) 33.79/17.02 Obligation: 33.79/17.02 mainModule Main 33.79/17.02 module Main where { 33.79/17.02 import qualified Prelude; 33.79/17.02 } 33.79/17.02 33.79/17.02 ---------------------------------------- 33.79/17.02 33.79/17.02 (1) IFR (EQUIVALENT) 33.79/17.02 If Reductions: 33.79/17.02 The following If expression 33.79/17.02 "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" 33.79/17.02 is transformed to 33.79/17.02 "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); 33.79/17.02 primDivNatS0 x y False = Zero; 33.79/17.02 " 33.79/17.02 The following If expression 33.79/17.02 "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" 33.79/17.02 is transformed to 33.79/17.02 "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); 33.79/17.03 primModNatS0 x y False = Succ x; 33.79/17.03 " 33.79/17.03 The following If expression 33.79/17.03 "if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x" 33.79/17.03 is transformed to 33.79/17.03 "primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y); 33.79/17.03 primModNatP0 x y False = primMinusNatS y x; 33.79/17.03 " 33.79/17.03 The following If expression 33.79/17.03 "if b then (showChar '(') . p . showChar ')' else p" 33.79/17.03 is transformed to 33.79/17.03 "showParen0 p True = (showChar '(') . p . showChar ')'; 33.79/17.03 showParen0 p False = p; 33.79/17.03 " 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (2) 33.79/17.03 Obligation: 33.79/17.03 mainModule Main 33.79/17.03 module Main where { 33.79/17.03 import qualified Prelude; 33.79/17.03 } 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (3) BR (EQUIVALENT) 33.79/17.03 Replaced joker patterns by fresh variables and removed binding patterns. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (4) 33.79/17.03 Obligation: 33.79/17.03 mainModule Main 33.79/17.03 module Main where { 33.79/17.03 import qualified Prelude; 33.79/17.03 } 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (5) COR (EQUIVALENT) 33.79/17.03 Cond Reductions: 33.79/17.03 The following Function with conditions 33.79/17.03 "undefined |Falseundefined; 33.79/17.03 " 33.79/17.03 is transformed to 33.79/17.03 "undefined = undefined1; 33.79/17.03 " 33.79/17.03 "undefined0 True = undefined; 33.79/17.03 " 33.79/17.03 "undefined1 = undefined0 False; 33.79/17.03 " 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (6) 33.79/17.03 Obligation: 33.79/17.03 mainModule Main 33.79/17.03 module Main where { 33.79/17.03 import qualified Prelude; 33.79/17.03 } 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (7) NumRed (SOUND) 33.79/17.03 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (8) 33.79/17.03 Obligation: 33.79/17.03 mainModule Main 33.79/17.03 module Main where { 33.79/17.03 import qualified Prelude; 33.79/17.03 } 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (9) Narrow (SOUND) 33.79/17.03 Haskell To QDPs 33.79/17.03 33.79/17.03 digraph dp_graph { 33.79/17.03 node [outthreshold=100, inthreshold=100];1[label="showsPrec",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 33.79/17.03 3[label="showsPrec ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 33.79/17.03 4[label="showsPrec ww3 ww4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 33.79/17.03 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]; 33.79/17.03 1308 -> 6[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 6[label="showsPrec ww3 (ww40 :% ww41) ww5",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 33.79/17.03 7 -> 27[label="",style="dashed", color="red", weight=0]; 33.79/17.03 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]; 33.79/17.03 7 -> 29[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 7 -> 30[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 7 -> 31[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 7 -> 32[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 7 -> 33[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 7 -> 34[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 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 (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];29[label="ww5",fontsize=16,color="green",shape="box"];30[label="ww41",fontsize=16,color="green",shape="box"];31[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"];32[label="ww40",fontsize=16,color="green",shape="box"];33[label="ww3",fontsize=16,color="green",shape="box"];34[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"];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]; 33.79/17.03 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]; 33.79/17.03 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]; 33.79/17.03 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]; 33.79/17.03 1309 -> 45[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1310[label="ww20/Neg ww200",fontsize=10,color="white",style="solid",shape="box"];44 -> 1310[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1310 -> 46[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 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]; 33.79/17.03 1311 -> 47[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1312[label="ww200/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 1312[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1312 -> 48[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 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]; 33.79/17.03 1313 -> 49[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1314[label="ww200/Zero",fontsize=10,color="white",style="solid",shape="box"];46 -> 1314[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1314 -> 50[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 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]; 33.79/17.03 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]; 33.79/17.03 49[label="showParen0 ((shows ww21) . 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(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]; 33.79/17.03 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]; 33.79/17.03 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]; 33.79/17.03 54 -> 53[label="",style="dashed", color="red", weight=0]; 33.79/17.03 54[label="showParen0 ((shows ww21) . 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33.79/17.03 94 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 94[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];94 -> 235[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 94 -> 236[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 95 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 95[label="show ww21 ++ (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];95 -> 237[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 95 -> 238[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 96[label="showsPrec (Pos Zero) (ww210 :% ww211) ((showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25)",fontsize=16,color="black",shape="box"];96 -> 116[label="",style="solid", color="black", weight=3]; 33.79/17.03 97 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 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]; 33.79/17.03 97 -> 240[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 98 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 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]; 33.79/17.03 98 -> 242[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 99 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 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]; 33.79/17.03 99 -> 244[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 100 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 100[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]; 33.79/17.03 100 -> 246[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 101 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 101[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]; 33.79/17.03 101 -> 248[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 102 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 102[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]; 33.79/17.03 102 -> 250[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 103 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 103[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]; 33.79/17.03 103 -> 252[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 104 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 104[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]; 33.79/17.03 104 -> 254[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 105 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 105[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]; 33.79/17.03 105 -> 256[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 106 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 106[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]; 33.79/17.03 106 -> 258[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 107[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]; 33.79/17.03 1340 -> 127[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1341[label="ww2000000/Zero",fontsize=10,color="white",style="solid",shape="box"];107 -> 1341[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1341 -> 128[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 108 -> 53[label="",style="dashed", color="red", weight=0]; 33.79/17.03 108[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];225[label="show ww21",fontsize=16,color="black",shape="triangle"];225 -> 284[label="",style="solid", color="black", weight=3]; 33.79/17.03 226 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 226[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];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]; 33.79/17.03 1342 -> 285[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1343[label="ww62/[]",fontsize=10,color="white",style="solid",shape="box"];224 -> 1343[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1343 -> 286[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 227[label="show ww21",fontsize=16,color="black",shape="triangle"];227 -> 287[label="",style="solid", color="black", weight=3]; 33.79/17.03 228 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 228[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];229[label="show ww21",fontsize=16,color="black",shape="triangle"];229 -> 288[label="",style="solid", color="black", weight=3]; 33.79/17.03 230 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 230[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];231[label="show ww21",fontsize=16,color="black",shape="triangle"];231 -> 289[label="",style="solid", color="black", weight=3]; 33.79/17.03 232 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 232[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];233[label="show ww21",fontsize=16,color="black",shape="triangle"];233 -> 290[label="",style="solid", color="black", weight=3]; 33.79/17.03 234 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 234[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];235[label="show ww21",fontsize=16,color="black",shape="triangle"];235 -> 291[label="",style="solid", color="black", weight=3]; 33.79/17.03 236 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 236[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];237[label="show ww21",fontsize=16,color="black",shape="triangle"];237 -> 292[label="",style="solid", color="black", weight=3]; 33.79/17.03 238 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 238[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];116 -> 27[label="",style="dashed", color="red", weight=0]; 33.79/17.03 116[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"];116 -> 129[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 116 -> 130[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 116 -> 131[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 116 -> 132[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 116 -> 133[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 116 -> 134[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 116 -> 135[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 239[label="show ww21",fontsize=16,color="black",shape="triangle"];239 -> 293[label="",style="solid", color="black", weight=3]; 33.79/17.03 240 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 240[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];241[label="show ww21",fontsize=16,color="black",shape="triangle"];241 -> 294[label="",style="solid", color="black", weight=3]; 33.79/17.03 242 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 242[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];243[label="show ww21",fontsize=16,color="black",shape="triangle"];243 -> 295[label="",style="solid", color="black", weight=3]; 33.79/17.03 244 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 244[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];245[label="show ww21",fontsize=16,color="black",shape="triangle"];245 -> 296[label="",style="solid", color="black", weight=3]; 33.79/17.03 246 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 246[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];247[label="show ww21",fontsize=16,color="black",shape="triangle"];247 -> 297[label="",style="solid", color="black", weight=3]; 33.79/17.03 248 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 248[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];249[label="show ww21",fontsize=16,color="black",shape="triangle"];249 -> 298[label="",style="solid", color="black", weight=3]; 33.79/17.03 250 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 250[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];251[label="show ww21",fontsize=16,color="black",shape="triangle"];251 -> 299[label="",style="solid", color="black", weight=3]; 33.79/17.03 252 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 252[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];253[label="show ww21",fontsize=16,color="black",shape="triangle"];253 -> 300[label="",style="solid", color="black", weight=3]; 33.79/17.03 254 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 254[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];255[label="show ww21",fontsize=16,color="black",shape="triangle"];255 -> 301[label="",style="solid", color="black", weight=3]; 33.79/17.03 256 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 256[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];257[label="show ww21",fontsize=16,color="black",shape="triangle"];257 -> 302[label="",style="solid", color="black", weight=3]; 33.79/17.03 258 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.03 258[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];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]; 33.79/17.03 128[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]; 33.79/17.03 284[label="error []",fontsize=16,color="red",shape="box"];130[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="black",shape="triangle"];130 -> 140[label="",style="solid", color="black", weight=3]; 33.79/17.03 285[label="(ww620 : ww621) ++ ww60",fontsize=16,color="black",shape="box"];285 -> 306[label="",style="solid", color="black", weight=3]; 33.79/17.03 286[label="[] ++ ww60",fontsize=16,color="black",shape="box"];286 -> 307[label="",style="solid", color="black", weight=3]; 33.79/17.03 287[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"];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 (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];131[label="ww211",fontsize=16,color="green",shape="box"];132[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="ww210",fontsize=16,color="green",shape="box"];134[label="Pos Zero",fontsize=16,color="green",shape="box"];135[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"];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="primShowInt ww21",fontsize=16,color="burlywood",shape="triangle"];1344[label="ww21/Pos ww210",fontsize=10,color="white",style="solid",shape="box"];296 -> 1344[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1344 -> 308[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1345[label="ww21/Neg ww210",fontsize=10,color="white",style="solid",shape="box"];296 -> 1345[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1345 -> 309[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 297[label="error []",fontsize=16,color="red",shape="box"];298[label="error []",fontsize=16,color="red",shape="box"];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]; 33.79/17.03 1346 -> 144[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1347[label="ww20000000/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 1347[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1347 -> 145[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 139 -> 53[label="",style="dashed", color="red", weight=0]; 33.79/17.03 139[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]; 33.79/17.03 306[label="ww620 : ww621 ++ ww60",fontsize=16,color="green",shape="box"];306 -> 330[label="",style="dashed", color="green", weight=3]; 33.79/17.03 307[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]; 33.79/17.03 1348 -> 331[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1349[label="ww210/Zero",fontsize=10,color="white",style="solid",shape="box"];308 -> 1349[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1349 -> 332[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 309[label="primShowInt (Neg ww210)",fontsize=16,color="black",shape="box"];309 -> 333[label="",style="solid", color="black", weight=3]; 33.79/17.03 144[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]; 33.79/17.03 145[label="showParen0 ((shows ww21) . 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33.79/17.03 340 -> 370[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 341[label="showsPrec (Pos Zero) (ww250 :% ww251) ww26",fontsize=16,color="black",shape="box"];341 -> 371[label="",style="solid", color="black", weight=3]; 33.79/17.03 342 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 342[label="show ww25 ++ ww26",fontsize=16,color="magenta"];342 -> 372[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 342 -> 373[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 343 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 343[label="show ww25 ++ ww26",fontsize=16,color="magenta"];343 -> 374[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 343 -> 375[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 344 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 344[label="show ww25 ++ ww26",fontsize=16,color="magenta"];344 -> 376[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 344 -> 377[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 345 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 345[label="show ww25 ++ ww26",fontsize=16,color="magenta"];345 -> 378[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 345 -> 379[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 346 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 346[label="show ww25 ++ ww26",fontsize=16,color="magenta"];346 -> 380[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 346 -> 381[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 347 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 347[label="show ww25 ++ ww26",fontsize=16,color="magenta"];347 -> 382[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 347 -> 383[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 348 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 348[label="show ww25 ++ ww26",fontsize=16,color="magenta"];348 -> 384[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 348 -> 385[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 349 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 349[label="show ww25 ++ ww26",fontsize=16,color="magenta"];349 -> 386[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 349 -> 387[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 350 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 350[label="show ww25 ++ ww26",fontsize=16,color="magenta"];350 -> 388[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 350 -> 389[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 351 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.03 351[label="show ww25 ++ ww26",fontsize=16,color="magenta"];351 -> 390[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 351 -> 391[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 447[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];448[label="ww2100",fontsize=16,color="green",shape="box"];446[label="div Pos (Succ ww81) Pos (Succ ww82)",fontsize=16,color="black",shape="triangle"];446 -> 452[label="",style="solid", color="black", weight=3]; 33.79/17.03 464 -> 476[label="",style="dashed", color="red", weight=0]; 33.79/17.03 464[label="primIntToChar (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];464 -> 477[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 464 -> 478[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 304[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]; 33.79/17.03 305[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]; 33.79/17.03 357 -> 225[label="",style="dashed", color="red", weight=0]; 33.79/17.03 357[label="show ww25",fontsize=16,color="magenta"];357 -> 403[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 358[label="ww26",fontsize=16,color="green",shape="box"];359 -> 227[label="",style="dashed", color="red", weight=0]; 33.79/17.03 359[label="show ww25",fontsize=16,color="magenta"];359 -> 404[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 360[label="ww26",fontsize=16,color="green",shape="box"];361 -> 229[label="",style="dashed", color="red", weight=0]; 33.79/17.03 361[label="show ww25",fontsize=16,color="magenta"];361 -> 405[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 362[label="ww26",fontsize=16,color="green",shape="box"];363 -> 231[label="",style="dashed", color="red", weight=0]; 33.79/17.03 363[label="show ww25",fontsize=16,color="magenta"];363 -> 406[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 364[label="ww26",fontsize=16,color="green",shape="box"];365 -> 233[label="",style="dashed", color="red", weight=0]; 33.79/17.03 365[label="show ww25",fontsize=16,color="magenta"];365 -> 407[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 366[label="ww26",fontsize=16,color="green",shape="box"];367 -> 235[label="",style="dashed", color="red", weight=0]; 33.79/17.03 367[label="show ww25",fontsize=16,color="magenta"];367 -> 408[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 368[label="ww26",fontsize=16,color="green",shape="box"];369 -> 237[label="",style="dashed", color="red", weight=0]; 33.79/17.03 369[label="show ww25",fontsize=16,color="magenta"];369 -> 409[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 370[label="ww26",fontsize=16,color="green",shape="box"];371 -> 27[label="",style="dashed", color="red", weight=0]; 33.79/17.03 371[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"];371 -> 410[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 371 -> 411[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 371 -> 412[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 371 -> 413[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 371 -> 414[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 371 -> 415[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 372 -> 239[label="",style="dashed", color="red", weight=0]; 33.79/17.03 372[label="show ww25",fontsize=16,color="magenta"];372 -> 416[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 373[label="ww26",fontsize=16,color="green",shape="box"];374 -> 241[label="",style="dashed", color="red", weight=0]; 33.79/17.03 374[label="show ww25",fontsize=16,color="magenta"];374 -> 417[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 375[label="ww26",fontsize=16,color="green",shape="box"];376 -> 243[label="",style="dashed", color="red", weight=0]; 33.79/17.03 376[label="show ww25",fontsize=16,color="magenta"];376 -> 418[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 377[label="ww26",fontsize=16,color="green",shape="box"];378 -> 245[label="",style="dashed", color="red", weight=0]; 33.79/17.03 378[label="show ww25",fontsize=16,color="magenta"];378 -> 419[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 379[label="ww26",fontsize=16,color="green",shape="box"];380 -> 247[label="",style="dashed", color="red", weight=0]; 33.79/17.03 380[label="show ww25",fontsize=16,color="magenta"];380 -> 420[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 381[label="ww26",fontsize=16,color="green",shape="box"];382 -> 249[label="",style="dashed", color="red", weight=0]; 33.79/17.03 382[label="show ww25",fontsize=16,color="magenta"];382 -> 421[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 383[label="ww26",fontsize=16,color="green",shape="box"];384 -> 251[label="",style="dashed", color="red", weight=0]; 33.79/17.03 384[label="show ww25",fontsize=16,color="magenta"];384 -> 422[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 385[label="ww26",fontsize=16,color="green",shape="box"];386 -> 253[label="",style="dashed", color="red", weight=0]; 33.79/17.03 386[label="show ww25",fontsize=16,color="magenta"];386 -> 423[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 387[label="ww26",fontsize=16,color="green",shape="box"];388 -> 255[label="",style="dashed", color="red", weight=0]; 33.79/17.03 388[label="show ww25",fontsize=16,color="magenta"];388 -> 424[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 389[label="ww26",fontsize=16,color="green",shape="box"];390 -> 257[label="",style="dashed", color="red", weight=0]; 33.79/17.03 390[label="show ww25",fontsize=16,color="magenta"];390 -> 425[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 391[label="ww26",fontsize=16,color="green",shape="box"];452[label="primDivInt (Pos (Succ ww81)) (Pos (Succ ww82))",fontsize=16,color="black",shape="box"];452 -> 463[label="",style="solid", color="black", weight=3]; 33.79/17.03 477[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];478[label="ww2100",fontsize=16,color="green",shape="box"];476[label="primIntToChar (mod Pos (Succ ww87) Pos (Succ ww88))",fontsize=16,color="black",shape="triangle"];476 -> 479[label="",style="solid", color="black", weight=3]; 33.79/17.03 328[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]; 33.79/17.03 329 -> 57[label="",style="dashed", color="red", weight=0]; 33.79/17.03 329[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="ww25",fontsize=16,color="green",shape="box"];405[label="ww25",fontsize=16,color="green",shape="box"];406[label="ww25",fontsize=16,color="green",shape="box"];407[label="ww25",fontsize=16,color="green",shape="box"];408[label="ww25",fontsize=16,color="green",shape="box"];409[label="ww25",fontsize=16,color="green",shape="box"];410[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"];411[label="ww251",fontsize=16,color="green",shape="box"];412[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"];413[label="ww250",fontsize=16,color="green",shape="box"];414[label="Pos Zero",fontsize=16,color="green",shape="box"];415[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"];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"];463[label="Pos (primDivNatS (Succ ww81) (Succ ww82))",fontsize=16,color="green",shape="box"];463 -> 475[label="",style="dashed", color="green", weight=3]; 33.79/17.03 479[label="primIntToChar (primModInt (Pos (Succ ww87)) (Pos (Succ ww88)))",fontsize=16,color="black",shape="box"];479 -> 482[label="",style="solid", color="black", weight=3]; 33.79/17.03 352 -> 426[label="",style="dashed", color="red", weight=0]; 33.79/17.03 352[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]; 33.79/17.03 352 -> 428[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 352 -> 429[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 352 -> 430[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 352 -> 431[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 352 -> 432[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 352 -> 433[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 352 -> 434[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 475[label="primDivNatS (Succ ww81) (Succ ww82)",fontsize=16,color="black",shape="triangle"];475 -> 480[label="",style="solid", color="black", weight=3]; 33.79/17.03 482[label="primIntToChar (Pos (primModNatS (Succ ww87) (Succ ww88)))",fontsize=16,color="black",shape="box"];482 -> 491[label="",style="solid", color="black", weight=3]; 33.79/17.03 427[label="ww22",fontsize=16,color="green",shape="box"];428[label="ww24",fontsize=16,color="green",shape="box"];429[label="ww21",fontsize=16,color="green",shape="box"];430[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"];431[label="ww25",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="ww26",fontsize=16,color="green",shape="box"];434[label="ww23",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]; 33.79/17.03 480[label="primDivNatS0 ww81 ww82 (primGEqNatS ww81 ww82)",fontsize=16,color="burlywood",shape="box"];1373[label="ww81/Succ ww810",fontsize=10,color="white",style="solid",shape="box"];480 -> 1373[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1373 -> 483[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1374[label="ww81/Zero",fontsize=10,color="white",style="solid",shape="box"];480 -> 1374[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1374 -> 484[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 491[label="Char (primModNatS (Succ ww87) (Succ ww88))",fontsize=16,color="green",shape="box"];491 -> 497[label="",style="dashed", color="green", weight=3]; 33.79/17.03 445[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]; 33.79/17.03 483[label="primDivNatS0 (Succ ww810) ww82 (primGEqNatS (Succ ww810) ww82)",fontsize=16,color="burlywood",shape="box"];1375[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];483 -> 1375[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1375 -> 492[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1376[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];483 -> 1376[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1376 -> 493[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 484[label="primDivNatS0 Zero ww82 (primGEqNatS Zero ww82)",fontsize=16,color="burlywood",shape="box"];1377[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];484 -> 1377[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1377 -> 494[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1378[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];484 -> 1378[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1378 -> 495[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 497[label="primModNatS (Succ ww87) (Succ ww88)",fontsize=16,color="black",shape="triangle"];497 -> 502[label="",style="solid", color="black", weight=3]; 33.79/17.03 462[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]; 33.79/17.03 492[label="primDivNatS0 (Succ ww810) (Succ ww820) (primGEqNatS (Succ ww810) (Succ ww820))",fontsize=16,color="black",shape="box"];492 -> 498[label="",style="solid", color="black", weight=3]; 33.79/17.03 493[label="primDivNatS0 (Succ ww810) Zero (primGEqNatS (Succ ww810) Zero)",fontsize=16,color="black",shape="box"];493 -> 499[label="",style="solid", color="black", weight=3]; 33.79/17.03 494[label="primDivNatS0 Zero (Succ ww820) (primGEqNatS Zero (Succ ww820))",fontsize=16,color="black",shape="box"];494 -> 500[label="",style="solid", color="black", weight=3]; 33.79/17.03 495[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];495 -> 501[label="",style="solid", color="black", weight=3]; 33.79/17.03 502[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"];502 -> 1379[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1379 -> 508[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1380[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];502 -> 1380[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1380 -> 509[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 474[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 -> 481[label="",style="solid", color="black", weight=3]; 33.79/17.03 498 -> 1014[label="",style="dashed", color="red", weight=0]; 33.79/17.03 498[label="primDivNatS0 (Succ ww810) (Succ ww820) (primGEqNatS ww810 ww820)",fontsize=16,color="magenta"];498 -> 1015[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 498 -> 1016[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 498 -> 1017[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 498 -> 1018[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 499[label="primDivNatS0 (Succ ww810) Zero True",fontsize=16,color="black",shape="box"];499 -> 505[label="",style="solid", color="black", weight=3]; 33.79/17.03 500[label="primDivNatS0 Zero (Succ ww820) False",fontsize=16,color="black",shape="box"];500 -> 506[label="",style="solid", color="black", weight=3]; 33.79/17.03 501[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];501 -> 507[label="",style="solid", color="black", weight=3]; 33.79/17.03 508[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"];508 -> 1381[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1381 -> 516[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1382[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];508 -> 1382[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1382 -> 517[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 509[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"];509 -> 1383[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1383 -> 518[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1384[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];509 -> 1384[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1384 -> 519[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 481 -> 60[label="",style="dashed", color="red", weight=0]; 33.79/17.03 481[label="(shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77",fontsize=16,color="magenta"];481 -> 485[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 481 -> 486[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 481 -> 487[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 481 -> 488[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 481 -> 489[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 481 -> 490[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1015[label="ww810",fontsize=16,color="green",shape="box"];1016[label="ww820",fontsize=16,color="green",shape="box"];1017[label="ww810",fontsize=16,color="green",shape="box"];1018[label="ww820",fontsize=16,color="green",shape="box"];1014[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"];1014 -> 1385[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1385 -> 1055[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1386[label="ww133/Zero",fontsize=10,color="white",style="solid",shape="box"];1014 -> 1386[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1386 -> 1056[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 505[label="Succ (primDivNatS (primMinusNatS (Succ ww810) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];505 -> 514[label="",style="dashed", color="green", weight=3]; 33.79/17.03 506[label="Zero",fontsize=16,color="green",shape="box"];507[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];507 -> 515[label="",style="dashed", color="green", weight=3]; 33.79/17.03 516[label="primModNatS0 (Succ ww870) (Succ ww880) (primGEqNatS (Succ ww870) (Succ ww880))",fontsize=16,color="black",shape="box"];516 -> 526[label="",style="solid", color="black", weight=3]; 33.79/17.03 517[label="primModNatS0 (Succ ww870) Zero (primGEqNatS (Succ ww870) Zero)",fontsize=16,color="black",shape="box"];517 -> 527[label="",style="solid", color="black", weight=3]; 33.79/17.03 518[label="primModNatS0 Zero (Succ ww880) (primGEqNatS Zero (Succ ww880))",fontsize=16,color="black",shape="box"];518 -> 528[label="",style="solid", color="black", weight=3]; 33.79/17.03 519[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];519 -> 529[label="",style="solid", color="black", weight=3]; 33.79/17.03 485[label="ww75",fontsize=16,color="green",shape="box"];486[label="showChar (Char (Succ ww78)) ww79",fontsize=16,color="black",shape="box"];486 -> 496[label="",style="solid", color="black", weight=3]; 33.79/17.03 487[label="ww77",fontsize=16,color="green",shape="box"];488[label="ww76",fontsize=16,color="green",shape="box"];489[label="ww73",fontsize=16,color="green",shape="box"];490[label="ww74",fontsize=16,color="green",shape="box"];1055[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"];1055 -> 1387[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1387 -> 1067[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1388[label="ww134/Zero",fontsize=10,color="white",style="solid",shape="box"];1055 -> 1388[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1388 -> 1068[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1056[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"];1056 -> 1389[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1389 -> 1069[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1390[label="ww134/Zero",fontsize=10,color="white",style="solid",shape="box"];1056 -> 1390[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1390 -> 1070[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 514 -> 1268[label="",style="dashed", color="red", weight=0]; 33.79/17.03 514[label="primDivNatS (primMinusNatS (Succ ww810) Zero) (Succ Zero)",fontsize=16,color="magenta"];514 -> 1269[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 514 -> 1270[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 514 -> 1271[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 515 -> 1268[label="",style="dashed", color="red", weight=0]; 33.79/17.03 515[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];515 -> 1272[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 515 -> 1273[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 515 -> 1274[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 526 -> 1089[label="",style="dashed", color="red", weight=0]; 33.79/17.03 526[label="primModNatS0 (Succ ww870) (Succ ww880) (primGEqNatS ww870 ww880)",fontsize=16,color="magenta"];526 -> 1090[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 526 -> 1091[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 526 -> 1092[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 526 -> 1093[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 527[label="primModNatS0 (Succ ww870) Zero True",fontsize=16,color="black",shape="box"];527 -> 540[label="",style="solid", color="black", weight=3]; 33.79/17.03 528[label="primModNatS0 Zero (Succ ww880) False",fontsize=16,color="black",shape="box"];528 -> 541[label="",style="solid", color="black", weight=3]; 33.79/17.03 529[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];529 -> 542[label="",style="solid", color="black", weight=3]; 33.79/17.03 496[label="(:) Char (Succ ww78) ww79",fontsize=16,color="green",shape="box"];1067[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) (Succ ww1340))",fontsize=16,color="black",shape="box"];1067 -> 1081[label="",style="solid", color="black", weight=3]; 33.79/17.03 1068[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) Zero)",fontsize=16,color="black",shape="box"];1068 -> 1082[label="",style="solid", color="black", weight=3]; 33.79/17.03 1069[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero (Succ ww1340))",fontsize=16,color="black",shape="box"];1069 -> 1083[label="",style="solid", color="black", weight=3]; 33.79/17.03 1070[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1070 -> 1084[label="",style="solid", color="black", weight=3]; 33.79/17.03 1269[label="Zero",fontsize=16,color="green",shape="box"];1270[label="Succ ww810",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"];1391[label="ww145/Succ ww1450",fontsize=10,color="white",style="solid",shape="box"];1268 -> 1391[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1391 -> 1293[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1392[label="ww145/Zero",fontsize=10,color="white",style="solid",shape="box"];1268 -> 1392[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1392 -> 1294[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 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"];1090[label="ww870",fontsize=16,color="green",shape="box"];1091[label="ww880",fontsize=16,color="green",shape="box"];1092[label="ww880",fontsize=16,color="green",shape="box"];1093[label="ww870",fontsize=16,color="green",shape="box"];1089[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS ww138 ww139)",fontsize=16,color="burlywood",shape="triangle"];1393[label="ww138/Succ ww1380",fontsize=10,color="white",style="solid",shape="box"];1089 -> 1393[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1393 -> 1130[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1394[label="ww138/Zero",fontsize=10,color="white",style="solid",shape="box"];1089 -> 1394[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1394 -> 1131[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 540 -> 1176[label="",style="dashed", color="red", weight=0]; 33.79/17.03 540[label="primModNatS (primMinusNatS (Succ ww870) Zero) (Succ Zero)",fontsize=16,color="magenta"];540 -> 1177[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 540 -> 1178[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 540 -> 1179[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 541[label="Succ Zero",fontsize=16,color="green",shape="box"];542 -> 1176[label="",style="dashed", color="red", weight=0]; 33.79/17.03 542[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];542 -> 1180[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 542 -> 1181[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 542 -> 1182[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1081 -> 1014[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1081[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS ww1330 ww1340)",fontsize=16,color="magenta"];1081 -> 1132[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1081 -> 1133[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1082[label="primDivNatS0 (Succ ww131) (Succ ww132) True",fontsize=16,color="black",shape="triangle"];1082 -> 1134[label="",style="solid", color="black", weight=3]; 33.79/17.03 1083[label="primDivNatS0 (Succ ww131) (Succ ww132) False",fontsize=16,color="black",shape="box"];1083 -> 1135[label="",style="solid", color="black", weight=3]; 33.79/17.03 1084 -> 1082[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1084[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"];1395[label="ww146/Succ ww1460",fontsize=10,color="white",style="solid",shape="box"];1293 -> 1395[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1395 -> 1295[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1396[label="ww146/Zero",fontsize=10,color="white",style="solid",shape="box"];1293 -> 1396[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1396 -> 1296[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1294[label="primDivNatS (primMinusNatS Zero ww146) (Succ ww147)",fontsize=16,color="burlywood",shape="box"];1397[label="ww146/Succ ww1460",fontsize=10,color="white",style="solid",shape="box"];1294 -> 1397[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1397 -> 1297[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1398[label="ww146/Zero",fontsize=10,color="white",style="solid",shape="box"];1294 -> 1398[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1398 -> 1298[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1130[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) ww139)",fontsize=16,color="burlywood",shape="box"];1399[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1130 -> 1399[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1399 -> 1140[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1400[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1130 -> 1400[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1400 -> 1141[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1131[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero ww139)",fontsize=16,color="burlywood",shape="box"];1401[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1131 -> 1401[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1401 -> 1142[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1402[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1131 -> 1402[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1402 -> 1143[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1177[label="Succ ww870",fontsize=16,color="green",shape="box"];1178[label="Zero",fontsize=16,color="green",shape="box"];1179[label="Zero",fontsize=16,color="green",shape="box"];1176[label="primModNatS (primMinusNatS ww141 ww142) (Succ ww143)",fontsize=16,color="burlywood",shape="triangle"];1403[label="ww141/Succ ww1410",fontsize=10,color="white",style="solid",shape="box"];1176 -> 1403[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1403 -> 1207[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1404[label="ww141/Zero",fontsize=10,color="white",style="solid",shape="box"];1176 -> 1404[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1404 -> 1208[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1180[label="Zero",fontsize=16,color="green",shape="box"];1181[label="Zero",fontsize=16,color="green",shape="box"];1182[label="Zero",fontsize=16,color="green",shape="box"];1132[label="ww1340",fontsize=16,color="green",shape="box"];1133[label="ww1330",fontsize=16,color="green",shape="box"];1134[label="Succ (primDivNatS (primMinusNatS (Succ ww131) (Succ ww132)) (Succ (Succ ww132)))",fontsize=16,color="green",shape="box"];1134 -> 1144[label="",style="dashed", color="green", weight=3]; 33.79/17.03 1135[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]; 33.79/17.03 1296[label="primDivNatS (primMinusNatS (Succ ww1450) Zero) (Succ ww147)",fontsize=16,color="black",shape="box"];1296 -> 1300[label="",style="solid", color="black", weight=3]; 33.79/17.03 1297[label="primDivNatS (primMinusNatS Zero (Succ ww1460)) (Succ ww147)",fontsize=16,color="black",shape="box"];1297 -> 1301[label="",style="solid", color="black", weight=3]; 33.79/17.03 1298[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww147)",fontsize=16,color="black",shape="box"];1298 -> 1302[label="",style="solid", color="black", weight=3]; 33.79/17.03 1140[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) (Succ ww1390))",fontsize=16,color="black",shape="box"];1140 -> 1151[label="",style="solid", color="black", weight=3]; 33.79/17.03 1141[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) Zero)",fontsize=16,color="black",shape="box"];1141 -> 1152[label="",style="solid", color="black", weight=3]; 33.79/17.03 1142[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero (Succ ww1390))",fontsize=16,color="black",shape="box"];1142 -> 1153[label="",style="solid", color="black", weight=3]; 33.79/17.03 1143[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1143 -> 1154[label="",style="solid", color="black", weight=3]; 33.79/17.03 1207[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"];1207 -> 1405[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1405 -> 1213[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1406[label="ww142/Zero",fontsize=10,color="white",style="solid",shape="box"];1207 -> 1406[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1406 -> 1214[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1208[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"];1208 -> 1407[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1407 -> 1215[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1408[label="ww142/Zero",fontsize=10,color="white",style="solid",shape="box"];1208 -> 1408[label="",style="solid", color="burlywood", weight=9]; 33.79/17.03 1408 -> 1216[label="",style="solid", color="burlywood", weight=3]; 33.79/17.03 1144 -> 1268[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1144[label="primDivNatS (primMinusNatS (Succ ww131) (Succ ww132)) (Succ (Succ ww132))",fontsize=16,color="magenta"];1144 -> 1275[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1144 -> 1276[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1144 -> 1277[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1299 -> 1268[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1299[label="primDivNatS (primMinusNatS ww1450 ww1460) (Succ ww147)",fontsize=16,color="magenta"];1299 -> 1303[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1299 -> 1304[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1300 -> 475[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1300[label="primDivNatS (Succ ww1450) (Succ ww147)",fontsize=16,color="magenta"];1300 -> 1305[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1300 -> 1306[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1301[label="primDivNatS Zero (Succ ww147)",fontsize=16,color="black",shape="triangle"];1301 -> 1307[label="",style="solid", color="black", weight=3]; 33.79/17.03 1302 -> 1301[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1302[label="primDivNatS Zero (Succ ww147)",fontsize=16,color="magenta"];1151 -> 1089[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1151[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS ww1380 ww1390)",fontsize=16,color="magenta"];1151 -> 1160[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1151 -> 1161[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1152[label="primModNatS0 (Succ ww136) (Succ ww137) True",fontsize=16,color="black",shape="triangle"];1152 -> 1162[label="",style="solid", color="black", weight=3]; 33.79/17.03 1153[label="primModNatS0 (Succ ww136) (Succ ww137) False",fontsize=16,color="black",shape="box"];1153 -> 1163[label="",style="solid", color="black", weight=3]; 33.79/17.03 1154 -> 1152[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1154[label="primModNatS0 (Succ ww136) (Succ ww137) True",fontsize=16,color="magenta"];1213[label="primModNatS (primMinusNatS (Succ ww1410) (Succ ww1420)) (Succ ww143)",fontsize=16,color="black",shape="box"];1213 -> 1223[label="",style="solid", color="black", weight=3]; 33.79/17.03 1214[label="primModNatS (primMinusNatS (Succ ww1410) Zero) (Succ ww143)",fontsize=16,color="black",shape="box"];1214 -> 1224[label="",style="solid", color="black", weight=3]; 33.79/17.03 1215[label="primModNatS (primMinusNatS Zero (Succ ww1420)) (Succ ww143)",fontsize=16,color="black",shape="box"];1215 -> 1225[label="",style="solid", color="black", weight=3]; 33.79/17.03 1216[label="primModNatS (primMinusNatS Zero Zero) (Succ ww143)",fontsize=16,color="black",shape="box"];1216 -> 1226[label="",style="solid", color="black", weight=3]; 33.79/17.03 1275[label="Succ ww132",fontsize=16,color="green",shape="box"];1276[label="Succ ww131",fontsize=16,color="green",shape="box"];1277[label="Succ ww132",fontsize=16,color="green",shape="box"];1303[label="ww1460",fontsize=16,color="green",shape="box"];1304[label="ww1450",fontsize=16,color="green",shape="box"];1305[label="ww147",fontsize=16,color="green",shape="box"];1306[label="ww1450",fontsize=16,color="green",shape="box"];1307[label="Zero",fontsize=16,color="green",shape="box"];1160[label="ww1390",fontsize=16,color="green",shape="box"];1161[label="ww1380",fontsize=16,color="green",shape="box"];1162 -> 1176[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1162[label="primModNatS (primMinusNatS (Succ ww136) (Succ ww137)) (Succ (Succ ww137))",fontsize=16,color="magenta"];1162 -> 1189[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1162 -> 1190[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1162 -> 1191[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1163[label="Succ (Succ ww136)",fontsize=16,color="green",shape="box"];1223 -> 1176[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1223[label="primModNatS (primMinusNatS ww1410 ww1420) (Succ ww143)",fontsize=16,color="magenta"];1223 -> 1231[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1223 -> 1232[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1224 -> 497[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1224[label="primModNatS (Succ ww1410) (Succ ww143)",fontsize=16,color="magenta"];1224 -> 1233[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1224 -> 1234[label="",style="dashed", color="magenta", weight=3]; 33.79/17.03 1225[label="primModNatS Zero (Succ ww143)",fontsize=16,color="black",shape="triangle"];1225 -> 1235[label="",style="solid", color="black", weight=3]; 33.79/17.03 1226 -> 1225[label="",style="dashed", color="red", weight=0]; 33.79/17.03 1226[label="primModNatS Zero (Succ ww143)",fontsize=16,color="magenta"];1189[label="Succ ww136",fontsize=16,color="green",shape="box"];1190[label="Succ ww137",fontsize=16,color="green",shape="box"];1191[label="Succ ww137",fontsize=16,color="green",shape="box"];1231[label="ww1410",fontsize=16,color="green",shape="box"];1232[label="ww1420",fontsize=16,color="green",shape="box"];1233[label="ww143",fontsize=16,color="green",shape="box"];1234[label="ww1410",fontsize=16,color="green",shape="box"];1235[label="Zero",fontsize=16,color="green",shape="box"];} 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (10) 33.79/17.03 Complex Obligation (AND) 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (11) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS0(ww131, ww132, Zero, Zero) -> new_primDivNatS00(ww131, ww132) 33.79/17.03 new_primDivNatS00(ww131, ww132) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) 33.79/17.03 new_primDivNatS(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS1(Succ(ww810), Zero) -> new_primDivNatS(Succ(ww810), Zero, Zero) 33.79/17.03 new_primDivNatS0(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS0(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) 33.79/17.03 new_primDivNatS1(Succ(ww810), Succ(ww820)) -> new_primDivNatS0(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) 33.79/17.03 new_primDivNatS(Succ(ww1450), Zero, ww147) -> new_primDivNatS1(ww1450, ww147) 33.79/17.03 33.79/17.03 R is empty. 33.79/17.03 Q is empty. 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (12) DependencyGraphProof (EQUIVALENT) 33.79/17.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (13) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS00(ww131, ww132) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) 33.79/17.03 new_primDivNatS(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS(Succ(ww1450), Zero, ww147) -> new_primDivNatS1(ww1450, ww147) 33.79/17.03 new_primDivNatS1(Succ(ww810), Zero) -> new_primDivNatS(Succ(ww810), Zero, Zero) 33.79/17.03 new_primDivNatS1(Succ(ww810), Succ(ww820)) -> new_primDivNatS0(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS0(ww131, ww132, Zero, Zero) -> new_primDivNatS00(ww131, ww132) 33.79/17.03 new_primDivNatS0(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS0(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) 33.79/17.03 33.79/17.03 R is empty. 33.79/17.03 Q is empty. 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (14) QDPOrderProof (EQUIVALENT) 33.79/17.03 We use the reduction pair processor [LPAR04,JAR06]. 33.79/17.03 33.79/17.03 33.79/17.03 The following pairs can be oriented strictly and are deleted. 33.79/17.03 33.79/17.03 new_primDivNatS(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS1(Succ(ww810), Zero) -> new_primDivNatS(Succ(ww810), Zero, Zero) 33.79/17.03 new_primDivNatS1(Succ(ww810), Succ(ww820)) -> new_primDivNatS0(ww810, ww820, ww810, ww820) 33.79/17.03 The remaining pairs can at least be oriented weakly. 33.79/17.03 Used ordering: Polynomial interpretation [POLO]: 33.79/17.03 33.79/17.03 POL(Succ(x_1)) = 1 + x_1 33.79/17.03 POL(Zero) = 0 33.79/17.03 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 33.79/17.03 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 33.79/17.03 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 33.79/17.03 POL(new_primDivNatS1(x_1, x_2)) = 1 + x_1 33.79/17.03 33.79/17.03 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 33.79/17.03 none 33.79/17.03 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (15) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS00(ww131, ww132) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) 33.79/17.03 new_primDivNatS(Succ(ww1450), Zero, ww147) -> new_primDivNatS1(ww1450, ww147) 33.79/17.03 new_primDivNatS0(ww131, ww132, Zero, Zero) -> new_primDivNatS00(ww131, ww132) 33.79/17.03 new_primDivNatS0(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS0(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS(Succ(ww131), Succ(ww132), Succ(ww132)) 33.79/17.03 33.79/17.03 R is empty. 33.79/17.03 Q is empty. 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (16) DependencyGraphProof (EQUIVALENT) 33.79/17.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (17) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS0(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) 33.79/17.03 33.79/17.03 R is empty. 33.79/17.03 Q is empty. 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (18) QDPSizeChangeProof (EQUIVALENT) 33.79/17.03 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. 33.79/17.03 33.79/17.03 From the DPs we obtained the following set of size-change graphs: 33.79/17.03 *new_primDivNatS0(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS0(ww131, ww132, ww1330, ww1340) 33.79/17.03 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 33.79/17.03 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (19) 33.79/17.03 YES 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (20) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Neg(ww210)) -> new_primShowInt(Pos(ww210)) 33.79/17.03 new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 new_div(x0, x1) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (21) DependencyGraphProof (EQUIVALENT) 33.79/17.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (22) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(new_div(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 new_div(x0, x1) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (23) TransformationProof (EQUIVALENT) 33.79/17.03 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]: 33.79/17.03 33.79/17.03 (new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (24) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 new_div(x0, x1) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (25) UsableRulesProof (EQUIVALENT) 33.79/17.03 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. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (26) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 new_div(x0, x1) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (27) QReductionProof (EQUIVALENT) 33.79/17.03 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 33.79/17.03 33.79/17.03 new_div(x0, x1) 33.79/17.03 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (28) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (29) MNOCProof (EQUIVALENT) 33.79/17.03 We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (30) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 Q is empty. 33.79/17.03 We have to consider all (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (31) InductionCalculusProof (EQUIVALENT) 33.79/17.03 Note that final constraints are written in bold face. 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 For Pair new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) the following chains were created: 33.79/17.03 *We consider the chain new_primShowInt(Pos(Succ(x0))) -> new_primShowInt(Pos(new_primDivNatS4(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), new_primShowInt(Pos(Succ(x1))) -> new_primShowInt(Pos(new_primDivNatS4(x1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) which results in the following constraint: 33.79/17.03 33.79/17.03 (1) (new_primShowInt(Pos(new_primDivNatS4(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))=new_primShowInt(Pos(Succ(x1))) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS4(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: 33.79/17.03 33.79/17.03 (2) (Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=x2 & new_primDivNatS4(x0, x2)=Succ(x1) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS4(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS4(x0, x2)=Succ(x1) which results in the following new constraints: 33.79/17.03 33.79/17.03 (3) (new_primDivNatS01(x4, x3, x4, x3)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Succ(x3) ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 (4) (Succ(new_primDivNatS2(Succ(x6), Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero ==> new_primShowInt(Pos(Succ(Succ(x6))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x6), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 (5) (Succ(new_primDivNatS2(Zero, Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero ==> new_primShowInt(Pos(Succ(Zero)))_>=_new_primShowInt(Pos(new_primDivNatS4(Zero, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint: 33.79/17.03 33.79/17.03 (6) (x4=x7 & x3=x8 & new_primDivNatS01(x4, x3, x7, x8)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 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_primDivNatS01(x4, x3, x7, x8)=Succ(x1) which results in the following new constraints: 33.79/17.03 33.79/17.03 (7) (new_primDivNatS02(x10, x9)=Succ(x1) & x10=Zero & x9=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x9 ==> new_primShowInt(Pos(Succ(Succ(x10))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x10), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 (8) (new_primDivNatS02(x16, x15)=Succ(x1) & x16=Succ(x14) & x15=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 ==> new_primShowInt(Pos(Succ(Succ(x16))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x16), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 (9) (new_primDivNatS01(x20, x19, x18, x17)=Succ(x1) & x20=Succ(x18) & x19=Succ(x17) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19 & (\/x21:new_primDivNatS01(x20, x19, x18, x17)=Succ(x21) & x20=x18 & x19=x17 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19 ==> new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ==> new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 We solved constraint (7) using rules (I), (II), (III).We solved constraint (8) using rules (I), (II), (III).We simplified constraint (9) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint: 33.79/17.03 33.79/17.03 (10) (new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 To summarize, we get the following constraints P__>=_ for the following pairs. 33.79/17.03 33.79/17.03 *new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.79/17.03 33.79/17.03 *(new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS4(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 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. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (32) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (33) TransformationProof (EQUIVALENT) 33.79/17.03 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(ww2100))) -> new_primShowInt(Pos(new_primDivNatS4(ww2100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 33.79/17.03 33.79/17.03 (new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(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_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.79/17.03 (new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero))) 33.79/17.03 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (34) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.79/17.03 new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (35) DependencyGraphProof (EQUIVALENT) 33.79/17.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (36) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (37) TransformationProof (EQUIVALENT) 33.79/17.03 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(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]: 33.79/17.03 33.79/17.03 (new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero))) 33.79/17.03 (new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(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_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (38) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)) 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (39) DependencyGraphProof (EQUIVALENT) 33.79/17.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (40) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (41) TransformationProof (EQUIVALENT) 33.79/17.03 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(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]: 33.79/17.03 33.79/17.03 (new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero))) 33.79/17.03 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(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_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (42) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)) 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (43) DependencyGraphProof (EQUIVALENT) 33.79/17.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (44) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (45) TransformationProof (EQUIVALENT) 33.79/17.03 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(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]: 33.79/17.03 33.79/17.03 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero))) 33.79/17.03 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(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_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (46) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)) 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (47) DependencyGraphProof (EQUIVALENT) 33.79/17.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (48) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 The set Q consists of the following terms: 33.79/17.03 33.79/17.03 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.03 new_primDivNatS3(x0) 33.79/17.03 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.03 new_primDivNatS4(Zero, Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.03 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.03 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.03 new_primDivNatS02(x0, x1) 33.79/17.03 new_primDivNatS2(Zero, Zero, x0) 33.79/17.03 new_primDivNatS4(Succ(x0), Zero) 33.79/17.03 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.03 33.79/17.03 We have to consider all minimal (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (49) MNOCProof (EQUIVALENT) 33.79/17.03 We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (50) 33.79/17.03 Obligation: 33.79/17.03 Q DP problem: 33.79/17.03 The TRS P consists of the following rules: 33.79/17.03 33.79/17.03 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.79/17.03 33.79/17.03 The TRS R consists of the following rules: 33.79/17.03 33.79/17.03 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.03 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.03 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.03 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.03 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.03 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.03 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.03 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.03 new_primDivNatS3(ww147) -> Zero 33.79/17.03 33.79/17.03 Q is empty. 33.79/17.03 We have to consider all (P,Q,R)-chains. 33.79/17.03 ---------------------------------------- 33.79/17.03 33.79/17.03 (51) InductionCalculusProof (EQUIVALENT) 33.79/17.03 Note that final constraints are written in bold face. 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 For Pair new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(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: 33.79/17.03 *We consider the chain new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0))))))) -> new_primShowInt(Pos(new_primDivNatS01(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_primDivNatS01(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: 33.79/17.03 33.79/17.03 (1) (new_primShowInt(Pos(new_primDivNatS01(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_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: 33.79/17.03 33.79/17.03 (2) (Succ(Succ(Succ(x0)))=x2 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x4 & new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: 33.79/17.03 33.79/17.03 (3) (new_primDivNatS02(x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Zero)))=x6 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x5 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Zero, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 (4) (new_primDivNatS02(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_primDivNatS01(Succ(Succ(Succ(Succ(x10)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x10), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 (5) (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Succ(x13) & (\/x17:new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x17))))) & Succ(Succ(Succ(x14)))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x13 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x14)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x14))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x14, Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 We solved constraint (3) using rules (I), (II).We solved constraint (4) using rules (I), (II).We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: 33.79/17.03 33.79/17.03 (6) (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Zero))))=x13 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: 33.79/17.03 33.79/17.03 (7) (new_primDivNatS02(x19, x18)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Zero))))=x19 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x18 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 (8) (new_primDivNatS02(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_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x23))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x23)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 (9) (new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x27)))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=Succ(x26) & (\/x30:new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x30))))) & Succ(Succ(Succ(Succ(x27))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=x26 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x27)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x27), Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 We solved constraint (7) using rules (I), (II).We solved constraint (8) using rules (I), (II).We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint: 33.79/17.03 33.79/17.03 (10) (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 33.79/17.03 To summarize, we get the following constraints P__>=_ for the following pairs. 33.79/17.03 33.79/17.03 *new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.79/17.03 33.79/17.03 *(new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.79/17.04 33.79/17.04 33.79/17.04 33.79/17.04 33.79/17.04 33.79/17.04 33.79/17.04 33.79/17.04 33.79/17.04 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. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (52) 33.79/17.04 Obligation: 33.79/17.04 Q DP problem: 33.79/17.04 The TRS P consists of the following rules: 33.79/17.04 33.79/17.04 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.79/17.04 33.79/17.04 The TRS R consists of the following rules: 33.79/17.04 33.79/17.04 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.04 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.04 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.04 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.04 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.04 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.04 new_primDivNatS3(ww147) -> Zero 33.79/17.04 33.79/17.04 The set Q consists of the following terms: 33.79/17.04 33.79/17.04 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_primDivNatS3(x0) 33.79/17.04 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.04 new_primDivNatS4(Zero, Zero) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.04 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.04 new_primDivNatS02(x0, x1) 33.79/17.04 new_primDivNatS2(Zero, Zero, x0) 33.79/17.04 new_primDivNatS4(Succ(x0), Zero) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.04 33.79/17.04 We have to consider all minimal (P,Q,R)-chains. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (53) 33.79/17.04 Obligation: 33.79/17.04 Q DP problem: 33.79/17.04 The TRS P consists of the following rules: 33.79/17.04 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Pos(Succ(Succ(Succ(Zero)))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Pos(Succ(Succ(Succ(Succ(Zero))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Pos(Succ(Zero)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_pt0(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(ww20000000000))))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> 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, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Pos(Succ(Succ(Zero))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 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) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), :%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen0(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_pt0(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), :%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen(Neg(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 33.79/17.04 The TRS R consists of the following rules: 33.79/17.04 33.79/17.04 new_showParen1(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.04 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))) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.04 new_show8(ww21) -> error([]) 33.79/17.04 new_pt4(ww72, ww73, ww74, ww75, ww76, ww77, ww78, ww79, h, ba) -> :(Char(Succ(ww72)), new_pt3(ww73, ww74, ww75, ww76, ww77, :(Char(Succ(ww78)), ww79), h, ba)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.04 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.04 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.04 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_psPs0([], ww60) -> ww60 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.04 new_primDivNatS3(ww147) -> Zero 33.79/17.04 new_show5(ww21) -> error([]) 33.79/17.04 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.04 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.04 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)))))))))), [])) 33.79/17.04 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.04 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.04 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_show11(ww21) -> error([]) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.04 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.04 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(ww20000000000))))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt4(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, bc) 33.79/17.04 new_show(ww21, bf) -> error([]) 33.79/17.04 new_show2(ww21, bb) -> error([]) 33.79/17.04 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.04 new_show14(ww21, cc) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show7(ww21, bd, be) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show1(ww21) -> error([]) 33.79/17.04 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show3(ww21) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.04 new_primModNatS4(ww143) -> Zero 33.79/17.04 new_show4(ww21) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showParen1(Neg(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_show0(ww21) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.04 new_show9(ww21) -> error([]) 33.79/17.04 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.04 new_show12(ww21) -> error([]) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.04 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.04 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_show6(ww21) -> error([]) 33.79/17.04 new_show10(ww21, ca, cb) -> error([]) 33.79/17.04 33.79/17.04 The set Q consists of the following terms: 33.79/17.04 33.79/17.04 new_primShowInt0(Pos(Succ(x0))) 33.79/17.04 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.04 new_primDivNatS4(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_IOError) 33.79/17.04 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.04 new_showsPrec(x0, x1, ty_Bool) 33.79/17.04 new_primShowInt0(Neg(x0)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, ty_@0) 33.79/17.04 new_primModNatS2(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_show10(x0, x1, x2) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS2(Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.04 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primShowInt0(Pos(Zero)) 33.79/17.04 new_show7(x0, x1, x2) 33.79/17.04 new_pt4(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.04 new_primDivNatS02(x0, x1) 33.79/17.04 new_show1(x0) 33.79/17.04 new_psPs0(:(x0, x1), x2) 33.79/17.04 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.04 new_primModNatS02(x0, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.04 new_showsPrec(x0, x1, ty_Float) 33.79/17.04 new_show14(x0, x1) 33.79/17.04 new_div(x0, x1) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_show12(x0) 33.79/17.04 new_show8(x0) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_primModNatS3(Zero, Zero, x0) 33.79/17.04 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.04 new_primDivNatS2(Zero, Zero, x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.04 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_show6(x0) 33.79/17.04 new_show15(x0, x1, x2, x3) 33.79/17.04 new_primDivNatS3(x0) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.04 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.04 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(x0)) 33.79/17.04 new_show5(x0) 33.79/17.04 new_showsPrec(x0, x1, ty_Integer) 33.79/17.04 new_show(x0, x1) 33.79/17.04 new_show2(x0, x1) 33.79/17.04 new_primModNatS4(x0) 33.79/17.04 new_primIntToChar(x0, x1) 33.79/17.04 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.04 new_showsPrec(x0, x1, ty_Int) 33.79/17.04 new_show9(x0) 33.79/17.04 new_show11(x0) 33.79/17.04 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.04 new_show4(x0) 33.79/17.04 new_psPs0([], x0) 33.79/17.04 new_primDivNatS4(Zero, Zero) 33.79/17.04 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.04 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.04 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show0(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show13(x0) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_show3(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.04 new_showsPrec(x0, x1, ty_Char) 33.79/17.04 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_Double) 33.79/17.04 33.79/17.04 We have to consider all minimal (P,Q,R)-chains. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (54) DependencyGraphProof (EQUIVALENT) 33.79/17.04 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 67 less nodes. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (55) 33.79/17.04 Obligation: 33.79/17.04 Q DP problem: 33.79/17.04 The TRS P consists of the following rules: 33.79/17.04 33.79/17.04 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 33.79/17.04 The TRS R consists of the following rules: 33.79/17.04 33.79/17.04 new_showParen1(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.04 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))) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.04 new_show8(ww21) -> error([]) 33.79/17.04 new_pt4(ww72, ww73, ww74, ww75, ww76, ww77, ww78, ww79, h, ba) -> :(Char(Succ(ww72)), new_pt3(ww73, ww74, ww75, ww76, ww77, :(Char(Succ(ww78)), ww79), h, ba)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.04 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.04 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.04 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_psPs0([], ww60) -> ww60 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.04 new_primDivNatS3(ww147) -> Zero 33.79/17.04 new_show5(ww21) -> error([]) 33.79/17.04 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.04 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.04 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)))))))))), [])) 33.79/17.04 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.04 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.04 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_show11(ww21) -> error([]) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.04 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.04 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(ww20000000000))))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt4(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, bc) 33.79/17.04 new_show(ww21, bf) -> error([]) 33.79/17.04 new_show2(ww21, bb) -> error([]) 33.79/17.04 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.04 new_show14(ww21, cc) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show7(ww21, bd, be) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show1(ww21) -> error([]) 33.79/17.04 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show3(ww21) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.04 new_primModNatS4(ww143) -> Zero 33.79/17.04 new_show4(ww21) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showParen1(Neg(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_show0(ww21) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.04 new_show9(ww21) -> error([]) 33.79/17.04 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.04 new_show12(ww21) -> error([]) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.04 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.04 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_show6(ww21) -> error([]) 33.79/17.04 new_show10(ww21, ca, cb) -> error([]) 33.79/17.04 33.79/17.04 The set Q consists of the following terms: 33.79/17.04 33.79/17.04 new_primShowInt0(Pos(Succ(x0))) 33.79/17.04 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.04 new_primDivNatS4(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_IOError) 33.79/17.04 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.04 new_showsPrec(x0, x1, ty_Bool) 33.79/17.04 new_primShowInt0(Neg(x0)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, ty_@0) 33.79/17.04 new_primModNatS2(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_show10(x0, x1, x2) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS2(Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.04 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primShowInt0(Pos(Zero)) 33.79/17.04 new_show7(x0, x1, x2) 33.79/17.04 new_pt4(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.04 new_primDivNatS02(x0, x1) 33.79/17.04 new_show1(x0) 33.79/17.04 new_psPs0(:(x0, x1), x2) 33.79/17.04 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.04 new_primModNatS02(x0, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.04 new_showsPrec(x0, x1, ty_Float) 33.79/17.04 new_show14(x0, x1) 33.79/17.04 new_div(x0, x1) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_show12(x0) 33.79/17.04 new_show8(x0) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_primModNatS3(Zero, Zero, x0) 33.79/17.04 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.04 new_primDivNatS2(Zero, Zero, x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.04 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_show6(x0) 33.79/17.04 new_show15(x0, x1, x2, x3) 33.79/17.04 new_primDivNatS3(x0) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.04 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.04 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(x0)) 33.79/17.04 new_show5(x0) 33.79/17.04 new_showsPrec(x0, x1, ty_Integer) 33.79/17.04 new_show(x0, x1) 33.79/17.04 new_show2(x0, x1) 33.79/17.04 new_primModNatS4(x0) 33.79/17.04 new_primIntToChar(x0, x1) 33.79/17.04 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.04 new_showsPrec(x0, x1, ty_Int) 33.79/17.04 new_show9(x0) 33.79/17.04 new_show11(x0) 33.79/17.04 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.04 new_show4(x0) 33.79/17.04 new_psPs0([], x0) 33.79/17.04 new_primDivNatS4(Zero, Zero) 33.79/17.04 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.04 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.04 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show0(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show13(x0) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_show3(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.04 new_showsPrec(x0, x1, ty_Char) 33.79/17.04 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_Double) 33.79/17.04 33.79/17.04 We have to consider all minimal (P,Q,R)-chains. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (56) TransformationProof (EQUIVALENT) 33.79/17.04 By instantiating [LPAR04] the rule new_showParen(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) we obtained the following new rules [LPAR04]: 33.79/17.04 33.79/17.04 (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)) 33.79/17.04 33.79/17.04 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (57) 33.79/17.04 Obligation: 33.79/17.04 Q DP problem: 33.79/17.04 The TRS P consists of the following rules: 33.79/17.04 33.79/17.04 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 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) 33.79/17.04 33.79/17.04 The TRS R consists of the following rules: 33.79/17.04 33.79/17.04 new_showParen1(Neg(Succ(ww2000)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.04 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))) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.04 new_show8(ww21) -> error([]) 33.79/17.04 new_pt4(ww72, ww73, ww74, ww75, ww76, ww77, ww78, ww79, h, ba) -> :(Char(Succ(ww72)), new_pt3(ww73, ww74, ww75, ww76, ww77, :(Char(Succ(ww78)), ww79), h, ba)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.04 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.04 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.04 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_psPs0([], ww60) -> ww60 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.04 new_primDivNatS3(ww147) -> Zero 33.79/17.04 new_show5(ww21) -> error([]) 33.79/17.04 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.04 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.04 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)))))))))), [])) 33.79/17.04 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.04 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.04 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_show11(ww21) -> error([]) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.04 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.04 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(ww20000000000))))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt4(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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, bc) 33.79/17.04 new_show(ww21, bf) -> error([]) 33.79/17.04 new_show2(ww21, bb) -> error([]) 33.79/17.04 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.04 new_show14(ww21, cc) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show7(ww21, bd, be) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show1(ww21) -> error([]) 33.79/17.04 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show3(ww21) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.04 new_primModNatS4(ww143) -> Zero 33.79/17.04 new_show4(ww21) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showParen1(Neg(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_show0(ww21) -> error([]) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.04 new_show9(ww21) -> error([]) 33.79/17.04 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.04 new_show12(ww21) -> error([]) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.04 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.04 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_show6(ww21) -> error([]) 33.79/17.04 new_show10(ww21, ca, cb) -> error([]) 33.79/17.04 33.79/17.04 The set Q consists of the following terms: 33.79/17.04 33.79/17.04 new_primShowInt0(Pos(Succ(x0))) 33.79/17.04 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.04 new_primDivNatS4(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_IOError) 33.79/17.04 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.04 new_showsPrec(x0, x1, ty_Bool) 33.79/17.04 new_primShowInt0(Neg(x0)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, ty_@0) 33.79/17.04 new_primModNatS2(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_show10(x0, x1, x2) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS2(Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.04 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primShowInt0(Pos(Zero)) 33.79/17.04 new_show7(x0, x1, x2) 33.79/17.04 new_pt4(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.04 new_primDivNatS02(x0, x1) 33.79/17.04 new_show1(x0) 33.79/17.04 new_psPs0(:(x0, x1), x2) 33.79/17.04 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.04 new_primModNatS02(x0, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.04 new_showsPrec(x0, x1, ty_Float) 33.79/17.04 new_show14(x0, x1) 33.79/17.04 new_div(x0, x1) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_show12(x0) 33.79/17.04 new_show8(x0) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_primModNatS3(Zero, Zero, x0) 33.79/17.04 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.04 new_primDivNatS2(Zero, Zero, x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.04 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_show6(x0) 33.79/17.04 new_show15(x0, x1, x2, x3) 33.79/17.04 new_primDivNatS3(x0) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.04 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.04 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(x0)) 33.79/17.04 new_show5(x0) 33.79/17.04 new_showsPrec(x0, x1, ty_Integer) 33.79/17.04 new_show(x0, x1) 33.79/17.04 new_show2(x0, x1) 33.79/17.04 new_primModNatS4(x0) 33.79/17.04 new_primIntToChar(x0, x1) 33.79/17.04 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.04 new_showsPrec(x0, x1, ty_Int) 33.79/17.04 new_show9(x0) 33.79/17.04 new_show11(x0) 33.79/17.04 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.04 new_show4(x0) 33.79/17.04 new_psPs0([], x0) 33.79/17.04 new_primDivNatS4(Zero, Zero) 33.79/17.04 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.04 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.04 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show0(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show13(x0) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_show3(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.04 new_showsPrec(x0, x1, ty_Char) 33.79/17.04 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_Double) 33.79/17.04 33.79/17.04 We have to consider all minimal (P,Q,R)-chains. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (58) UsableRulesProof (EQUIVALENT) 33.79/17.04 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. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (59) 33.79/17.04 Obligation: 33.79/17.04 Q DP problem: 33.79/17.04 The TRS P consists of the following rules: 33.79/17.04 33.79/17.04 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 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) 33.79/17.04 33.79/17.04 The TRS R consists of the following rules: 33.79/17.04 33.79/17.04 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.04 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.04 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.04 new_psPs0([], ww60) -> ww60 33.79/17.04 new_show11(ww21) -> error([]) 33.79/17.04 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.04 new_show2(ww21, bb) -> error([]) 33.79/17.04 new_show12(ww21) -> error([]) 33.79/17.04 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show1(ww21) -> error([]) 33.79/17.04 new_show5(ww21) -> error([]) 33.79/17.04 new_show3(ww21) -> error([]) 33.79/17.04 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.04 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))) 33.79/17.04 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)))))))))), [])) 33.79/17.04 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.04 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.04 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.04 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.04 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.04 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.04 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.04 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.04 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.04 new_primModNatS4(ww143) -> Zero 33.79/17.04 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.04 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.04 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.04 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS3(ww147) -> Zero 33.79/17.04 new_show(ww21, bf) -> error([]) 33.79/17.04 new_show9(ww21) -> error([]) 33.79/17.04 new_show8(ww21) -> error([]) 33.79/17.04 new_show10(ww21, ca, cb) -> error([]) 33.79/17.04 new_show14(ww21, cc) -> error([]) 33.79/17.04 new_show4(ww21) -> error([]) 33.79/17.04 new_show7(ww21, bd, be) -> error([]) 33.79/17.04 new_show6(ww21) -> error([]) 33.79/17.04 new_show0(ww21) -> error([]) 33.79/17.04 33.79/17.04 The set Q consists of the following terms: 33.79/17.04 33.79/17.04 new_primShowInt0(Pos(Succ(x0))) 33.79/17.04 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.04 new_primDivNatS4(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_IOError) 33.79/17.04 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.04 new_showsPrec(x0, x1, ty_Bool) 33.79/17.04 new_primShowInt0(Neg(x0)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, ty_@0) 33.79/17.04 new_primModNatS2(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_show10(x0, x1, x2) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS2(Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.04 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primShowInt0(Pos(Zero)) 33.79/17.04 new_show7(x0, x1, x2) 33.79/17.04 new_pt4(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.04 new_primDivNatS02(x0, x1) 33.79/17.04 new_show1(x0) 33.79/17.04 new_psPs0(:(x0, x1), x2) 33.79/17.04 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.04 new_primModNatS02(x0, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.04 new_showsPrec(x0, x1, ty_Float) 33.79/17.04 new_show14(x0, x1) 33.79/17.04 new_div(x0, x1) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_show12(x0) 33.79/17.04 new_show8(x0) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_primModNatS3(Zero, Zero, x0) 33.79/17.04 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.04 new_primDivNatS2(Zero, Zero, x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.04 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_show6(x0) 33.79/17.04 new_show15(x0, x1, x2, x3) 33.79/17.04 new_primDivNatS3(x0) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.04 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.04 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(x0)) 33.79/17.04 new_show5(x0) 33.79/17.04 new_showsPrec(x0, x1, ty_Integer) 33.79/17.04 new_show(x0, x1) 33.79/17.04 new_show2(x0, x1) 33.79/17.04 new_primModNatS4(x0) 33.79/17.04 new_primIntToChar(x0, x1) 33.79/17.04 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.04 new_showsPrec(x0, x1, ty_Int) 33.79/17.04 new_show9(x0) 33.79/17.04 new_show11(x0) 33.79/17.04 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.04 new_show4(x0) 33.79/17.04 new_psPs0([], x0) 33.79/17.04 new_primDivNatS4(Zero, Zero) 33.79/17.04 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.04 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.04 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show0(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show13(x0) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_show3(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.04 new_showsPrec(x0, x1, ty_Char) 33.79/17.04 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_Double) 33.79/17.04 33.79/17.04 We have to consider all minimal (P,Q,R)-chains. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (60) QReductionProof (EQUIVALENT) 33.79/17.04 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 33.79/17.04 33.79/17.04 new_pt4(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) 33.79/17.04 33.79/17.04 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (61) 33.79/17.04 Obligation: 33.79/17.04 Q DP problem: 33.79/17.04 The TRS P consists of the following rules: 33.79/17.04 33.79/17.04 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 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) 33.79/17.04 33.79/17.04 The TRS R consists of the following rules: 33.79/17.04 33.79/17.04 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.04 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.04 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.04 new_psPs0([], ww60) -> ww60 33.79/17.04 new_show11(ww21) -> error([]) 33.79/17.04 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.04 new_show2(ww21, bb) -> error([]) 33.79/17.04 new_show12(ww21) -> error([]) 33.79/17.04 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show1(ww21) -> error([]) 33.79/17.04 new_show5(ww21) -> error([]) 33.79/17.04 new_show3(ww21) -> error([]) 33.79/17.04 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.04 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))) 33.79/17.04 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)))))))))), [])) 33.79/17.04 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.04 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.04 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.04 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.04 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.04 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.04 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.04 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.04 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.04 new_primModNatS4(ww143) -> Zero 33.79/17.04 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.04 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.04 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.04 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS3(ww147) -> Zero 33.79/17.04 new_show(ww21, bf) -> error([]) 33.79/17.04 new_show9(ww21) -> error([]) 33.79/17.04 new_show8(ww21) -> error([]) 33.79/17.04 new_show10(ww21, ca, cb) -> error([]) 33.79/17.04 new_show14(ww21, cc) -> error([]) 33.79/17.04 new_show4(ww21) -> error([]) 33.79/17.04 new_show7(ww21, bd, be) -> error([]) 33.79/17.04 new_show6(ww21) -> error([]) 33.79/17.04 new_show0(ww21) -> error([]) 33.79/17.04 33.79/17.04 The set Q consists of the following terms: 33.79/17.04 33.79/17.04 new_primShowInt0(Pos(Succ(x0))) 33.79/17.04 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.04 new_primDivNatS4(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_IOError) 33.79/17.04 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.04 new_showsPrec(x0, x1, ty_Bool) 33.79/17.04 new_primShowInt0(Neg(x0)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, ty_@0) 33.79/17.04 new_primModNatS2(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_show10(x0, x1, x2) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS2(Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.04 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primShowInt0(Pos(Zero)) 33.79/17.04 new_show7(x0, x1, x2) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.04 new_primDivNatS02(x0, x1) 33.79/17.04 new_show1(x0) 33.79/17.04 new_psPs0(:(x0, x1), x2) 33.79/17.04 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.04 new_primModNatS02(x0, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.04 new_showsPrec(x0, x1, ty_Float) 33.79/17.04 new_show14(x0, x1) 33.79/17.04 new_div(x0, x1) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_show12(x0) 33.79/17.04 new_show8(x0) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_primModNatS3(Zero, Zero, x0) 33.79/17.04 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.04 new_primDivNatS2(Zero, Zero, x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.04 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_show6(x0) 33.79/17.04 new_show15(x0, x1, x2, x3) 33.79/17.04 new_primDivNatS3(x0) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.04 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.04 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(x0)) 33.79/17.04 new_show5(x0) 33.79/17.04 new_showsPrec(x0, x1, ty_Integer) 33.79/17.04 new_show(x0, x1) 33.79/17.04 new_show2(x0, x1) 33.79/17.04 new_primModNatS4(x0) 33.79/17.04 new_primIntToChar(x0, x1) 33.79/17.04 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.04 new_showsPrec(x0, x1, ty_Int) 33.79/17.04 new_show9(x0) 33.79/17.04 new_show11(x0) 33.79/17.04 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.04 new_show4(x0) 33.79/17.04 new_psPs0([], x0) 33.79/17.04 new_primDivNatS4(Zero, Zero) 33.79/17.04 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.04 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.04 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show0(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show13(x0) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_show3(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.04 new_showsPrec(x0, x1, ty_Char) 33.79/17.04 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_Double) 33.79/17.04 33.79/17.04 We have to consider all minimal (P,Q,R)-chains. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (62) TransformationProof (EQUIVALENT) 33.79/17.04 By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) at position [6] we obtained the following new rules [LPAR04]: 33.79/17.04 33.79/17.04 (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)), bg, bg),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)), bg, bg)) 33.79/17.04 33.79/17.04 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (63) 33.79/17.04 Obligation: 33.79/17.04 Q DP problem: 33.79/17.04 The TRS P consists of the following rules: 33.79/17.04 33.79/17.04 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 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) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)), bg, bg) 33.79/17.04 33.79/17.04 The TRS R consists of the following rules: 33.79/17.04 33.79/17.04 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.04 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.04 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.04 new_psPs0([], ww60) -> ww60 33.79/17.04 new_show11(ww21) -> error([]) 33.79/17.04 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.04 new_show2(ww21, bb) -> error([]) 33.79/17.04 new_show12(ww21) -> error([]) 33.79/17.04 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show1(ww21) -> error([]) 33.79/17.04 new_show5(ww21) -> error([]) 33.79/17.04 new_show3(ww21) -> error([]) 33.79/17.04 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.04 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))) 33.79/17.04 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)))))))))), [])) 33.79/17.04 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.04 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.04 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.04 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.04 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.04 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.04 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.04 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.04 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.04 new_primModNatS4(ww143) -> Zero 33.79/17.04 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.04 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.04 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.04 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS3(ww147) -> Zero 33.79/17.04 new_show(ww21, bf) -> error([]) 33.79/17.04 new_show9(ww21) -> error([]) 33.79/17.04 new_show8(ww21) -> error([]) 33.79/17.04 new_show10(ww21, ca, cb) -> error([]) 33.79/17.04 new_show14(ww21, cc) -> error([]) 33.79/17.04 new_show4(ww21) -> error([]) 33.79/17.04 new_show7(ww21, bd, be) -> error([]) 33.79/17.04 new_show6(ww21) -> error([]) 33.79/17.04 new_show0(ww21) -> error([]) 33.79/17.04 33.79/17.04 The set Q consists of the following terms: 33.79/17.04 33.79/17.04 new_primShowInt0(Pos(Succ(x0))) 33.79/17.04 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.04 new_primDivNatS4(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_IOError) 33.79/17.04 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.04 new_showsPrec(x0, x1, ty_Bool) 33.79/17.04 new_primShowInt0(Neg(x0)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, ty_@0) 33.79/17.04 new_primModNatS2(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_show10(x0, x1, x2) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS2(Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.04 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primShowInt0(Pos(Zero)) 33.79/17.04 new_show7(x0, x1, x2) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.04 new_primDivNatS02(x0, x1) 33.79/17.04 new_show1(x0) 33.79/17.04 new_psPs0(:(x0, x1), x2) 33.79/17.04 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.04 new_primModNatS02(x0, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.04 new_showsPrec(x0, x1, ty_Float) 33.79/17.04 new_show14(x0, x1) 33.79/17.04 new_div(x0, x1) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_show12(x0) 33.79/17.04 new_show8(x0) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_primModNatS3(Zero, Zero, x0) 33.79/17.04 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.04 new_primDivNatS2(Zero, Zero, x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.04 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_show6(x0) 33.79/17.04 new_show15(x0, x1, x2, x3) 33.79/17.04 new_primDivNatS3(x0) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.04 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.04 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(x0)) 33.79/17.04 new_show5(x0) 33.79/17.04 new_showsPrec(x0, x1, ty_Integer) 33.79/17.04 new_show(x0, x1) 33.79/17.04 new_show2(x0, x1) 33.79/17.04 new_primModNatS4(x0) 33.79/17.04 new_primIntToChar(x0, x1) 33.79/17.04 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.04 new_showsPrec(x0, x1, ty_Int) 33.79/17.04 new_show9(x0) 33.79/17.04 new_show11(x0) 33.79/17.04 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.04 new_show4(x0) 33.79/17.04 new_psPs0([], x0) 33.79/17.04 new_primDivNatS4(Zero, Zero) 33.79/17.04 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.04 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.04 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show0(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show13(x0) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_show3(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.04 new_showsPrec(x0, x1, ty_Char) 33.79/17.04 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_Double) 33.79/17.04 33.79/17.04 We have to consider all minimal (P,Q,R)-chains. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (64) TransformationProof (EQUIVALENT) 33.79/17.04 By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)), bg, bg) at position [6] we obtained the following new rules [LPAR04]: 33.79/17.04 33.79/17.04 (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg))), bg, bg),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg))), bg, bg)) 33.79/17.04 33.79/17.04 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (65) 33.79/17.04 Obligation: 33.79/17.04 Q DP problem: 33.79/17.04 The TRS P consists of the following rules: 33.79/17.04 33.79/17.04 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.04 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) 33.79/17.04 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg))), bg, bg) 33.79/17.04 33.79/17.04 The TRS R consists of the following rules: 33.79/17.04 33.79/17.04 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.04 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.04 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.04 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.04 new_psPs0([], ww60) -> ww60 33.79/17.04 new_show11(ww21) -> error([]) 33.79/17.04 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.04 new_show2(ww21, bb) -> error([]) 33.79/17.04 new_show12(ww21) -> error([]) 33.79/17.04 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.04 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.04 new_show1(ww21) -> error([]) 33.79/17.04 new_show5(ww21) -> error([]) 33.79/17.04 new_show3(ww21) -> error([]) 33.79/17.04 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.04 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))) 33.79/17.04 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)))))))))), [])) 33.79/17.04 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.04 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.04 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.04 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.04 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.04 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.04 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.04 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.04 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.04 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.04 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.04 new_primModNatS4(ww143) -> Zero 33.79/17.04 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.04 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.04 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.04 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.04 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.04 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.04 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.04 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.04 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.04 new_primDivNatS3(ww147) -> Zero 33.79/17.04 new_show(ww21, bf) -> error([]) 33.79/17.04 new_show9(ww21) -> error([]) 33.79/17.04 new_show8(ww21) -> error([]) 33.79/17.04 new_show10(ww21, ca, cb) -> error([]) 33.79/17.04 new_show14(ww21, cc) -> error([]) 33.79/17.04 new_show4(ww21) -> error([]) 33.79/17.04 new_show7(ww21, bd, be) -> error([]) 33.79/17.04 new_show6(ww21) -> error([]) 33.79/17.04 new_show0(ww21) -> error([]) 33.79/17.04 33.79/17.04 The set Q consists of the following terms: 33.79/17.04 33.79/17.04 new_primShowInt0(Pos(Succ(x0))) 33.79/17.04 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.04 new_primDivNatS4(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_IOError) 33.79/17.04 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.04 new_showsPrec(x0, x1, ty_Bool) 33.79/17.04 new_primShowInt0(Neg(x0)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, ty_@0) 33.79/17.04 new_primModNatS2(Succ(x0), Zero) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_show10(x0, x1, x2) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS2(Zero, Zero) 33.79/17.04 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.04 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primShowInt0(Pos(Zero)) 33.79/17.04 new_show7(x0, x1, x2) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.04 new_primDivNatS02(x0, x1) 33.79/17.04 new_show1(x0) 33.79/17.04 new_psPs0(:(x0, x1), x2) 33.79/17.04 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.04 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.04 new_primModNatS02(x0, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.04 new_showsPrec(x0, x1, ty_Float) 33.79/17.04 new_show14(x0, x1) 33.79/17.04 new_div(x0, x1) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_show12(x0) 33.79/17.04 new_show8(x0) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.04 new_primModNatS3(Zero, Zero, x0) 33.79/17.04 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.04 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.04 new_primDivNatS2(Zero, Zero, x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.04 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_show6(x0) 33.79/17.04 new_show15(x0, x1, x2, x3) 33.79/17.04 new_primDivNatS3(x0) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.04 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.04 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.04 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.04 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.04 new_primModNatS2(Zero, Succ(x0)) 33.79/17.04 new_show5(x0) 33.79/17.04 new_showsPrec(x0, x1, ty_Integer) 33.79/17.04 new_show(x0, x1) 33.79/17.04 new_show2(x0, x1) 33.79/17.04 new_primModNatS4(x0) 33.79/17.04 new_primIntToChar(x0, x1) 33.79/17.04 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.04 new_showsPrec(x0, x1, ty_Int) 33.79/17.04 new_show9(x0) 33.79/17.04 new_show11(x0) 33.79/17.04 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.04 new_show4(x0) 33.79/17.04 new_psPs0([], x0) 33.79/17.04 new_primDivNatS4(Zero, Zero) 33.79/17.04 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.04 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.04 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show0(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.04 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.04 new_show13(x0) 33.79/17.04 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.04 new_show3(x0) 33.79/17.04 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.04 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.04 new_showsPrec(x0, x1, ty_Char) 33.79/17.04 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.04 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.04 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.04 new_showsPrec(x0, x1, ty_Double) 33.79/17.04 33.79/17.04 We have to consider all minimal (P,Q,R)-chains. 33.79/17.04 ---------------------------------------- 33.79/17.04 33.79/17.04 (66) TransformationProof (EQUIVALENT) 33.79/17.04 By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg))), bg, bg) at position [6,1] we obtained the following new rules [LPAR04]: 33.79/17.05 33.79/17.05 (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg)) 33.79/17.05 33.79/17.05 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (67) 33.79/17.05 Obligation: 33.79/17.05 Q DP problem: 33.79/17.05 The TRS P consists of the following rules: 33.79/17.05 33.79/17.05 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 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) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.05 33.79/17.05 The TRS R consists of the following rules: 33.79/17.05 33.79/17.05 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.05 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.05 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.05 new_psPs0([], ww60) -> ww60 33.79/17.05 new_show11(ww21) -> error([]) 33.79/17.05 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.05 new_show2(ww21, bb) -> error([]) 33.79/17.05 new_show12(ww21) -> error([]) 33.79/17.05 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.05 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_show1(ww21) -> error([]) 33.79/17.05 new_show5(ww21) -> error([]) 33.79/17.05 new_show3(ww21) -> error([]) 33.79/17.05 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.05 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))) 33.79/17.05 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)))))))))), [])) 33.79/17.05 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.05 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.05 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.05 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.05 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.05 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.05 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.05 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.05 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.05 new_primModNatS4(ww143) -> Zero 33.79/17.05 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.05 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.05 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.05 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.05 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS3(ww147) -> Zero 33.79/17.05 new_show(ww21, bf) -> error([]) 33.79/17.05 new_show9(ww21) -> error([]) 33.79/17.05 new_show8(ww21) -> error([]) 33.79/17.05 new_show10(ww21, ca, cb) -> error([]) 33.79/17.05 new_show14(ww21, cc) -> error([]) 33.79/17.05 new_show4(ww21) -> error([]) 33.79/17.05 new_show7(ww21, bd, be) -> error([]) 33.79/17.05 new_show6(ww21) -> error([]) 33.79/17.05 new_show0(ww21) -> error([]) 33.79/17.05 33.79/17.05 The set Q consists of the following terms: 33.79/17.05 33.79/17.05 new_primShowInt0(Pos(Succ(x0))) 33.79/17.05 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.05 new_primDivNatS4(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_IOError) 33.79/17.05 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.05 new_showsPrec(x0, x1, ty_Bool) 33.79/17.05 new_primShowInt0(Neg(x0)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, ty_@0) 33.79/17.05 new_primModNatS2(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_show10(x0, x1, x2) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.05 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS2(Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.05 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primShowInt0(Pos(Zero)) 33.79/17.05 new_show7(x0, x1, x2) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.05 new_primDivNatS02(x0, x1) 33.79/17.05 new_show1(x0) 33.79/17.05 new_psPs0(:(x0, x1), x2) 33.79/17.05 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.05 new_primModNatS02(x0, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.05 new_showsPrec(x0, x1, ty_Float) 33.79/17.05 new_show14(x0, x1) 33.79/17.05 new_div(x0, x1) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_show12(x0) 33.79/17.05 new_show8(x0) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_primModNatS3(Zero, Zero, x0) 33.79/17.05 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.05 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.05 new_primDivNatS2(Zero, Zero, x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.05 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_show6(x0) 33.79/17.05 new_show15(x0, x1, x2, x3) 33.79/17.05 new_primDivNatS3(x0) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.05 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.05 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(x0)) 33.79/17.05 new_show5(x0) 33.79/17.05 new_showsPrec(x0, x1, ty_Integer) 33.79/17.05 new_show(x0, x1) 33.79/17.05 new_show2(x0, x1) 33.79/17.05 new_primModNatS4(x0) 33.79/17.05 new_primIntToChar(x0, x1) 33.79/17.05 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.05 new_showsPrec(x0, x1, ty_Int) 33.79/17.05 new_show9(x0) 33.79/17.05 new_show11(x0) 33.79/17.05 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.05 new_show4(x0) 33.79/17.05 new_psPs0([], x0) 33.79/17.05 new_primDivNatS4(Zero, Zero) 33.79/17.05 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.05 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.05 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show0(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show13(x0) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_show3(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.05 new_showsPrec(x0, x1, ty_Char) 33.79/17.05 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_Double) 33.79/17.05 33.79/17.05 We have to consider all minimal (P,Q,R)-chains. 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (68) TransformationProof (EQUIVALENT) 33.79/17.05 By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) at position [6,1,1] we obtained the following new rules [LPAR04]: 33.79/17.05 33.79/17.05 (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg))))), bg, bg),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg))))), bg, bg)) 33.79/17.05 33.79/17.05 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (69) 33.79/17.05 Obligation: 33.79/17.05 Q DP problem: 33.79/17.05 The TRS P consists of the following rules: 33.79/17.05 33.79/17.05 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 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) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg))))), bg, bg) 33.79/17.05 33.79/17.05 The TRS R consists of the following rules: 33.79/17.05 33.79/17.05 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.05 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.05 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.05 new_psPs0([], ww60) -> ww60 33.79/17.05 new_show11(ww21) -> error([]) 33.79/17.05 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.05 new_show2(ww21, bb) -> error([]) 33.79/17.05 new_show12(ww21) -> error([]) 33.79/17.05 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.05 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_show1(ww21) -> error([]) 33.79/17.05 new_show5(ww21) -> error([]) 33.79/17.05 new_show3(ww21) -> error([]) 33.79/17.05 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.05 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))) 33.79/17.05 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)))))))))), [])) 33.79/17.05 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.05 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.05 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.05 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.05 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.05 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.05 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.05 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.05 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.05 new_primModNatS4(ww143) -> Zero 33.79/17.05 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.05 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.05 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.05 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.05 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS3(ww147) -> Zero 33.79/17.05 new_show(ww21, bf) -> error([]) 33.79/17.05 new_show9(ww21) -> error([]) 33.79/17.05 new_show8(ww21) -> error([]) 33.79/17.05 new_show10(ww21, ca, cb) -> error([]) 33.79/17.05 new_show14(ww21, cc) -> error([]) 33.79/17.05 new_show4(ww21) -> error([]) 33.79/17.05 new_show7(ww21, bd, be) -> error([]) 33.79/17.05 new_show6(ww21) -> error([]) 33.79/17.05 new_show0(ww21) -> error([]) 33.79/17.05 33.79/17.05 The set Q consists of the following terms: 33.79/17.05 33.79/17.05 new_primShowInt0(Pos(Succ(x0))) 33.79/17.05 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.05 new_primDivNatS4(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_IOError) 33.79/17.05 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.05 new_showsPrec(x0, x1, ty_Bool) 33.79/17.05 new_primShowInt0(Neg(x0)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, ty_@0) 33.79/17.05 new_primModNatS2(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_show10(x0, x1, x2) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.05 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS2(Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.05 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primShowInt0(Pos(Zero)) 33.79/17.05 new_show7(x0, x1, x2) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.05 new_primDivNatS02(x0, x1) 33.79/17.05 new_show1(x0) 33.79/17.05 new_psPs0(:(x0, x1), x2) 33.79/17.05 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.05 new_primModNatS02(x0, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.05 new_showsPrec(x0, x1, ty_Float) 33.79/17.05 new_show14(x0, x1) 33.79/17.05 new_div(x0, x1) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_show12(x0) 33.79/17.05 new_show8(x0) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_primModNatS3(Zero, Zero, x0) 33.79/17.05 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.05 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.05 new_primDivNatS2(Zero, Zero, x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.05 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_show6(x0) 33.79/17.05 new_show15(x0, x1, x2, x3) 33.79/17.05 new_primDivNatS3(x0) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.05 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.05 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(x0)) 33.79/17.05 new_show5(x0) 33.79/17.05 new_showsPrec(x0, x1, ty_Integer) 33.79/17.05 new_show(x0, x1) 33.79/17.05 new_show2(x0, x1) 33.79/17.05 new_primModNatS4(x0) 33.79/17.05 new_primIntToChar(x0, x1) 33.79/17.05 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.05 new_showsPrec(x0, x1, ty_Int) 33.79/17.05 new_show9(x0) 33.79/17.05 new_show11(x0) 33.79/17.05 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.05 new_show4(x0) 33.79/17.05 new_psPs0([], x0) 33.79/17.05 new_primDivNatS4(Zero, Zero) 33.79/17.05 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.05 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.05 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show0(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show13(x0) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_show3(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.05 new_showsPrec(x0, x1, ty_Char) 33.79/17.05 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_Double) 33.79/17.05 33.79/17.05 We have to consider all minimal (P,Q,R)-chains. 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (70) TransformationProof (EQUIVALENT) 33.79/17.05 By rewriting [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg))))), bg, bg) at position [6,1,1,1] we obtained the following new rules [LPAR04]: 33.79/17.05 33.79/17.05 (new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg),new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg)) 33.79/17.05 33.79/17.05 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (71) 33.79/17.05 Obligation: 33.79/17.05 Q DP problem: 33.79/17.05 The TRS P consists of the following rules: 33.79/17.05 33.79/17.05 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 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) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.05 33.79/17.05 The TRS R consists of the following rules: 33.79/17.05 33.79/17.05 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.05 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.05 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.05 new_psPs0([], ww60) -> ww60 33.79/17.05 new_show11(ww21) -> error([]) 33.79/17.05 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.05 new_show2(ww21, bb) -> error([]) 33.79/17.05 new_show12(ww21) -> error([]) 33.79/17.05 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.05 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_show1(ww21) -> error([]) 33.79/17.05 new_show5(ww21) -> error([]) 33.79/17.05 new_show3(ww21) -> error([]) 33.79/17.05 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.05 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))) 33.79/17.05 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)))))))))), [])) 33.79/17.05 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.05 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.05 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.05 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.05 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.05 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.05 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.05 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.05 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.05 new_primModNatS4(ww143) -> Zero 33.79/17.05 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.05 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.05 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.05 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.05 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS3(ww147) -> Zero 33.79/17.05 new_show(ww21, bf) -> error([]) 33.79/17.05 new_show9(ww21) -> error([]) 33.79/17.05 new_show8(ww21) -> error([]) 33.79/17.05 new_show10(ww21, ca, cb) -> error([]) 33.79/17.05 new_show14(ww21, cc) -> error([]) 33.79/17.05 new_show4(ww21) -> error([]) 33.79/17.05 new_show7(ww21, bd, be) -> error([]) 33.79/17.05 new_show6(ww21) -> error([]) 33.79/17.05 new_show0(ww21) -> error([]) 33.79/17.05 33.79/17.05 The set Q consists of the following terms: 33.79/17.05 33.79/17.05 new_primShowInt0(Pos(Succ(x0))) 33.79/17.05 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.05 new_primDivNatS4(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_IOError) 33.79/17.05 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.05 new_showsPrec(x0, x1, ty_Bool) 33.79/17.05 new_primShowInt0(Neg(x0)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, ty_@0) 33.79/17.05 new_primModNatS2(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_show10(x0, x1, x2) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.05 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS2(Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.05 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primShowInt0(Pos(Zero)) 33.79/17.05 new_show7(x0, x1, x2) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.05 new_primDivNatS02(x0, x1) 33.79/17.05 new_show1(x0) 33.79/17.05 new_psPs0(:(x0, x1), x2) 33.79/17.05 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.05 new_primModNatS02(x0, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.05 new_showsPrec(x0, x1, ty_Float) 33.79/17.05 new_show14(x0, x1) 33.79/17.05 new_div(x0, x1) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_show12(x0) 33.79/17.05 new_show8(x0) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_primModNatS3(Zero, Zero, x0) 33.79/17.05 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.05 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.05 new_primDivNatS2(Zero, Zero, x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.05 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_show6(x0) 33.79/17.05 new_show15(x0, x1, x2, x3) 33.79/17.05 new_primDivNatS3(x0) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.05 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.05 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(x0)) 33.79/17.05 new_show5(x0) 33.79/17.05 new_showsPrec(x0, x1, ty_Integer) 33.79/17.05 new_show(x0, x1) 33.79/17.05 new_show2(x0, x1) 33.79/17.05 new_primModNatS4(x0) 33.79/17.05 new_primIntToChar(x0, x1) 33.79/17.05 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.05 new_showsPrec(x0, x1, ty_Int) 33.79/17.05 new_show9(x0) 33.79/17.05 new_show11(x0) 33.79/17.05 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.05 new_show4(x0) 33.79/17.05 new_psPs0([], x0) 33.79/17.05 new_primDivNatS4(Zero, Zero) 33.79/17.05 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.05 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.05 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show0(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show13(x0) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_show3(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.05 new_showsPrec(x0, x1, ty_Char) 33.79/17.05 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_Double) 33.79/17.05 33.79/17.05 We have to consider all minimal (P,Q,R)-chains. 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (72) TransformationProof (EQUIVALENT) 33.79/17.05 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.05 33.79/17.05 (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)) 33.79/17.05 33.79/17.05 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (73) 33.79/17.05 Obligation: 33.79/17.05 Q DP problem: 33.79/17.05 The TRS P consists of the following rules: 33.79/17.05 33.79/17.05 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 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) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.05 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) 33.79/17.05 33.79/17.05 The TRS R consists of the following rules: 33.79/17.05 33.79/17.05 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.05 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.05 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.05 new_psPs0([], ww60) -> ww60 33.79/17.05 new_show11(ww21) -> error([]) 33.79/17.05 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.05 new_show2(ww21, bb) -> error([]) 33.79/17.05 new_show12(ww21) -> error([]) 33.79/17.05 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.05 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_show1(ww21) -> error([]) 33.79/17.05 new_show5(ww21) -> error([]) 33.79/17.05 new_show3(ww21) -> error([]) 33.79/17.05 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.05 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))) 33.79/17.05 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)))))))))), [])) 33.79/17.05 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.05 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.05 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.05 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.05 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.05 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.05 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.05 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.05 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.05 new_primModNatS4(ww143) -> Zero 33.79/17.05 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.05 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.05 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.05 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.05 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS3(ww147) -> Zero 33.79/17.05 new_show(ww21, bf) -> error([]) 33.79/17.05 new_show9(ww21) -> error([]) 33.79/17.05 new_show8(ww21) -> error([]) 33.79/17.05 new_show10(ww21, ca, cb) -> error([]) 33.79/17.05 new_show14(ww21, cc) -> error([]) 33.79/17.05 new_show4(ww21) -> error([]) 33.79/17.05 new_show7(ww21, bd, be) -> error([]) 33.79/17.05 new_show6(ww21) -> error([]) 33.79/17.05 new_show0(ww21) -> error([]) 33.79/17.05 33.79/17.05 The set Q consists of the following terms: 33.79/17.05 33.79/17.05 new_primShowInt0(Pos(Succ(x0))) 33.79/17.05 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.05 new_primDivNatS4(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_IOError) 33.79/17.05 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.05 new_showsPrec(x0, x1, ty_Bool) 33.79/17.05 new_primShowInt0(Neg(x0)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, ty_@0) 33.79/17.05 new_primModNatS2(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_show10(x0, x1, x2) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.05 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS2(Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.05 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primShowInt0(Pos(Zero)) 33.79/17.05 new_show7(x0, x1, x2) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.05 new_primDivNatS02(x0, x1) 33.79/17.05 new_show1(x0) 33.79/17.05 new_psPs0(:(x0, x1), x2) 33.79/17.05 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.05 new_primModNatS02(x0, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.05 new_showsPrec(x0, x1, ty_Float) 33.79/17.05 new_show14(x0, x1) 33.79/17.05 new_div(x0, x1) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_show12(x0) 33.79/17.05 new_show8(x0) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_primModNatS3(Zero, Zero, x0) 33.79/17.05 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.05 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.05 new_primDivNatS2(Zero, Zero, x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.05 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_show6(x0) 33.79/17.05 new_show15(x0, x1, x2, x3) 33.79/17.05 new_primDivNatS3(x0) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.05 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.05 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(x0)) 33.79/17.05 new_show5(x0) 33.79/17.05 new_showsPrec(x0, x1, ty_Integer) 33.79/17.05 new_show(x0, x1) 33.79/17.05 new_show2(x0, x1) 33.79/17.05 new_primModNatS4(x0) 33.79/17.05 new_primIntToChar(x0, x1) 33.79/17.05 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.05 new_showsPrec(x0, x1, ty_Int) 33.79/17.05 new_show9(x0) 33.79/17.05 new_show11(x0) 33.79/17.05 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.05 new_show4(x0) 33.79/17.05 new_psPs0([], x0) 33.79/17.05 new_primDivNatS4(Zero, Zero) 33.79/17.05 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.05 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.05 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show0(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show13(x0) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_show3(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.05 new_showsPrec(x0, x1, ty_Char) 33.79/17.05 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_Double) 33.79/17.05 33.79/17.05 We have to consider all minimal (P,Q,R)-chains. 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (74) DependencyGraphProof (EQUIVALENT) 33.79/17.05 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (75) 33.79/17.05 Obligation: 33.79/17.05 Q DP problem: 33.79/17.05 The TRS P consists of the following rules: 33.79/17.05 33.79/17.05 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) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.05 33.79/17.05 The TRS R consists of the following rules: 33.79/17.05 33.79/17.05 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.05 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.05 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.05 new_psPs0([], ww60) -> ww60 33.79/17.05 new_show11(ww21) -> error([]) 33.79/17.05 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.05 new_show2(ww21, bb) -> error([]) 33.79/17.05 new_show12(ww21) -> error([]) 33.79/17.05 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.05 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_show1(ww21) -> error([]) 33.79/17.05 new_show5(ww21) -> error([]) 33.79/17.05 new_show3(ww21) -> error([]) 33.79/17.05 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.05 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))) 33.79/17.05 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)))))))))), [])) 33.79/17.05 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.05 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.05 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.05 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.05 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.05 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.05 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.05 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.05 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.05 new_primModNatS4(ww143) -> Zero 33.79/17.05 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.05 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.05 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.05 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.05 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS3(ww147) -> Zero 33.79/17.05 new_show(ww21, bf) -> error([]) 33.79/17.05 new_show9(ww21) -> error([]) 33.79/17.05 new_show8(ww21) -> error([]) 33.79/17.05 new_show10(ww21, ca, cb) -> error([]) 33.79/17.05 new_show14(ww21, cc) -> error([]) 33.79/17.05 new_show4(ww21) -> error([]) 33.79/17.05 new_show7(ww21, bd, be) -> error([]) 33.79/17.05 new_show6(ww21) -> error([]) 33.79/17.05 new_show0(ww21) -> error([]) 33.79/17.05 33.79/17.05 The set Q consists of the following terms: 33.79/17.05 33.79/17.05 new_primShowInt0(Pos(Succ(x0))) 33.79/17.05 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.05 new_primDivNatS4(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_IOError) 33.79/17.05 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.05 new_showsPrec(x0, x1, ty_Bool) 33.79/17.05 new_primShowInt0(Neg(x0)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, ty_@0) 33.79/17.05 new_primModNatS2(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_show10(x0, x1, x2) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.05 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS2(Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.05 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primShowInt0(Pos(Zero)) 33.79/17.05 new_show7(x0, x1, x2) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.05 new_primDivNatS02(x0, x1) 33.79/17.05 new_show1(x0) 33.79/17.05 new_psPs0(:(x0, x1), x2) 33.79/17.05 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.05 new_primModNatS02(x0, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.05 new_showsPrec(x0, x1, ty_Float) 33.79/17.05 new_show14(x0, x1) 33.79/17.05 new_div(x0, x1) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_show12(x0) 33.79/17.05 new_show8(x0) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_primModNatS3(Zero, Zero, x0) 33.79/17.05 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.05 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.05 new_primDivNatS2(Zero, Zero, x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.05 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_show6(x0) 33.79/17.05 new_show15(x0, x1, x2, x3) 33.79/17.05 new_primDivNatS3(x0) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.05 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.05 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(x0)) 33.79/17.05 new_show5(x0) 33.79/17.05 new_showsPrec(x0, x1, ty_Integer) 33.79/17.05 new_show(x0, x1) 33.79/17.05 new_show2(x0, x1) 33.79/17.05 new_primModNatS4(x0) 33.79/17.05 new_primIntToChar(x0, x1) 33.79/17.05 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.05 new_showsPrec(x0, x1, ty_Int) 33.79/17.05 new_show9(x0) 33.79/17.05 new_show11(x0) 33.79/17.05 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.05 new_show4(x0) 33.79/17.05 new_psPs0([], x0) 33.79/17.05 new_primDivNatS4(Zero, Zero) 33.79/17.05 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.05 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.05 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show0(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show13(x0) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_show3(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.05 new_showsPrec(x0, x1, ty_Char) 33.79/17.05 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_Double) 33.79/17.05 33.79/17.05 We have to consider all minimal (P,Q,R)-chains. 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (76) TransformationProof (EQUIVALENT) 33.79/17.05 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.05 33.79/17.05 (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)) 33.79/17.05 33.79/17.05 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (77) 33.79/17.05 Obligation: 33.79/17.05 Q DP problem: 33.79/17.05 The TRS P consists of the following rules: 33.79/17.05 33.79/17.05 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) 33.79/17.05 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.05 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) 33.79/17.05 33.79/17.05 The TRS R consists of the following rules: 33.79/17.05 33.79/17.05 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.05 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.05 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.05 new_psPs0([], ww60) -> ww60 33.79/17.05 new_show11(ww21) -> error([]) 33.79/17.05 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.05 new_show2(ww21, bb) -> error([]) 33.79/17.05 new_show12(ww21) -> error([]) 33.79/17.05 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.05 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_show1(ww21) -> error([]) 33.79/17.05 new_show5(ww21) -> error([]) 33.79/17.05 new_show3(ww21) -> error([]) 33.79/17.05 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.05 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))) 33.79/17.05 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)))))))))), [])) 33.79/17.05 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.05 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.05 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.05 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.05 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.05 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.05 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.05 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.05 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.05 new_primModNatS4(ww143) -> Zero 33.79/17.05 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.05 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.05 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.05 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.05 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS3(ww147) -> Zero 33.79/17.05 new_show(ww21, bf) -> error([]) 33.79/17.05 new_show9(ww21) -> error([]) 33.79/17.05 new_show8(ww21) -> error([]) 33.79/17.05 new_show10(ww21, ca, cb) -> error([]) 33.79/17.05 new_show14(ww21, cc) -> error([]) 33.79/17.05 new_show4(ww21) -> error([]) 33.79/17.05 new_show7(ww21, bd, be) -> error([]) 33.79/17.05 new_show6(ww21) -> error([]) 33.79/17.05 new_show0(ww21) -> error([]) 33.79/17.05 33.79/17.05 The set Q consists of the following terms: 33.79/17.05 33.79/17.05 new_primShowInt0(Pos(Succ(x0))) 33.79/17.05 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.05 new_primDivNatS4(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_IOError) 33.79/17.05 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.05 new_showsPrec(x0, x1, ty_Bool) 33.79/17.05 new_primShowInt0(Neg(x0)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, ty_@0) 33.79/17.05 new_primModNatS2(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_show10(x0, x1, x2) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.05 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS2(Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.05 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primShowInt0(Pos(Zero)) 33.79/17.05 new_show7(x0, x1, x2) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.05 new_primDivNatS02(x0, x1) 33.79/17.05 new_show1(x0) 33.79/17.05 new_psPs0(:(x0, x1), x2) 33.79/17.05 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.05 new_primModNatS02(x0, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.05 new_showsPrec(x0, x1, ty_Float) 33.79/17.05 new_show14(x0, x1) 33.79/17.05 new_div(x0, x1) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_show12(x0) 33.79/17.05 new_show8(x0) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_primModNatS3(Zero, Zero, x0) 33.79/17.05 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.05 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.05 new_primDivNatS2(Zero, Zero, x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.05 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_show6(x0) 33.79/17.05 new_show15(x0, x1, x2, x3) 33.79/17.05 new_primDivNatS3(x0) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.05 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.05 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(x0)) 33.79/17.05 new_show5(x0) 33.79/17.05 new_showsPrec(x0, x1, ty_Integer) 33.79/17.05 new_show(x0, x1) 33.79/17.05 new_show2(x0, x1) 33.79/17.05 new_primModNatS4(x0) 33.79/17.05 new_primIntToChar(x0, x1) 33.79/17.05 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.05 new_showsPrec(x0, x1, ty_Int) 33.79/17.05 new_show9(x0) 33.79/17.05 new_show11(x0) 33.79/17.05 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.05 new_show4(x0) 33.79/17.05 new_psPs0([], x0) 33.79/17.05 new_primDivNatS4(Zero, Zero) 33.79/17.05 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.05 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.05 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show0(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show13(x0) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_show3(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.05 new_showsPrec(x0, x1, ty_Char) 33.79/17.05 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_Double) 33.79/17.05 33.79/17.05 We have to consider all minimal (P,Q,R)-chains. 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (78) DependencyGraphProof (EQUIVALENT) 33.79/17.05 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (79) 33.79/17.05 Obligation: 33.79/17.05 Q DP problem: 33.79/17.05 The TRS P consists of the following rules: 33.79/17.05 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 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) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.05 33.79/17.05 The TRS R consists of the following rules: 33.79/17.05 33.79/17.05 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.05 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.05 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.05 new_psPs0([], ww60) -> ww60 33.79/17.05 new_show11(ww21) -> error([]) 33.79/17.05 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.05 new_show2(ww21, bb) -> error([]) 33.79/17.05 new_show12(ww21) -> error([]) 33.79/17.05 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.05 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_show1(ww21) -> error([]) 33.79/17.05 new_show5(ww21) -> error([]) 33.79/17.05 new_show3(ww21) -> error([]) 33.79/17.05 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.05 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))) 33.79/17.05 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)))))))))), [])) 33.79/17.05 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.05 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.05 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.05 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.05 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.05 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.05 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.05 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.05 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.05 new_primModNatS4(ww143) -> Zero 33.79/17.05 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.05 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.05 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.05 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.05 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS3(ww147) -> Zero 33.79/17.05 new_show(ww21, bf) -> error([]) 33.79/17.05 new_show9(ww21) -> error([]) 33.79/17.05 new_show8(ww21) -> error([]) 33.79/17.05 new_show10(ww21, ca, cb) -> error([]) 33.79/17.05 new_show14(ww21, cc) -> error([]) 33.79/17.05 new_show4(ww21) -> error([]) 33.79/17.05 new_show7(ww21, bd, be) -> error([]) 33.79/17.05 new_show6(ww21) -> error([]) 33.79/17.05 new_show0(ww21) -> error([]) 33.79/17.05 33.79/17.05 The set Q consists of the following terms: 33.79/17.05 33.79/17.05 new_primShowInt0(Pos(Succ(x0))) 33.79/17.05 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.05 new_primDivNatS4(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_IOError) 33.79/17.05 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.05 new_showsPrec(x0, x1, ty_Bool) 33.79/17.05 new_primShowInt0(Neg(x0)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, ty_@0) 33.79/17.05 new_primModNatS2(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_show10(x0, x1, x2) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.05 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS2(Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.05 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primShowInt0(Pos(Zero)) 33.79/17.05 new_show7(x0, x1, x2) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.05 new_primDivNatS02(x0, x1) 33.79/17.05 new_show1(x0) 33.79/17.05 new_psPs0(:(x0, x1), x2) 33.79/17.05 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.05 new_primModNatS02(x0, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.05 new_showsPrec(x0, x1, ty_Float) 33.79/17.05 new_show14(x0, x1) 33.79/17.05 new_div(x0, x1) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_show12(x0) 33.79/17.05 new_show8(x0) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_primModNatS3(Zero, Zero, x0) 33.79/17.05 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.05 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.05 new_primDivNatS2(Zero, Zero, x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.05 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_show6(x0) 33.79/17.05 new_show15(x0, x1, x2, x3) 33.79/17.05 new_primDivNatS3(x0) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.05 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.05 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(x0)) 33.79/17.05 new_show5(x0) 33.79/17.05 new_showsPrec(x0, x1, ty_Integer) 33.79/17.05 new_show(x0, x1) 33.79/17.05 new_show2(x0, x1) 33.79/17.05 new_primModNatS4(x0) 33.79/17.05 new_primIntToChar(x0, x1) 33.79/17.05 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.05 new_showsPrec(x0, x1, ty_Int) 33.79/17.05 new_show9(x0) 33.79/17.05 new_show11(x0) 33.79/17.05 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.05 new_show4(x0) 33.79/17.05 new_psPs0([], x0) 33.79/17.05 new_primDivNatS4(Zero, Zero) 33.79/17.05 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.05 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.05 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show0(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_show13(x0) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.05 new_show3(x0) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.05 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.05 new_showsPrec(x0, x1, ty_Char) 33.79/17.05 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.05 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_Double) 33.79/17.05 33.79/17.05 We have to consider all minimal (P,Q,R)-chains. 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (80) TransformationProof (EQUIVALENT) 33.79/17.05 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.05 33.79/17.05 (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))) 33.79/17.05 33.79/17.05 33.79/17.05 ---------------------------------------- 33.79/17.05 33.79/17.05 (81) 33.79/17.05 Obligation: 33.79/17.05 Q DP problem: 33.79/17.05 The TRS P consists of the following rules: 33.79/17.05 33.79/17.05 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 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) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.05 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.05 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)) 33.79/17.05 33.79/17.05 The TRS R consists of the following rules: 33.79/17.05 33.79/17.05 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.05 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.05 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.05 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.05 new_psPs0([], ww60) -> ww60 33.79/17.05 new_show11(ww21) -> error([]) 33.79/17.05 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.05 new_show2(ww21, bb) -> error([]) 33.79/17.05 new_show12(ww21) -> error([]) 33.79/17.05 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.05 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.05 new_show1(ww21) -> error([]) 33.79/17.05 new_show5(ww21) -> error([]) 33.79/17.05 new_show3(ww21) -> error([]) 33.79/17.05 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.05 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))) 33.79/17.05 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)))))))))), [])) 33.79/17.05 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.05 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.05 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.05 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.05 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.05 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.05 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.05 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.05 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.05 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.05 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.05 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.05 new_primModNatS4(ww143) -> Zero 33.79/17.05 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.05 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.05 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.05 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.05 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.05 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.05 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.05 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.05 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.05 new_primDivNatS3(ww147) -> Zero 33.79/17.05 new_show(ww21, bf) -> error([]) 33.79/17.05 new_show9(ww21) -> error([]) 33.79/17.05 new_show8(ww21) -> error([]) 33.79/17.05 new_show10(ww21, ca, cb) -> error([]) 33.79/17.05 new_show14(ww21, cc) -> error([]) 33.79/17.05 new_show4(ww21) -> error([]) 33.79/17.05 new_show7(ww21, bd, be) -> error([]) 33.79/17.05 new_show6(ww21) -> error([]) 33.79/17.05 new_show0(ww21) -> error([]) 33.79/17.05 33.79/17.05 The set Q consists of the following terms: 33.79/17.05 33.79/17.05 new_primShowInt0(Pos(Succ(x0))) 33.79/17.05 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.05 new_primDivNatS4(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.05 new_showsPrec(x0, x1, ty_IOError) 33.79/17.05 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.05 new_showsPrec(x0, x1, ty_Bool) 33.79/17.05 new_primShowInt0(Neg(x0)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.05 new_showsPrec(x0, x1, ty_@0) 33.79/17.05 new_primModNatS2(Succ(x0), Zero) 33.79/17.05 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_show10(x0, x1, x2) 33.79/17.05 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.05 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS2(Zero, Zero) 33.79/17.05 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.05 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.05 new_primShowInt0(Pos(Zero)) 33.79/17.05 new_show7(x0, x1, x2) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.05 new_primDivNatS02(x0, x1) 33.79/17.05 new_show1(x0) 33.79/17.05 new_psPs0(:(x0, x1), x2) 33.79/17.05 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.05 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.05 new_primModNatS02(x0, x1) 33.79/17.05 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.05 new_showsPrec(x0, x1, ty_Float) 33.79/17.05 new_show14(x0, x1) 33.79/17.05 new_div(x0, x1) 33.79/17.05 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_show12(x0) 33.79/17.05 new_show8(x0) 33.79/17.05 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.05 new_primModNatS3(Zero, Zero, x0) 33.79/17.05 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.05 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.06 new_primDivNatS2(Zero, Zero, x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.06 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_show6(x0) 33.79/17.06 new_show15(x0, x1, x2, x3) 33.79/17.06 new_primDivNatS3(x0) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.06 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.06 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(x0)) 33.79/17.06 new_show5(x0) 33.79/17.06 new_showsPrec(x0, x1, ty_Integer) 33.79/17.06 new_show(x0, x1) 33.79/17.06 new_show2(x0, x1) 33.79/17.06 new_primModNatS4(x0) 33.79/17.06 new_primIntToChar(x0, x1) 33.79/17.06 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.06 new_showsPrec(x0, x1, ty_Int) 33.79/17.06 new_show9(x0) 33.79/17.06 new_show11(x0) 33.79/17.06 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.06 new_show4(x0) 33.79/17.06 new_psPs0([], x0) 33.79/17.06 new_primDivNatS4(Zero, Zero) 33.79/17.06 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.06 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.06 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show0(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show13(x0) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_show3(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.06 new_showsPrec(x0, x1, ty_Char) 33.79/17.06 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_Double) 33.79/17.06 33.79/17.06 We have to consider all minimal (P,Q,R)-chains. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (82) DependencyGraphProof (EQUIVALENT) 33.79/17.06 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (83) 33.79/17.06 Obligation: 33.79/17.06 Q DP problem: 33.79/17.06 The TRS P consists of the following rules: 33.79/17.06 33.79/17.06 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) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.06 33.79/17.06 The TRS R consists of the following rules: 33.79/17.06 33.79/17.06 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.06 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.06 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.06 new_psPs0([], ww60) -> ww60 33.79/17.06 new_show11(ww21) -> error([]) 33.79/17.06 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.06 new_show2(ww21, bb) -> error([]) 33.79/17.06 new_show12(ww21) -> error([]) 33.79/17.06 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.06 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_show1(ww21) -> error([]) 33.79/17.06 new_show5(ww21) -> error([]) 33.79/17.06 new_show3(ww21) -> error([]) 33.79/17.06 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.06 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))) 33.79/17.06 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)))))))))), [])) 33.79/17.06 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.06 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.06 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.06 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.06 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.06 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.06 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.06 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.06 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.06 new_primModNatS4(ww143) -> Zero 33.79/17.06 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.06 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.06 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.06 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.06 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS3(ww147) -> Zero 33.79/17.06 new_show(ww21, bf) -> error([]) 33.79/17.06 new_show9(ww21) -> error([]) 33.79/17.06 new_show8(ww21) -> error([]) 33.79/17.06 new_show10(ww21, ca, cb) -> error([]) 33.79/17.06 new_show14(ww21, cc) -> error([]) 33.79/17.06 new_show4(ww21) -> error([]) 33.79/17.06 new_show7(ww21, bd, be) -> error([]) 33.79/17.06 new_show6(ww21) -> error([]) 33.79/17.06 new_show0(ww21) -> error([]) 33.79/17.06 33.79/17.06 The set Q consists of the following terms: 33.79/17.06 33.79/17.06 new_primShowInt0(Pos(Succ(x0))) 33.79/17.06 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.06 new_primDivNatS4(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_IOError) 33.79/17.06 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.06 new_showsPrec(x0, x1, ty_Bool) 33.79/17.06 new_primShowInt0(Neg(x0)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, ty_@0) 33.79/17.06 new_primModNatS2(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_show10(x0, x1, x2) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.06 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS2(Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.06 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primShowInt0(Pos(Zero)) 33.79/17.06 new_show7(x0, x1, x2) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.06 new_primDivNatS02(x0, x1) 33.79/17.06 new_show1(x0) 33.79/17.06 new_psPs0(:(x0, x1), x2) 33.79/17.06 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.06 new_primModNatS02(x0, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.06 new_showsPrec(x0, x1, ty_Float) 33.79/17.06 new_show14(x0, x1) 33.79/17.06 new_div(x0, x1) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_show12(x0) 33.79/17.06 new_show8(x0) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_primModNatS3(Zero, Zero, x0) 33.79/17.06 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.06 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.06 new_primDivNatS2(Zero, Zero, x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.06 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_show6(x0) 33.79/17.06 new_show15(x0, x1, x2, x3) 33.79/17.06 new_primDivNatS3(x0) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.06 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.06 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(x0)) 33.79/17.06 new_show5(x0) 33.79/17.06 new_showsPrec(x0, x1, ty_Integer) 33.79/17.06 new_show(x0, x1) 33.79/17.06 new_show2(x0, x1) 33.79/17.06 new_primModNatS4(x0) 33.79/17.06 new_primIntToChar(x0, x1) 33.79/17.06 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.06 new_showsPrec(x0, x1, ty_Int) 33.79/17.06 new_show9(x0) 33.79/17.06 new_show11(x0) 33.79/17.06 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.06 new_show4(x0) 33.79/17.06 new_psPs0([], x0) 33.79/17.06 new_primDivNatS4(Zero, Zero) 33.79/17.06 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.06 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.06 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show0(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show13(x0) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_show3(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.06 new_showsPrec(x0, x1, ty_Char) 33.79/17.06 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_Double) 33.79/17.06 33.79/17.06 We have to consider all minimal (P,Q,R)-chains. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (84) TransformationProof (EQUIVALENT) 33.79/17.06 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.06 33.79/17.06 (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)) 33.79/17.06 33.79/17.06 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (85) 33.79/17.06 Obligation: 33.79/17.06 Q DP problem: 33.79/17.06 The TRS P consists of the following rules: 33.79/17.06 33.79/17.06 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) 33.79/17.06 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.06 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) 33.79/17.06 33.79/17.06 The TRS R consists of the following rules: 33.79/17.06 33.79/17.06 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.06 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.06 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.06 new_psPs0([], ww60) -> ww60 33.79/17.06 new_show11(ww21) -> error([]) 33.79/17.06 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.06 new_show2(ww21, bb) -> error([]) 33.79/17.06 new_show12(ww21) -> error([]) 33.79/17.06 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.06 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_show1(ww21) -> error([]) 33.79/17.06 new_show5(ww21) -> error([]) 33.79/17.06 new_show3(ww21) -> error([]) 33.79/17.06 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.06 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))) 33.79/17.06 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)))))))))), [])) 33.79/17.06 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.06 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.06 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.06 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.06 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.06 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.06 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.06 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.06 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.06 new_primModNatS4(ww143) -> Zero 33.79/17.06 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.06 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.06 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.06 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.06 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS3(ww147) -> Zero 33.79/17.06 new_show(ww21, bf) -> error([]) 33.79/17.06 new_show9(ww21) -> error([]) 33.79/17.06 new_show8(ww21) -> error([]) 33.79/17.06 new_show10(ww21, ca, cb) -> error([]) 33.79/17.06 new_show14(ww21, cc) -> error([]) 33.79/17.06 new_show4(ww21) -> error([]) 33.79/17.06 new_show7(ww21, bd, be) -> error([]) 33.79/17.06 new_show6(ww21) -> error([]) 33.79/17.06 new_show0(ww21) -> error([]) 33.79/17.06 33.79/17.06 The set Q consists of the following terms: 33.79/17.06 33.79/17.06 new_primShowInt0(Pos(Succ(x0))) 33.79/17.06 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.06 new_primDivNatS4(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_IOError) 33.79/17.06 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.06 new_showsPrec(x0, x1, ty_Bool) 33.79/17.06 new_primShowInt0(Neg(x0)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, ty_@0) 33.79/17.06 new_primModNatS2(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_show10(x0, x1, x2) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.06 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS2(Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.06 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primShowInt0(Pos(Zero)) 33.79/17.06 new_show7(x0, x1, x2) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.06 new_primDivNatS02(x0, x1) 33.79/17.06 new_show1(x0) 33.79/17.06 new_psPs0(:(x0, x1), x2) 33.79/17.06 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.06 new_primModNatS02(x0, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.06 new_showsPrec(x0, x1, ty_Float) 33.79/17.06 new_show14(x0, x1) 33.79/17.06 new_div(x0, x1) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_show12(x0) 33.79/17.06 new_show8(x0) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_primModNatS3(Zero, Zero, x0) 33.79/17.06 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.06 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.06 new_primDivNatS2(Zero, Zero, x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.06 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_show6(x0) 33.79/17.06 new_show15(x0, x1, x2, x3) 33.79/17.06 new_primDivNatS3(x0) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.06 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.06 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(x0)) 33.79/17.06 new_show5(x0) 33.79/17.06 new_showsPrec(x0, x1, ty_Integer) 33.79/17.06 new_show(x0, x1) 33.79/17.06 new_show2(x0, x1) 33.79/17.06 new_primModNatS4(x0) 33.79/17.06 new_primIntToChar(x0, x1) 33.79/17.06 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.06 new_showsPrec(x0, x1, ty_Int) 33.79/17.06 new_show9(x0) 33.79/17.06 new_show11(x0) 33.79/17.06 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.06 new_show4(x0) 33.79/17.06 new_psPs0([], x0) 33.79/17.06 new_primDivNatS4(Zero, Zero) 33.79/17.06 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.06 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.06 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show0(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show13(x0) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_show3(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.06 new_showsPrec(x0, x1, ty_Char) 33.79/17.06 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_Double) 33.79/17.06 33.79/17.06 We have to consider all minimal (P,Q,R)-chains. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (86) DependencyGraphProof (EQUIVALENT) 33.79/17.06 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (87) 33.79/17.06 Obligation: 33.79/17.06 Q DP problem: 33.79/17.06 The TRS P consists of the following rules: 33.79/17.06 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 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) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.06 33.79/17.06 The TRS R consists of the following rules: 33.79/17.06 33.79/17.06 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.06 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.06 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.06 new_psPs0([], ww60) -> ww60 33.79/17.06 new_show11(ww21) -> error([]) 33.79/17.06 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.06 new_show2(ww21, bb) -> error([]) 33.79/17.06 new_show12(ww21) -> error([]) 33.79/17.06 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.06 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_show1(ww21) -> error([]) 33.79/17.06 new_show5(ww21) -> error([]) 33.79/17.06 new_show3(ww21) -> error([]) 33.79/17.06 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.06 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))) 33.79/17.06 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)))))))))), [])) 33.79/17.06 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.06 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.06 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.06 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.06 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.06 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.06 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.06 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.06 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.06 new_primModNatS4(ww143) -> Zero 33.79/17.06 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.06 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.06 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.06 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.06 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS3(ww147) -> Zero 33.79/17.06 new_show(ww21, bf) -> error([]) 33.79/17.06 new_show9(ww21) -> error([]) 33.79/17.06 new_show8(ww21) -> error([]) 33.79/17.06 new_show10(ww21, ca, cb) -> error([]) 33.79/17.06 new_show14(ww21, cc) -> error([]) 33.79/17.06 new_show4(ww21) -> error([]) 33.79/17.06 new_show7(ww21, bd, be) -> error([]) 33.79/17.06 new_show6(ww21) -> error([]) 33.79/17.06 new_show0(ww21) -> error([]) 33.79/17.06 33.79/17.06 The set Q consists of the following terms: 33.79/17.06 33.79/17.06 new_primShowInt0(Pos(Succ(x0))) 33.79/17.06 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.06 new_primDivNatS4(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_IOError) 33.79/17.06 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.06 new_showsPrec(x0, x1, ty_Bool) 33.79/17.06 new_primShowInt0(Neg(x0)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, ty_@0) 33.79/17.06 new_primModNatS2(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_show10(x0, x1, x2) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.06 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS2(Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.06 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primShowInt0(Pos(Zero)) 33.79/17.06 new_show7(x0, x1, x2) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.06 new_primDivNatS02(x0, x1) 33.79/17.06 new_show1(x0) 33.79/17.06 new_psPs0(:(x0, x1), x2) 33.79/17.06 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.06 new_primModNatS02(x0, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.06 new_showsPrec(x0, x1, ty_Float) 33.79/17.06 new_show14(x0, x1) 33.79/17.06 new_div(x0, x1) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_show12(x0) 33.79/17.06 new_show8(x0) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_primModNatS3(Zero, Zero, x0) 33.79/17.06 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.06 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.06 new_primDivNatS2(Zero, Zero, x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.06 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_show6(x0) 33.79/17.06 new_show15(x0, x1, x2, x3) 33.79/17.06 new_primDivNatS3(x0) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.06 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.06 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(x0)) 33.79/17.06 new_show5(x0) 33.79/17.06 new_showsPrec(x0, x1, ty_Integer) 33.79/17.06 new_show(x0, x1) 33.79/17.06 new_show2(x0, x1) 33.79/17.06 new_primModNatS4(x0) 33.79/17.06 new_primIntToChar(x0, x1) 33.79/17.06 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.06 new_showsPrec(x0, x1, ty_Int) 33.79/17.06 new_show9(x0) 33.79/17.06 new_show11(x0) 33.79/17.06 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.06 new_show4(x0) 33.79/17.06 new_psPs0([], x0) 33.79/17.06 new_primDivNatS4(Zero, Zero) 33.79/17.06 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.06 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.06 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show0(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show13(x0) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_show3(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.06 new_showsPrec(x0, x1, ty_Char) 33.79/17.06 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_Double) 33.79/17.06 33.79/17.06 We have to consider all minimal (P,Q,R)-chains. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (88) TransformationProof (EQUIVALENT) 33.79/17.06 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.06 33.79/17.06 (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)) 33.79/17.06 33.79/17.06 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (89) 33.79/17.06 Obligation: 33.79/17.06 Q DP problem: 33.79/17.06 The TRS P consists of the following rules: 33.79/17.06 33.79/17.06 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 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) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.06 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) 33.79/17.06 33.79/17.06 The TRS R consists of the following rules: 33.79/17.06 33.79/17.06 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.06 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.06 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.06 new_psPs0([], ww60) -> ww60 33.79/17.06 new_show11(ww21) -> error([]) 33.79/17.06 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.06 new_show2(ww21, bb) -> error([]) 33.79/17.06 new_show12(ww21) -> error([]) 33.79/17.06 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.06 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_show1(ww21) -> error([]) 33.79/17.06 new_show5(ww21) -> error([]) 33.79/17.06 new_show3(ww21) -> error([]) 33.79/17.06 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.06 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))) 33.79/17.06 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)))))))))), [])) 33.79/17.06 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.06 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.06 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.06 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.06 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.06 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.06 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.06 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.06 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.06 new_primModNatS4(ww143) -> Zero 33.79/17.06 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.06 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.06 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.06 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.06 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS3(ww147) -> Zero 33.79/17.06 new_show(ww21, bf) -> error([]) 33.79/17.06 new_show9(ww21) -> error([]) 33.79/17.06 new_show8(ww21) -> error([]) 33.79/17.06 new_show10(ww21, ca, cb) -> error([]) 33.79/17.06 new_show14(ww21, cc) -> error([]) 33.79/17.06 new_show4(ww21) -> error([]) 33.79/17.06 new_show7(ww21, bd, be) -> error([]) 33.79/17.06 new_show6(ww21) -> error([]) 33.79/17.06 new_show0(ww21) -> error([]) 33.79/17.06 33.79/17.06 The set Q consists of the following terms: 33.79/17.06 33.79/17.06 new_primShowInt0(Pos(Succ(x0))) 33.79/17.06 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.06 new_primDivNatS4(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_IOError) 33.79/17.06 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.06 new_showsPrec(x0, x1, ty_Bool) 33.79/17.06 new_primShowInt0(Neg(x0)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, ty_@0) 33.79/17.06 new_primModNatS2(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_show10(x0, x1, x2) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.06 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS2(Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.06 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primShowInt0(Pos(Zero)) 33.79/17.06 new_show7(x0, x1, x2) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.06 new_primDivNatS02(x0, x1) 33.79/17.06 new_show1(x0) 33.79/17.06 new_psPs0(:(x0, x1), x2) 33.79/17.06 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.06 new_primModNatS02(x0, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.06 new_showsPrec(x0, x1, ty_Float) 33.79/17.06 new_show14(x0, x1) 33.79/17.06 new_div(x0, x1) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_show12(x0) 33.79/17.06 new_show8(x0) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_primModNatS3(Zero, Zero, x0) 33.79/17.06 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.06 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.06 new_primDivNatS2(Zero, Zero, x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.06 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_show6(x0) 33.79/17.06 new_show15(x0, x1, x2, x3) 33.79/17.06 new_primDivNatS3(x0) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.06 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.06 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(x0)) 33.79/17.06 new_show5(x0) 33.79/17.06 new_showsPrec(x0, x1, ty_Integer) 33.79/17.06 new_show(x0, x1) 33.79/17.06 new_show2(x0, x1) 33.79/17.06 new_primModNatS4(x0) 33.79/17.06 new_primIntToChar(x0, x1) 33.79/17.06 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.06 new_showsPrec(x0, x1, ty_Int) 33.79/17.06 new_show9(x0) 33.79/17.06 new_show11(x0) 33.79/17.06 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.06 new_show4(x0) 33.79/17.06 new_psPs0([], x0) 33.79/17.06 new_primDivNatS4(Zero, Zero) 33.79/17.06 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.06 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.06 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show0(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show13(x0) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_show3(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.06 new_showsPrec(x0, x1, ty_Char) 33.79/17.06 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_Double) 33.79/17.06 33.79/17.06 We have to consider all minimal (P,Q,R)-chains. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (90) DependencyGraphProof (EQUIVALENT) 33.79/17.06 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (91) 33.79/17.06 Obligation: 33.79/17.06 Q DP problem: 33.79/17.06 The TRS P consists of the following rules: 33.79/17.06 33.79/17.06 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) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.06 33.79/17.06 The TRS R consists of the following rules: 33.79/17.06 33.79/17.06 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.06 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.06 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.06 new_psPs0([], ww60) -> ww60 33.79/17.06 new_show11(ww21) -> error([]) 33.79/17.06 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.06 new_show2(ww21, bb) -> error([]) 33.79/17.06 new_show12(ww21) -> error([]) 33.79/17.06 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.06 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_show1(ww21) -> error([]) 33.79/17.06 new_show5(ww21) -> error([]) 33.79/17.06 new_show3(ww21) -> error([]) 33.79/17.06 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.06 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))) 33.79/17.06 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)))))))))), [])) 33.79/17.06 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.06 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.06 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.06 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.06 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.06 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.06 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.06 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.06 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.06 new_primModNatS4(ww143) -> Zero 33.79/17.06 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.06 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.06 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.06 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.06 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS3(ww147) -> Zero 33.79/17.06 new_show(ww21, bf) -> error([]) 33.79/17.06 new_show9(ww21) -> error([]) 33.79/17.06 new_show8(ww21) -> error([]) 33.79/17.06 new_show10(ww21, ca, cb) -> error([]) 33.79/17.06 new_show14(ww21, cc) -> error([]) 33.79/17.06 new_show4(ww21) -> error([]) 33.79/17.06 new_show7(ww21, bd, be) -> error([]) 33.79/17.06 new_show6(ww21) -> error([]) 33.79/17.06 new_show0(ww21) -> error([]) 33.79/17.06 33.79/17.06 The set Q consists of the following terms: 33.79/17.06 33.79/17.06 new_primShowInt0(Pos(Succ(x0))) 33.79/17.06 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.06 new_primDivNatS4(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_IOError) 33.79/17.06 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.06 new_showsPrec(x0, x1, ty_Bool) 33.79/17.06 new_primShowInt0(Neg(x0)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, ty_@0) 33.79/17.06 new_primModNatS2(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_show10(x0, x1, x2) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.06 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS2(Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.06 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primShowInt0(Pos(Zero)) 33.79/17.06 new_show7(x0, x1, x2) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.06 new_primDivNatS02(x0, x1) 33.79/17.06 new_show1(x0) 33.79/17.06 new_psPs0(:(x0, x1), x2) 33.79/17.06 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.06 new_primModNatS02(x0, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.06 new_showsPrec(x0, x1, ty_Float) 33.79/17.06 new_show14(x0, x1) 33.79/17.06 new_div(x0, x1) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_show12(x0) 33.79/17.06 new_show8(x0) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_primModNatS3(Zero, Zero, x0) 33.79/17.06 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.06 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.06 new_primDivNatS2(Zero, Zero, x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.06 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_show6(x0) 33.79/17.06 new_show15(x0, x1, x2, x3) 33.79/17.06 new_primDivNatS3(x0) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.06 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.06 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(x0)) 33.79/17.06 new_show5(x0) 33.79/17.06 new_showsPrec(x0, x1, ty_Integer) 33.79/17.06 new_show(x0, x1) 33.79/17.06 new_show2(x0, x1) 33.79/17.06 new_primModNatS4(x0) 33.79/17.06 new_primIntToChar(x0, x1) 33.79/17.06 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.06 new_showsPrec(x0, x1, ty_Int) 33.79/17.06 new_show9(x0) 33.79/17.06 new_show11(x0) 33.79/17.06 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.06 new_show4(x0) 33.79/17.06 new_psPs0([], x0) 33.79/17.06 new_primDivNatS4(Zero, Zero) 33.79/17.06 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.06 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.06 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show0(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show13(x0) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_show3(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.06 new_showsPrec(x0, x1, ty_Char) 33.79/17.06 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_Double) 33.79/17.06 33.79/17.06 We have to consider all minimal (P,Q,R)-chains. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (92) TransformationProof (EQUIVALENT) 33.79/17.06 By instantiating [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bg), app(ty_Ratio, bh)) -> 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, bh, bh) we obtained the following new rules [LPAR04]: 33.79/17.06 33.79/17.06 (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)) 33.79/17.06 33.79/17.06 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (93) 33.79/17.06 Obligation: 33.79/17.06 Q DP problem: 33.79/17.06 The TRS P consists of the following rules: 33.79/17.06 33.79/17.06 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) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.06 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) 33.79/17.06 33.79/17.06 The TRS R consists of the following rules: 33.79/17.06 33.79/17.06 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.06 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.06 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.06 new_psPs0([], ww60) -> ww60 33.79/17.06 new_show11(ww21) -> error([]) 33.79/17.06 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.06 new_show2(ww21, bb) -> error([]) 33.79/17.06 new_show12(ww21) -> error([]) 33.79/17.06 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.06 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_show1(ww21) -> error([]) 33.79/17.06 new_show5(ww21) -> error([]) 33.79/17.06 new_show3(ww21) -> error([]) 33.79/17.06 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.06 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))) 33.79/17.06 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)))))))))), [])) 33.79/17.06 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.06 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.06 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.06 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.06 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.06 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.06 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.06 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.06 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.06 new_primModNatS4(ww143) -> Zero 33.79/17.06 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.06 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.06 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.06 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.06 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS3(ww147) -> Zero 33.79/17.06 new_show(ww21, bf) -> error([]) 33.79/17.06 new_show9(ww21) -> error([]) 33.79/17.06 new_show8(ww21) -> error([]) 33.79/17.06 new_show10(ww21, ca, cb) -> error([]) 33.79/17.06 new_show14(ww21, cc) -> error([]) 33.79/17.06 new_show4(ww21) -> error([]) 33.79/17.06 new_show7(ww21, bd, be) -> error([]) 33.79/17.06 new_show6(ww21) -> error([]) 33.79/17.06 new_show0(ww21) -> error([]) 33.79/17.06 33.79/17.06 The set Q consists of the following terms: 33.79/17.06 33.79/17.06 new_primShowInt0(Pos(Succ(x0))) 33.79/17.06 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.06 new_primDivNatS4(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_IOError) 33.79/17.06 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.06 new_showsPrec(x0, x1, ty_Bool) 33.79/17.06 new_primShowInt0(Neg(x0)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, ty_@0) 33.79/17.06 new_primModNatS2(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_show10(x0, x1, x2) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.06 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS2(Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.06 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primShowInt0(Pos(Zero)) 33.79/17.06 new_show7(x0, x1, x2) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.06 new_primDivNatS02(x0, x1) 33.79/17.06 new_show1(x0) 33.79/17.06 new_psPs0(:(x0, x1), x2) 33.79/17.06 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.06 new_primModNatS02(x0, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.06 new_showsPrec(x0, x1, ty_Float) 33.79/17.06 new_show14(x0, x1) 33.79/17.06 new_div(x0, x1) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_show12(x0) 33.79/17.06 new_show8(x0) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_primModNatS3(Zero, Zero, x0) 33.79/17.06 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.06 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.06 new_primDivNatS2(Zero, Zero, x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.06 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_show6(x0) 33.79/17.06 new_show15(x0, x1, x2, x3) 33.79/17.06 new_primDivNatS3(x0) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.06 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.06 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(x0)) 33.79/17.06 new_show5(x0) 33.79/17.06 new_showsPrec(x0, x1, ty_Integer) 33.79/17.06 new_show(x0, x1) 33.79/17.06 new_show2(x0, x1) 33.79/17.06 new_primModNatS4(x0) 33.79/17.06 new_primIntToChar(x0, x1) 33.79/17.06 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.06 new_showsPrec(x0, x1, ty_Int) 33.79/17.06 new_show9(x0) 33.79/17.06 new_show11(x0) 33.79/17.06 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.06 new_show4(x0) 33.79/17.06 new_psPs0([], x0) 33.79/17.06 new_primDivNatS4(Zero, Zero) 33.79/17.06 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.06 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.06 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show0(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show13(x0) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_show3(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.06 new_showsPrec(x0, x1, ty_Char) 33.79/17.06 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_Double) 33.79/17.06 33.79/17.06 We have to consider all minimal (P,Q,R)-chains. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (94) TransformationProof (EQUIVALENT) 33.79/17.06 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.06 33.79/17.06 (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))) 33.79/17.06 33.79/17.06 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (95) 33.79/17.06 Obligation: 33.79/17.06 Q DP problem: 33.79/17.06 The TRS P consists of the following rules: 33.79/17.06 33.79/17.06 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) 33.79/17.06 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.06 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) 33.79/17.06 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)) 33.79/17.06 33.79/17.06 The TRS R consists of the following rules: 33.79/17.06 33.79/17.06 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.06 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.06 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.06 new_psPs0([], ww60) -> ww60 33.79/17.06 new_show11(ww21) -> error([]) 33.79/17.06 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.06 new_show2(ww21, bb) -> error([]) 33.79/17.06 new_show12(ww21) -> error([]) 33.79/17.06 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.06 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_show1(ww21) -> error([]) 33.79/17.06 new_show5(ww21) -> error([]) 33.79/17.06 new_show3(ww21) -> error([]) 33.79/17.06 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.06 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))) 33.79/17.06 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)))))))))), [])) 33.79/17.06 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.06 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.06 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.06 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.06 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.06 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.06 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.06 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.06 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.06 new_primModNatS4(ww143) -> Zero 33.79/17.06 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.06 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.06 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.06 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.06 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS3(ww147) -> Zero 33.79/17.06 new_show(ww21, bf) -> error([]) 33.79/17.06 new_show9(ww21) -> error([]) 33.79/17.06 new_show8(ww21) -> error([]) 33.79/17.06 new_show10(ww21, ca, cb) -> error([]) 33.79/17.06 new_show14(ww21, cc) -> error([]) 33.79/17.06 new_show4(ww21) -> error([]) 33.79/17.06 new_show7(ww21, bd, be) -> error([]) 33.79/17.06 new_show6(ww21) -> error([]) 33.79/17.06 new_show0(ww21) -> error([]) 33.79/17.06 33.79/17.06 The set Q consists of the following terms: 33.79/17.06 33.79/17.06 new_primShowInt0(Pos(Succ(x0))) 33.79/17.06 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.06 new_primDivNatS4(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_IOError) 33.79/17.06 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.06 new_showsPrec(x0, x1, ty_Bool) 33.79/17.06 new_primShowInt0(Neg(x0)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, ty_@0) 33.79/17.06 new_primModNatS2(Succ(x0), Zero) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_show10(x0, x1, x2) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.06 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS2(Zero, Zero) 33.79/17.06 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.06 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primShowInt0(Pos(Zero)) 33.79/17.06 new_show7(x0, x1, x2) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.06 new_primDivNatS02(x0, x1) 33.79/17.06 new_show1(x0) 33.79/17.06 new_psPs0(:(x0, x1), x2) 33.79/17.06 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.06 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.06 new_primModNatS02(x0, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.06 new_showsPrec(x0, x1, ty_Float) 33.79/17.06 new_show14(x0, x1) 33.79/17.06 new_div(x0, x1) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_show12(x0) 33.79/17.06 new_show8(x0) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.06 new_primModNatS3(Zero, Zero, x0) 33.79/17.06 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.06 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.06 new_primDivNatS2(Zero, Zero, x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.06 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_show6(x0) 33.79/17.06 new_show15(x0, x1, x2, x3) 33.79/17.06 new_primDivNatS3(x0) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.06 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.06 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.06 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.06 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(x0)) 33.79/17.06 new_show5(x0) 33.79/17.06 new_showsPrec(x0, x1, ty_Integer) 33.79/17.06 new_show(x0, x1) 33.79/17.06 new_show2(x0, x1) 33.79/17.06 new_primModNatS4(x0) 33.79/17.06 new_primIntToChar(x0, x1) 33.79/17.06 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.06 new_showsPrec(x0, x1, ty_Int) 33.79/17.06 new_show9(x0) 33.79/17.06 new_show11(x0) 33.79/17.06 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.06 new_show4(x0) 33.79/17.06 new_psPs0([], x0) 33.79/17.06 new_primDivNatS4(Zero, Zero) 33.79/17.06 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.06 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.06 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show0(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.06 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.06 new_show13(x0) 33.79/17.06 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.06 new_show3(x0) 33.79/17.06 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.06 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.06 new_showsPrec(x0, x1, ty_Char) 33.79/17.06 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.06 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.06 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.06 new_showsPrec(x0, x1, ty_Double) 33.79/17.06 33.79/17.06 We have to consider all minimal (P,Q,R)-chains. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (96) DependencyGraphProof (EQUIVALENT) 33.79/17.06 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.06 ---------------------------------------- 33.79/17.06 33.79/17.06 (97) 33.79/17.06 Obligation: 33.79/17.06 Q DP problem: 33.79/17.06 The TRS P consists of the following rules: 33.79/17.06 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 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) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.06 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.06 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) 33.79/17.06 33.79/17.06 The TRS R consists of the following rules: 33.79/17.06 33.79/17.06 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.06 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.06 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.06 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.06 new_psPs0([], ww60) -> ww60 33.79/17.06 new_show11(ww21) -> error([]) 33.79/17.06 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.06 new_show2(ww21, bb) -> error([]) 33.79/17.06 new_show12(ww21) -> error([]) 33.79/17.06 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.06 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.06 new_show1(ww21) -> error([]) 33.79/17.06 new_show5(ww21) -> error([]) 33.79/17.06 new_show3(ww21) -> error([]) 33.79/17.06 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.06 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))) 33.79/17.06 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)))))))))), [])) 33.79/17.06 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.06 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.06 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.06 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.06 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.06 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.06 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.06 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.06 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.06 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.06 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.06 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.06 new_primModNatS4(ww143) -> Zero 33.79/17.06 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.06 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.06 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.06 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.06 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.06 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.06 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.06 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.06 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.06 new_primDivNatS3(ww147) -> Zero 33.79/17.06 new_show(ww21, bf) -> error([]) 33.79/17.06 new_show9(ww21) -> error([]) 33.79/17.06 new_show8(ww21) -> error([]) 33.79/17.07 new_show10(ww21, ca, cb) -> error([]) 33.79/17.07 new_show14(ww21, cc) -> error([]) 33.79/17.07 new_show4(ww21) -> error([]) 33.79/17.07 new_show7(ww21, bd, be) -> error([]) 33.79/17.07 new_show6(ww21) -> error([]) 33.79/17.07 new_show0(ww21) -> error([]) 33.79/17.07 33.79/17.07 The set Q consists of the following terms: 33.79/17.07 33.79/17.07 new_primShowInt0(Pos(Succ(x0))) 33.79/17.07 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.07 new_primDivNatS4(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_IOError) 33.79/17.07 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.07 new_showsPrec(x0, x1, ty_Bool) 33.79/17.07 new_primShowInt0(Neg(x0)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, ty_@0) 33.79/17.07 new_primModNatS2(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_show10(x0, x1, x2) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.07 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS2(Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.07 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primShowInt0(Pos(Zero)) 33.79/17.07 new_show7(x0, x1, x2) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.07 new_primDivNatS02(x0, x1) 33.79/17.07 new_show1(x0) 33.79/17.07 new_psPs0(:(x0, x1), x2) 33.79/17.07 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.07 new_primModNatS02(x0, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.07 new_showsPrec(x0, x1, ty_Float) 33.79/17.07 new_show14(x0, x1) 33.79/17.07 new_div(x0, x1) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_show12(x0) 33.79/17.07 new_show8(x0) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_primModNatS3(Zero, Zero, x0) 33.79/17.07 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.07 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.07 new_primDivNatS2(Zero, Zero, x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.07 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_show6(x0) 33.79/17.07 new_show15(x0, x1, x2, x3) 33.79/17.07 new_primDivNatS3(x0) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.07 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.07 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(x0)) 33.79/17.07 new_show5(x0) 33.79/17.07 new_showsPrec(x0, x1, ty_Integer) 33.79/17.07 new_show(x0, x1) 33.79/17.07 new_show2(x0, x1) 33.79/17.07 new_primModNatS4(x0) 33.79/17.07 new_primIntToChar(x0, x1) 33.79/17.07 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.07 new_showsPrec(x0, x1, ty_Int) 33.79/17.07 new_show9(x0) 33.79/17.07 new_show11(x0) 33.79/17.07 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.07 new_show4(x0) 33.79/17.07 new_psPs0([], x0) 33.79/17.07 new_primDivNatS4(Zero, Zero) 33.79/17.07 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.07 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.07 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show0(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show13(x0) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_show3(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.07 new_showsPrec(x0, x1, ty_Char) 33.79/17.07 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_Double) 33.79/17.07 33.79/17.07 We have to consider all minimal (P,Q,R)-chains. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (98) TransformationProof (EQUIVALENT) 33.79/17.07 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.07 33.79/17.07 (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)) 33.79/17.07 33.79/17.07 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (99) 33.79/17.07 Obligation: 33.79/17.07 Q DP problem: 33.79/17.07 The TRS P consists of the following rules: 33.79/17.07 33.79/17.07 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 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) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.07 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) 33.79/17.07 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) 33.79/17.07 33.79/17.07 The TRS R consists of the following rules: 33.79/17.07 33.79/17.07 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.07 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.07 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.07 new_psPs0([], ww60) -> ww60 33.79/17.07 new_show11(ww21) -> error([]) 33.79/17.07 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.07 new_show2(ww21, bb) -> error([]) 33.79/17.07 new_show12(ww21) -> error([]) 33.79/17.07 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.07 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_show1(ww21) -> error([]) 33.79/17.07 new_show5(ww21) -> error([]) 33.79/17.07 new_show3(ww21) -> error([]) 33.79/17.07 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.07 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))) 33.79/17.07 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)))))))))), [])) 33.79/17.07 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.07 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.07 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.07 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.07 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.07 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.07 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.07 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.07 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.07 new_primModNatS4(ww143) -> Zero 33.79/17.07 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.07 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.07 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.07 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.07 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS3(ww147) -> Zero 33.79/17.07 new_show(ww21, bf) -> error([]) 33.79/17.07 new_show9(ww21) -> error([]) 33.79/17.07 new_show8(ww21) -> error([]) 33.79/17.07 new_show10(ww21, ca, cb) -> error([]) 33.79/17.07 new_show14(ww21, cc) -> error([]) 33.79/17.07 new_show4(ww21) -> error([]) 33.79/17.07 new_show7(ww21, bd, be) -> error([]) 33.79/17.07 new_show6(ww21) -> error([]) 33.79/17.07 new_show0(ww21) -> error([]) 33.79/17.07 33.79/17.07 The set Q consists of the following terms: 33.79/17.07 33.79/17.07 new_primShowInt0(Pos(Succ(x0))) 33.79/17.07 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.07 new_primDivNatS4(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_IOError) 33.79/17.07 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.07 new_showsPrec(x0, x1, ty_Bool) 33.79/17.07 new_primShowInt0(Neg(x0)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, ty_@0) 33.79/17.07 new_primModNatS2(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_show10(x0, x1, x2) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.07 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS2(Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.07 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primShowInt0(Pos(Zero)) 33.79/17.07 new_show7(x0, x1, x2) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.07 new_primDivNatS02(x0, x1) 33.79/17.07 new_show1(x0) 33.79/17.07 new_psPs0(:(x0, x1), x2) 33.79/17.07 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.07 new_primModNatS02(x0, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.07 new_showsPrec(x0, x1, ty_Float) 33.79/17.07 new_show14(x0, x1) 33.79/17.07 new_div(x0, x1) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_show12(x0) 33.79/17.07 new_show8(x0) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_primModNatS3(Zero, Zero, x0) 33.79/17.07 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.07 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.07 new_primDivNatS2(Zero, Zero, x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.07 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_show6(x0) 33.79/17.07 new_show15(x0, x1, x2, x3) 33.79/17.07 new_primDivNatS3(x0) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.07 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.07 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(x0)) 33.79/17.07 new_show5(x0) 33.79/17.07 new_showsPrec(x0, x1, ty_Integer) 33.79/17.07 new_show(x0, x1) 33.79/17.07 new_show2(x0, x1) 33.79/17.07 new_primModNatS4(x0) 33.79/17.07 new_primIntToChar(x0, x1) 33.79/17.07 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.07 new_showsPrec(x0, x1, ty_Int) 33.79/17.07 new_show9(x0) 33.79/17.07 new_show11(x0) 33.79/17.07 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.07 new_show4(x0) 33.79/17.07 new_psPs0([], x0) 33.79/17.07 new_primDivNatS4(Zero, Zero) 33.79/17.07 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.07 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.07 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show0(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show13(x0) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_show3(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.07 new_showsPrec(x0, x1, ty_Char) 33.79/17.07 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_Double) 33.79/17.07 33.79/17.07 We have to consider all minimal (P,Q,R)-chains. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (100) DependencyGraphProof (EQUIVALENT) 33.79/17.07 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (101) 33.79/17.07 Obligation: 33.79/17.07 Q DP problem: 33.79/17.07 The TRS P consists of the following rules: 33.79/17.07 33.79/17.07 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) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.07 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) 33.79/17.07 33.79/17.07 The TRS R consists of the following rules: 33.79/17.07 33.79/17.07 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.07 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.07 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.07 new_psPs0([], ww60) -> ww60 33.79/17.07 new_show11(ww21) -> error([]) 33.79/17.07 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.07 new_show2(ww21, bb) -> error([]) 33.79/17.07 new_show12(ww21) -> error([]) 33.79/17.07 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.07 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_show1(ww21) -> error([]) 33.79/17.07 new_show5(ww21) -> error([]) 33.79/17.07 new_show3(ww21) -> error([]) 33.79/17.07 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.07 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))) 33.79/17.07 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)))))))))), [])) 33.79/17.07 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.07 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.07 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.07 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.07 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.07 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.07 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.07 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.07 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.07 new_primModNatS4(ww143) -> Zero 33.79/17.07 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.07 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.07 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.07 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.07 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS3(ww147) -> Zero 33.79/17.07 new_show(ww21, bf) -> error([]) 33.79/17.07 new_show9(ww21) -> error([]) 33.79/17.07 new_show8(ww21) -> error([]) 33.79/17.07 new_show10(ww21, ca, cb) -> error([]) 33.79/17.07 new_show14(ww21, cc) -> error([]) 33.79/17.07 new_show4(ww21) -> error([]) 33.79/17.07 new_show7(ww21, bd, be) -> error([]) 33.79/17.07 new_show6(ww21) -> error([]) 33.79/17.07 new_show0(ww21) -> error([]) 33.79/17.07 33.79/17.07 The set Q consists of the following terms: 33.79/17.07 33.79/17.07 new_primShowInt0(Pos(Succ(x0))) 33.79/17.07 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.07 new_primDivNatS4(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_IOError) 33.79/17.07 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.07 new_showsPrec(x0, x1, ty_Bool) 33.79/17.07 new_primShowInt0(Neg(x0)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, ty_@0) 33.79/17.07 new_primModNatS2(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_show10(x0, x1, x2) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.07 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS2(Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.07 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primShowInt0(Pos(Zero)) 33.79/17.07 new_show7(x0, x1, x2) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.07 new_primDivNatS02(x0, x1) 33.79/17.07 new_show1(x0) 33.79/17.07 new_psPs0(:(x0, x1), x2) 33.79/17.07 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.07 new_primModNatS02(x0, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.07 new_showsPrec(x0, x1, ty_Float) 33.79/17.07 new_show14(x0, x1) 33.79/17.07 new_div(x0, x1) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_show12(x0) 33.79/17.07 new_show8(x0) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_primModNatS3(Zero, Zero, x0) 33.79/17.07 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.07 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.07 new_primDivNatS2(Zero, Zero, x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.07 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_show6(x0) 33.79/17.07 new_show15(x0, x1, x2, x3) 33.79/17.07 new_primDivNatS3(x0) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.07 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.07 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(x0)) 33.79/17.07 new_show5(x0) 33.79/17.07 new_showsPrec(x0, x1, ty_Integer) 33.79/17.07 new_show(x0, x1) 33.79/17.07 new_show2(x0, x1) 33.79/17.07 new_primModNatS4(x0) 33.79/17.07 new_primIntToChar(x0, x1) 33.79/17.07 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.07 new_showsPrec(x0, x1, ty_Int) 33.79/17.07 new_show9(x0) 33.79/17.07 new_show11(x0) 33.79/17.07 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.07 new_show4(x0) 33.79/17.07 new_psPs0([], x0) 33.79/17.07 new_primDivNatS4(Zero, Zero) 33.79/17.07 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.07 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.07 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show0(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show13(x0) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_show3(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.07 new_showsPrec(x0, x1, ty_Char) 33.79/17.07 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_Double) 33.79/17.07 33.79/17.07 We have to consider all minimal (P,Q,R)-chains. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (102) TransformationProof (EQUIVALENT) 33.79/17.07 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.07 33.79/17.07 (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))) 33.79/17.07 33.79/17.07 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (103) 33.79/17.07 Obligation: 33.79/17.07 Q DP problem: 33.79/17.07 The TRS P consists of the following rules: 33.79/17.07 33.79/17.07 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) 33.79/17.07 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.07 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) 33.79/17.07 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)) 33.79/17.07 33.79/17.07 The TRS R consists of the following rules: 33.79/17.07 33.79/17.07 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.07 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.07 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.07 new_psPs0([], ww60) -> ww60 33.79/17.07 new_show11(ww21) -> error([]) 33.79/17.07 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.07 new_show2(ww21, bb) -> error([]) 33.79/17.07 new_show12(ww21) -> error([]) 33.79/17.07 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.07 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_show1(ww21) -> error([]) 33.79/17.07 new_show5(ww21) -> error([]) 33.79/17.07 new_show3(ww21) -> error([]) 33.79/17.07 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.07 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))) 33.79/17.07 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)))))))))), [])) 33.79/17.07 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.07 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.07 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.07 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.07 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.07 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.07 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.07 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.07 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.07 new_primModNatS4(ww143) -> Zero 33.79/17.07 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.07 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.07 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.07 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.07 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS3(ww147) -> Zero 33.79/17.07 new_show(ww21, bf) -> error([]) 33.79/17.07 new_show9(ww21) -> error([]) 33.79/17.07 new_show8(ww21) -> error([]) 33.79/17.07 new_show10(ww21, ca, cb) -> error([]) 33.79/17.07 new_show14(ww21, cc) -> error([]) 33.79/17.07 new_show4(ww21) -> error([]) 33.79/17.07 new_show7(ww21, bd, be) -> error([]) 33.79/17.07 new_show6(ww21) -> error([]) 33.79/17.07 new_show0(ww21) -> error([]) 33.79/17.07 33.79/17.07 The set Q consists of the following terms: 33.79/17.07 33.79/17.07 new_primShowInt0(Pos(Succ(x0))) 33.79/17.07 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.07 new_primDivNatS4(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_IOError) 33.79/17.07 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.07 new_showsPrec(x0, x1, ty_Bool) 33.79/17.07 new_primShowInt0(Neg(x0)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, ty_@0) 33.79/17.07 new_primModNatS2(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_show10(x0, x1, x2) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.07 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS2(Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.07 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primShowInt0(Pos(Zero)) 33.79/17.07 new_show7(x0, x1, x2) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.07 new_primDivNatS02(x0, x1) 33.79/17.07 new_show1(x0) 33.79/17.07 new_psPs0(:(x0, x1), x2) 33.79/17.07 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.07 new_primModNatS02(x0, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.07 new_showsPrec(x0, x1, ty_Float) 33.79/17.07 new_show14(x0, x1) 33.79/17.07 new_div(x0, x1) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_show12(x0) 33.79/17.07 new_show8(x0) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_primModNatS3(Zero, Zero, x0) 33.79/17.07 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.07 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.07 new_primDivNatS2(Zero, Zero, x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.07 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_show6(x0) 33.79/17.07 new_show15(x0, x1, x2, x3) 33.79/17.07 new_primDivNatS3(x0) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.07 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.07 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(x0)) 33.79/17.07 new_show5(x0) 33.79/17.07 new_showsPrec(x0, x1, ty_Integer) 33.79/17.07 new_show(x0, x1) 33.79/17.07 new_show2(x0, x1) 33.79/17.07 new_primModNatS4(x0) 33.79/17.07 new_primIntToChar(x0, x1) 33.79/17.07 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.07 new_showsPrec(x0, x1, ty_Int) 33.79/17.07 new_show9(x0) 33.79/17.07 new_show11(x0) 33.79/17.07 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.07 new_show4(x0) 33.79/17.07 new_psPs0([], x0) 33.79/17.07 new_primDivNatS4(Zero, Zero) 33.79/17.07 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.07 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.07 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show0(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show13(x0) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_show3(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.07 new_showsPrec(x0, x1, ty_Char) 33.79/17.07 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_Double) 33.79/17.07 33.79/17.07 We have to consider all minimal (P,Q,R)-chains. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (104) DependencyGraphProof (EQUIVALENT) 33.79/17.07 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (105) 33.79/17.07 Obligation: 33.79/17.07 Q DP problem: 33.79/17.07 The TRS P consists of the following rules: 33.79/17.07 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 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) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.07 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) 33.79/17.07 33.79/17.07 The TRS R consists of the following rules: 33.79/17.07 33.79/17.07 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.07 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.07 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.07 new_psPs0([], ww60) -> ww60 33.79/17.07 new_show11(ww21) -> error([]) 33.79/17.07 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.07 new_show2(ww21, bb) -> error([]) 33.79/17.07 new_show12(ww21) -> error([]) 33.79/17.07 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.07 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_show1(ww21) -> error([]) 33.79/17.07 new_show5(ww21) -> error([]) 33.79/17.07 new_show3(ww21) -> error([]) 33.79/17.07 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.07 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))) 33.79/17.07 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)))))))))), [])) 33.79/17.07 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.07 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.07 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.07 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.07 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.07 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.07 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.07 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.07 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.07 new_primModNatS4(ww143) -> Zero 33.79/17.07 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.07 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.07 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.07 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.07 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS3(ww147) -> Zero 33.79/17.07 new_show(ww21, bf) -> error([]) 33.79/17.07 new_show9(ww21) -> error([]) 33.79/17.07 new_show8(ww21) -> error([]) 33.79/17.07 new_show10(ww21, ca, cb) -> error([]) 33.79/17.07 new_show14(ww21, cc) -> error([]) 33.79/17.07 new_show4(ww21) -> error([]) 33.79/17.07 new_show7(ww21, bd, be) -> error([]) 33.79/17.07 new_show6(ww21) -> error([]) 33.79/17.07 new_show0(ww21) -> error([]) 33.79/17.07 33.79/17.07 The set Q consists of the following terms: 33.79/17.07 33.79/17.07 new_primShowInt0(Pos(Succ(x0))) 33.79/17.07 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.07 new_primDivNatS4(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_IOError) 33.79/17.07 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.07 new_showsPrec(x0, x1, ty_Bool) 33.79/17.07 new_primShowInt0(Neg(x0)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, ty_@0) 33.79/17.07 new_primModNatS2(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_show10(x0, x1, x2) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.07 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS2(Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.07 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primShowInt0(Pos(Zero)) 33.79/17.07 new_show7(x0, x1, x2) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.07 new_primDivNatS02(x0, x1) 33.79/17.07 new_show1(x0) 33.79/17.07 new_psPs0(:(x0, x1), x2) 33.79/17.07 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.07 new_primModNatS02(x0, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.07 new_showsPrec(x0, x1, ty_Float) 33.79/17.07 new_show14(x0, x1) 33.79/17.07 new_div(x0, x1) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_show12(x0) 33.79/17.07 new_show8(x0) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_primModNatS3(Zero, Zero, x0) 33.79/17.07 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.07 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.07 new_primDivNatS2(Zero, Zero, x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.07 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_show6(x0) 33.79/17.07 new_show15(x0, x1, x2, x3) 33.79/17.07 new_primDivNatS3(x0) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.07 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.07 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(x0)) 33.79/17.07 new_show5(x0) 33.79/17.07 new_showsPrec(x0, x1, ty_Integer) 33.79/17.07 new_show(x0, x1) 33.79/17.07 new_show2(x0, x1) 33.79/17.07 new_primModNatS4(x0) 33.79/17.07 new_primIntToChar(x0, x1) 33.79/17.07 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.07 new_showsPrec(x0, x1, ty_Int) 33.79/17.07 new_show9(x0) 33.79/17.07 new_show11(x0) 33.79/17.07 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.07 new_show4(x0) 33.79/17.07 new_psPs0([], x0) 33.79/17.07 new_primDivNatS4(Zero, Zero) 33.79/17.07 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.07 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.07 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show0(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show13(x0) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_show3(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.07 new_showsPrec(x0, x1, ty_Char) 33.79/17.07 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_Double) 33.79/17.07 33.79/17.07 We have to consider all minimal (P,Q,R)-chains. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (106) TransformationProof (EQUIVALENT) 33.79/17.07 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.07 33.79/17.07 (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))) 33.79/17.07 33.79/17.07 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (107) 33.79/17.07 Obligation: 33.79/17.07 Q DP problem: 33.79/17.07 The TRS P consists of the following rules: 33.79/17.07 33.79/17.07 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 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) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.07 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) 33.79/17.07 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)) 33.79/17.07 33.79/17.07 The TRS R consists of the following rules: 33.79/17.07 33.79/17.07 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.07 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.07 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.07 new_psPs0([], ww60) -> ww60 33.79/17.07 new_show11(ww21) -> error([]) 33.79/17.07 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.07 new_show2(ww21, bb) -> error([]) 33.79/17.07 new_show12(ww21) -> error([]) 33.79/17.07 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.07 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_show1(ww21) -> error([]) 33.79/17.07 new_show5(ww21) -> error([]) 33.79/17.07 new_show3(ww21) -> error([]) 33.79/17.07 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.07 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))) 33.79/17.07 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)))))))))), [])) 33.79/17.07 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.07 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.07 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.07 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.07 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.07 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.07 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.07 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.07 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.07 new_primModNatS4(ww143) -> Zero 33.79/17.07 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.07 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.07 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.07 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.07 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS3(ww147) -> Zero 33.79/17.07 new_show(ww21, bf) -> error([]) 33.79/17.07 new_show9(ww21) -> error([]) 33.79/17.07 new_show8(ww21) -> error([]) 33.79/17.07 new_show10(ww21, ca, cb) -> error([]) 33.79/17.07 new_show14(ww21, cc) -> error([]) 33.79/17.07 new_show4(ww21) -> error([]) 33.79/17.07 new_show7(ww21, bd, be) -> error([]) 33.79/17.07 new_show6(ww21) -> error([]) 33.79/17.07 new_show0(ww21) -> error([]) 33.79/17.07 33.79/17.07 The set Q consists of the following terms: 33.79/17.07 33.79/17.07 new_primShowInt0(Pos(Succ(x0))) 33.79/17.07 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.07 new_primDivNatS4(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_IOError) 33.79/17.07 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.07 new_showsPrec(x0, x1, ty_Bool) 33.79/17.07 new_primShowInt0(Neg(x0)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, ty_@0) 33.79/17.07 new_primModNatS2(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_show10(x0, x1, x2) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.07 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS2(Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.07 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primShowInt0(Pos(Zero)) 33.79/17.07 new_show7(x0, x1, x2) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.07 new_primDivNatS02(x0, x1) 33.79/17.07 new_show1(x0) 33.79/17.07 new_psPs0(:(x0, x1), x2) 33.79/17.07 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.07 new_primModNatS02(x0, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.07 new_showsPrec(x0, x1, ty_Float) 33.79/17.07 new_show14(x0, x1) 33.79/17.07 new_div(x0, x1) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_show12(x0) 33.79/17.07 new_show8(x0) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_primModNatS3(Zero, Zero, x0) 33.79/17.07 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.07 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.07 new_primDivNatS2(Zero, Zero, x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.07 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_show6(x0) 33.79/17.07 new_show15(x0, x1, x2, x3) 33.79/17.07 new_primDivNatS3(x0) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.07 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.07 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(x0)) 33.79/17.07 new_show5(x0) 33.79/17.07 new_showsPrec(x0, x1, ty_Integer) 33.79/17.07 new_show(x0, x1) 33.79/17.07 new_show2(x0, x1) 33.79/17.07 new_primModNatS4(x0) 33.79/17.07 new_primIntToChar(x0, x1) 33.79/17.07 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.07 new_showsPrec(x0, x1, ty_Int) 33.79/17.07 new_show9(x0) 33.79/17.07 new_show11(x0) 33.79/17.07 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.07 new_show4(x0) 33.79/17.07 new_psPs0([], x0) 33.79/17.07 new_primDivNatS4(Zero, Zero) 33.79/17.07 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.07 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.07 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show0(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show13(x0) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_show3(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.07 new_showsPrec(x0, x1, ty_Char) 33.79/17.07 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_Double) 33.79/17.07 33.79/17.07 We have to consider all minimal (P,Q,R)-chains. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (108) DependencyGraphProof (EQUIVALENT) 33.79/17.07 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (109) 33.79/17.07 Obligation: 33.79/17.07 Q DP problem: 33.79/17.07 The TRS P consists of the following rules: 33.79/17.07 33.79/17.07 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) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.07 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) 33.79/17.07 33.79/17.07 The TRS R consists of the following rules: 33.79/17.07 33.79/17.07 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.07 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.07 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.07 new_psPs0([], ww60) -> ww60 33.79/17.07 new_show11(ww21) -> error([]) 33.79/17.07 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.07 new_show2(ww21, bb) -> error([]) 33.79/17.07 new_show12(ww21) -> error([]) 33.79/17.07 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.07 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_show1(ww21) -> error([]) 33.79/17.07 new_show5(ww21) -> error([]) 33.79/17.07 new_show3(ww21) -> error([]) 33.79/17.07 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.07 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))) 33.79/17.07 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)))))))))), [])) 33.79/17.07 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.07 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.07 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.07 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.07 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.07 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.07 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.07 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.07 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.07 new_primModNatS4(ww143) -> Zero 33.79/17.07 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.07 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.07 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.07 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.07 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS3(ww147) -> Zero 33.79/17.07 new_show(ww21, bf) -> error([]) 33.79/17.07 new_show9(ww21) -> error([]) 33.79/17.07 new_show8(ww21) -> error([]) 33.79/17.07 new_show10(ww21, ca, cb) -> error([]) 33.79/17.07 new_show14(ww21, cc) -> error([]) 33.79/17.07 new_show4(ww21) -> error([]) 33.79/17.07 new_show7(ww21, bd, be) -> error([]) 33.79/17.07 new_show6(ww21) -> error([]) 33.79/17.07 new_show0(ww21) -> error([]) 33.79/17.07 33.79/17.07 The set Q consists of the following terms: 33.79/17.07 33.79/17.07 new_primShowInt0(Pos(Succ(x0))) 33.79/17.07 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.07 new_primDivNatS4(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_IOError) 33.79/17.07 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.07 new_showsPrec(x0, x1, ty_Bool) 33.79/17.07 new_primShowInt0(Neg(x0)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, ty_@0) 33.79/17.07 new_primModNatS2(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_show10(x0, x1, x2) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.07 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS2(Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.07 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primShowInt0(Pos(Zero)) 33.79/17.07 new_show7(x0, x1, x2) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.07 new_primDivNatS02(x0, x1) 33.79/17.07 new_show1(x0) 33.79/17.07 new_psPs0(:(x0, x1), x2) 33.79/17.07 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.07 new_primModNatS02(x0, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.07 new_showsPrec(x0, x1, ty_Float) 33.79/17.07 new_show14(x0, x1) 33.79/17.07 new_div(x0, x1) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_show12(x0) 33.79/17.07 new_show8(x0) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_primModNatS3(Zero, Zero, x0) 33.79/17.07 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.07 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.07 new_primDivNatS2(Zero, Zero, x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.07 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_show6(x0) 33.79/17.07 new_show15(x0, x1, x2, x3) 33.79/17.07 new_primDivNatS3(x0) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.07 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.07 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(x0)) 33.79/17.07 new_show5(x0) 33.79/17.07 new_showsPrec(x0, x1, ty_Integer) 33.79/17.07 new_show(x0, x1) 33.79/17.07 new_show2(x0, x1) 33.79/17.07 new_primModNatS4(x0) 33.79/17.07 new_primIntToChar(x0, x1) 33.79/17.07 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.07 new_showsPrec(x0, x1, ty_Int) 33.79/17.07 new_show9(x0) 33.79/17.07 new_show11(x0) 33.79/17.07 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.07 new_show4(x0) 33.79/17.07 new_psPs0([], x0) 33.79/17.07 new_primDivNatS4(Zero, Zero) 33.79/17.07 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.07 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.07 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show0(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show13(x0) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_show3(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.07 new_showsPrec(x0, x1, ty_Char) 33.79/17.07 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_Double) 33.79/17.07 33.79/17.07 We have to consider all minimal (P,Q,R)-chains. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (110) TransformationProof (EQUIVALENT) 33.79/17.07 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.07 33.79/17.07 (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)) 33.79/17.07 33.79/17.07 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (111) 33.79/17.07 Obligation: 33.79/17.07 Q DP problem: 33.79/17.07 The TRS P consists of the following rules: 33.79/17.07 33.79/17.07 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) 33.79/17.07 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.07 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) 33.79/17.07 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) 33.79/17.07 33.79/17.07 The TRS R consists of the following rules: 33.79/17.07 33.79/17.07 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.07 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.07 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.07 new_psPs0([], ww60) -> ww60 33.79/17.07 new_show11(ww21) -> error([]) 33.79/17.07 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.07 new_show2(ww21, bb) -> error([]) 33.79/17.07 new_show12(ww21) -> error([]) 33.79/17.07 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.07 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_show1(ww21) -> error([]) 33.79/17.07 new_show5(ww21) -> error([]) 33.79/17.07 new_show3(ww21) -> error([]) 33.79/17.07 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.07 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))) 33.79/17.07 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)))))))))), [])) 33.79/17.07 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.07 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.07 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.07 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.07 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.07 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.07 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.07 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.07 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.07 new_primModNatS4(ww143) -> Zero 33.79/17.07 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.07 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.07 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.07 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.07 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.07 new_primDivNatS3(ww147) -> Zero 33.79/17.07 new_show(ww21, bf) -> error([]) 33.79/17.07 new_show9(ww21) -> error([]) 33.79/17.07 new_show8(ww21) -> error([]) 33.79/17.07 new_show10(ww21, ca, cb) -> error([]) 33.79/17.07 new_show14(ww21, cc) -> error([]) 33.79/17.07 new_show4(ww21) -> error([]) 33.79/17.07 new_show7(ww21, bd, be) -> error([]) 33.79/17.07 new_show6(ww21) -> error([]) 33.79/17.07 new_show0(ww21) -> error([]) 33.79/17.07 33.79/17.07 The set Q consists of the following terms: 33.79/17.07 33.79/17.07 new_primShowInt0(Pos(Succ(x0))) 33.79/17.07 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.07 new_primDivNatS4(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_IOError) 33.79/17.07 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.07 new_showsPrec(x0, x1, ty_Bool) 33.79/17.07 new_primShowInt0(Neg(x0)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, ty_@0) 33.79/17.07 new_primModNatS2(Succ(x0), Zero) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_show10(x0, x1, x2) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.07 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS2(Zero, Zero) 33.79/17.07 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.07 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primShowInt0(Pos(Zero)) 33.79/17.07 new_show7(x0, x1, x2) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.07 new_primDivNatS02(x0, x1) 33.79/17.07 new_show1(x0) 33.79/17.07 new_psPs0(:(x0, x1), x2) 33.79/17.07 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.07 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.07 new_primModNatS02(x0, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.07 new_showsPrec(x0, x1, ty_Float) 33.79/17.07 new_show14(x0, x1) 33.79/17.07 new_div(x0, x1) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_show12(x0) 33.79/17.07 new_show8(x0) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.07 new_primModNatS3(Zero, Zero, x0) 33.79/17.07 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.07 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.07 new_primDivNatS2(Zero, Zero, x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.07 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_show6(x0) 33.79/17.07 new_show15(x0, x1, x2, x3) 33.79/17.07 new_primDivNatS3(x0) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.07 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.07 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.07 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.07 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(x0)) 33.79/17.07 new_show5(x0) 33.79/17.07 new_showsPrec(x0, x1, ty_Integer) 33.79/17.07 new_show(x0, x1) 33.79/17.07 new_show2(x0, x1) 33.79/17.07 new_primModNatS4(x0) 33.79/17.07 new_primIntToChar(x0, x1) 33.79/17.07 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.07 new_showsPrec(x0, x1, ty_Int) 33.79/17.07 new_show9(x0) 33.79/17.07 new_show11(x0) 33.79/17.07 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.07 new_show4(x0) 33.79/17.07 new_psPs0([], x0) 33.79/17.07 new_primDivNatS4(Zero, Zero) 33.79/17.07 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.07 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.07 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show0(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.07 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.07 new_show13(x0) 33.79/17.07 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.07 new_show3(x0) 33.79/17.07 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.07 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.07 new_showsPrec(x0, x1, ty_Char) 33.79/17.07 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.07 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.07 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.07 new_showsPrec(x0, x1, ty_Double) 33.79/17.07 33.79/17.07 We have to consider all minimal (P,Q,R)-chains. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (112) DependencyGraphProof (EQUIVALENT) 33.79/17.07 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.07 ---------------------------------------- 33.79/17.07 33.79/17.07 (113) 33.79/17.07 Obligation: 33.79/17.07 Q DP problem: 33.79/17.07 The TRS P consists of the following rules: 33.79/17.07 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 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) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.07 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.07 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) 33.79/17.07 33.79/17.07 The TRS R consists of the following rules: 33.79/17.07 33.79/17.07 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.07 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.07 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.07 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.07 new_psPs0([], ww60) -> ww60 33.79/17.07 new_show11(ww21) -> error([]) 33.79/17.07 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.07 new_show2(ww21, bb) -> error([]) 33.79/17.07 new_show12(ww21) -> error([]) 33.79/17.07 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.07 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.07 new_show1(ww21) -> error([]) 33.79/17.07 new_show5(ww21) -> error([]) 33.79/17.07 new_show3(ww21) -> error([]) 33.79/17.07 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.07 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))) 33.79/17.07 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)))))))))), [])) 33.79/17.07 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.07 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.07 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.07 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.07 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.07 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.07 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.07 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.07 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.07 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.07 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.07 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.07 new_primModNatS4(ww143) -> Zero 33.79/17.07 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.07 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.07 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.07 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.07 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.07 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.07 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.07 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.08 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS3(ww147) -> Zero 33.79/17.08 new_show(ww21, bf) -> error([]) 33.79/17.08 new_show9(ww21) -> error([]) 33.79/17.08 new_show8(ww21) -> error([]) 33.79/17.08 new_show10(ww21, ca, cb) -> error([]) 33.79/17.08 new_show14(ww21, cc) -> error([]) 33.79/17.08 new_show4(ww21) -> error([]) 33.79/17.08 new_show7(ww21, bd, be) -> error([]) 33.79/17.08 new_show6(ww21) -> error([]) 33.79/17.08 new_show0(ww21) -> error([]) 33.79/17.08 33.79/17.08 The set Q consists of the following terms: 33.79/17.08 33.79/17.08 new_primShowInt0(Pos(Succ(x0))) 33.79/17.08 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.08 new_primDivNatS4(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_IOError) 33.79/17.08 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.08 new_showsPrec(x0, x1, ty_Bool) 33.79/17.08 new_primShowInt0(Neg(x0)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, ty_@0) 33.79/17.08 new_primModNatS2(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_show10(x0, x1, x2) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.08 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS2(Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.08 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primShowInt0(Pos(Zero)) 33.79/17.08 new_show7(x0, x1, x2) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.08 new_primDivNatS02(x0, x1) 33.79/17.08 new_show1(x0) 33.79/17.08 new_psPs0(:(x0, x1), x2) 33.79/17.08 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.08 new_primModNatS02(x0, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.08 new_showsPrec(x0, x1, ty_Float) 33.79/17.08 new_show14(x0, x1) 33.79/17.08 new_div(x0, x1) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_show12(x0) 33.79/17.08 new_show8(x0) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_primModNatS3(Zero, Zero, x0) 33.79/17.08 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.08 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.08 new_primDivNatS2(Zero, Zero, x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.08 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_show6(x0) 33.79/17.08 new_show15(x0, x1, x2, x3) 33.79/17.08 new_primDivNatS3(x0) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.08 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.08 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(x0)) 33.79/17.08 new_show5(x0) 33.79/17.08 new_showsPrec(x0, x1, ty_Integer) 33.79/17.08 new_show(x0, x1) 33.79/17.08 new_show2(x0, x1) 33.79/17.08 new_primModNatS4(x0) 33.79/17.08 new_primIntToChar(x0, x1) 33.79/17.08 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.08 new_showsPrec(x0, x1, ty_Int) 33.79/17.08 new_show9(x0) 33.79/17.08 new_show11(x0) 33.79/17.08 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.08 new_show4(x0) 33.79/17.08 new_psPs0([], x0) 33.79/17.08 new_primDivNatS4(Zero, Zero) 33.79/17.08 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.08 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.08 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show0(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show13(x0) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_show3(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.08 new_showsPrec(x0, x1, ty_Char) 33.79/17.08 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_Double) 33.79/17.08 33.79/17.08 We have to consider all minimal (P,Q,R)-chains. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (114) TransformationProof (EQUIVALENT) 33.79/17.08 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.08 33.79/17.08 (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)) 33.79/17.08 33.79/17.08 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (115) 33.79/17.08 Obligation: 33.79/17.08 Q DP problem: 33.79/17.08 The TRS P consists of the following rules: 33.79/17.08 33.79/17.08 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 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) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.08 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) 33.79/17.08 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) 33.79/17.08 33.79/17.08 The TRS R consists of the following rules: 33.79/17.08 33.79/17.08 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.08 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.08 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.08 new_psPs0([], ww60) -> ww60 33.79/17.08 new_show11(ww21) -> error([]) 33.79/17.08 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.08 new_show2(ww21, bb) -> error([]) 33.79/17.08 new_show12(ww21) -> error([]) 33.79/17.08 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.08 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_show1(ww21) -> error([]) 33.79/17.08 new_show5(ww21) -> error([]) 33.79/17.08 new_show3(ww21) -> error([]) 33.79/17.08 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.08 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))) 33.79/17.08 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)))))))))), [])) 33.79/17.08 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.08 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.08 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.08 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.08 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.08 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.08 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.08 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.08 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.08 new_primModNatS4(ww143) -> Zero 33.79/17.08 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.08 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.08 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.08 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.08 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS3(ww147) -> Zero 33.79/17.08 new_show(ww21, bf) -> error([]) 33.79/17.08 new_show9(ww21) -> error([]) 33.79/17.08 new_show8(ww21) -> error([]) 33.79/17.08 new_show10(ww21, ca, cb) -> error([]) 33.79/17.08 new_show14(ww21, cc) -> error([]) 33.79/17.08 new_show4(ww21) -> error([]) 33.79/17.08 new_show7(ww21, bd, be) -> error([]) 33.79/17.08 new_show6(ww21) -> error([]) 33.79/17.08 new_show0(ww21) -> error([]) 33.79/17.08 33.79/17.08 The set Q consists of the following terms: 33.79/17.08 33.79/17.08 new_primShowInt0(Pos(Succ(x0))) 33.79/17.08 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.08 new_primDivNatS4(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_IOError) 33.79/17.08 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.08 new_showsPrec(x0, x1, ty_Bool) 33.79/17.08 new_primShowInt0(Neg(x0)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, ty_@0) 33.79/17.08 new_primModNatS2(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_show10(x0, x1, x2) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.08 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS2(Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.08 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primShowInt0(Pos(Zero)) 33.79/17.08 new_show7(x0, x1, x2) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.08 new_primDivNatS02(x0, x1) 33.79/17.08 new_show1(x0) 33.79/17.08 new_psPs0(:(x0, x1), x2) 33.79/17.08 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.08 new_primModNatS02(x0, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.08 new_showsPrec(x0, x1, ty_Float) 33.79/17.08 new_show14(x0, x1) 33.79/17.08 new_div(x0, x1) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_show12(x0) 33.79/17.08 new_show8(x0) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_primModNatS3(Zero, Zero, x0) 33.79/17.08 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.08 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.08 new_primDivNatS2(Zero, Zero, x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.08 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_show6(x0) 33.79/17.08 new_show15(x0, x1, x2, x3) 33.79/17.08 new_primDivNatS3(x0) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.08 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.08 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(x0)) 33.79/17.08 new_show5(x0) 33.79/17.08 new_showsPrec(x0, x1, ty_Integer) 33.79/17.08 new_show(x0, x1) 33.79/17.08 new_show2(x0, x1) 33.79/17.08 new_primModNatS4(x0) 33.79/17.08 new_primIntToChar(x0, x1) 33.79/17.08 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.08 new_showsPrec(x0, x1, ty_Int) 33.79/17.08 new_show9(x0) 33.79/17.08 new_show11(x0) 33.79/17.08 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.08 new_show4(x0) 33.79/17.08 new_psPs0([], x0) 33.79/17.08 new_primDivNatS4(Zero, Zero) 33.79/17.08 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.08 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.08 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show0(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show13(x0) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_show3(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.08 new_showsPrec(x0, x1, ty_Char) 33.79/17.08 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_Double) 33.79/17.08 33.79/17.08 We have to consider all minimal (P,Q,R)-chains. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (116) DependencyGraphProof (EQUIVALENT) 33.79/17.08 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (117) 33.79/17.08 Obligation: 33.79/17.08 Q DP problem: 33.79/17.08 The TRS P consists of the following rules: 33.79/17.08 33.79/17.08 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) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.08 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) 33.79/17.08 33.79/17.08 The TRS R consists of the following rules: 33.79/17.08 33.79/17.08 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.08 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.08 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.08 new_psPs0([], ww60) -> ww60 33.79/17.08 new_show11(ww21) -> error([]) 33.79/17.08 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.08 new_show2(ww21, bb) -> error([]) 33.79/17.08 new_show12(ww21) -> error([]) 33.79/17.08 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.08 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_show1(ww21) -> error([]) 33.79/17.08 new_show5(ww21) -> error([]) 33.79/17.08 new_show3(ww21) -> error([]) 33.79/17.08 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.08 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))) 33.79/17.08 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)))))))))), [])) 33.79/17.08 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.08 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.08 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.08 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.08 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.08 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.08 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.08 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.08 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.08 new_primModNatS4(ww143) -> Zero 33.79/17.08 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.08 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.08 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.08 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.08 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS3(ww147) -> Zero 33.79/17.08 new_show(ww21, bf) -> error([]) 33.79/17.08 new_show9(ww21) -> error([]) 33.79/17.08 new_show8(ww21) -> error([]) 33.79/17.08 new_show10(ww21, ca, cb) -> error([]) 33.79/17.08 new_show14(ww21, cc) -> error([]) 33.79/17.08 new_show4(ww21) -> error([]) 33.79/17.08 new_show7(ww21, bd, be) -> error([]) 33.79/17.08 new_show6(ww21) -> error([]) 33.79/17.08 new_show0(ww21) -> error([]) 33.79/17.08 33.79/17.08 The set Q consists of the following terms: 33.79/17.08 33.79/17.08 new_primShowInt0(Pos(Succ(x0))) 33.79/17.08 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.08 new_primDivNatS4(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_IOError) 33.79/17.08 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.08 new_showsPrec(x0, x1, ty_Bool) 33.79/17.08 new_primShowInt0(Neg(x0)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, ty_@0) 33.79/17.08 new_primModNatS2(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_show10(x0, x1, x2) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.08 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS2(Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.08 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primShowInt0(Pos(Zero)) 33.79/17.08 new_show7(x0, x1, x2) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.08 new_primDivNatS02(x0, x1) 33.79/17.08 new_show1(x0) 33.79/17.08 new_psPs0(:(x0, x1), x2) 33.79/17.08 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.08 new_primModNatS02(x0, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.08 new_showsPrec(x0, x1, ty_Float) 33.79/17.08 new_show14(x0, x1) 33.79/17.08 new_div(x0, x1) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_show12(x0) 33.79/17.08 new_show8(x0) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_primModNatS3(Zero, Zero, x0) 33.79/17.08 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.08 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.08 new_primDivNatS2(Zero, Zero, x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.08 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_show6(x0) 33.79/17.08 new_show15(x0, x1, x2, x3) 33.79/17.08 new_primDivNatS3(x0) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.08 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.08 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(x0)) 33.79/17.08 new_show5(x0) 33.79/17.08 new_showsPrec(x0, x1, ty_Integer) 33.79/17.08 new_show(x0, x1) 33.79/17.08 new_show2(x0, x1) 33.79/17.08 new_primModNatS4(x0) 33.79/17.08 new_primIntToChar(x0, x1) 33.79/17.08 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.08 new_showsPrec(x0, x1, ty_Int) 33.79/17.08 new_show9(x0) 33.79/17.08 new_show11(x0) 33.79/17.08 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.08 new_show4(x0) 33.79/17.08 new_psPs0([], x0) 33.79/17.08 new_primDivNatS4(Zero, Zero) 33.79/17.08 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.08 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.08 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show0(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show13(x0) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_show3(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.08 new_showsPrec(x0, x1, ty_Char) 33.79/17.08 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_Double) 33.79/17.08 33.79/17.08 We have to consider all minimal (P,Q,R)-chains. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (118) TransformationProof (EQUIVALENT) 33.79/17.08 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.08 33.79/17.08 (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))) 33.79/17.08 33.79/17.08 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (119) 33.79/17.08 Obligation: 33.79/17.08 Q DP problem: 33.79/17.08 The TRS P consists of the following rules: 33.79/17.08 33.79/17.08 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) 33.79/17.08 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.08 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) 33.79/17.08 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)) 33.79/17.08 33.79/17.08 The TRS R consists of the following rules: 33.79/17.08 33.79/17.08 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.08 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.08 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.08 new_psPs0([], ww60) -> ww60 33.79/17.08 new_show11(ww21) -> error([]) 33.79/17.08 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.08 new_show2(ww21, bb) -> error([]) 33.79/17.08 new_show12(ww21) -> error([]) 33.79/17.08 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.08 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_show1(ww21) -> error([]) 33.79/17.08 new_show5(ww21) -> error([]) 33.79/17.08 new_show3(ww21) -> error([]) 33.79/17.08 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.08 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))) 33.79/17.08 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)))))))))), [])) 33.79/17.08 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.08 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.08 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.08 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.08 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.08 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.08 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.08 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.08 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.08 new_primModNatS4(ww143) -> Zero 33.79/17.08 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.08 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.08 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.08 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.08 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS3(ww147) -> Zero 33.79/17.08 new_show(ww21, bf) -> error([]) 33.79/17.08 new_show9(ww21) -> error([]) 33.79/17.08 new_show8(ww21) -> error([]) 33.79/17.08 new_show10(ww21, ca, cb) -> error([]) 33.79/17.08 new_show14(ww21, cc) -> error([]) 33.79/17.08 new_show4(ww21) -> error([]) 33.79/17.08 new_show7(ww21, bd, be) -> error([]) 33.79/17.08 new_show6(ww21) -> error([]) 33.79/17.08 new_show0(ww21) -> error([]) 33.79/17.08 33.79/17.08 The set Q consists of the following terms: 33.79/17.08 33.79/17.08 new_primShowInt0(Pos(Succ(x0))) 33.79/17.08 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.08 new_primDivNatS4(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_IOError) 33.79/17.08 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.08 new_showsPrec(x0, x1, ty_Bool) 33.79/17.08 new_primShowInt0(Neg(x0)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, ty_@0) 33.79/17.08 new_primModNatS2(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_show10(x0, x1, x2) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.08 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS2(Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.08 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primShowInt0(Pos(Zero)) 33.79/17.08 new_show7(x0, x1, x2) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.08 new_primDivNatS02(x0, x1) 33.79/17.08 new_show1(x0) 33.79/17.08 new_psPs0(:(x0, x1), x2) 33.79/17.08 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.08 new_primModNatS02(x0, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.08 new_showsPrec(x0, x1, ty_Float) 33.79/17.08 new_show14(x0, x1) 33.79/17.08 new_div(x0, x1) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_show12(x0) 33.79/17.08 new_show8(x0) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_primModNatS3(Zero, Zero, x0) 33.79/17.08 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.08 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.08 new_primDivNatS2(Zero, Zero, x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.08 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_show6(x0) 33.79/17.08 new_show15(x0, x1, x2, x3) 33.79/17.08 new_primDivNatS3(x0) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.08 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.08 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(x0)) 33.79/17.08 new_show5(x0) 33.79/17.08 new_showsPrec(x0, x1, ty_Integer) 33.79/17.08 new_show(x0, x1) 33.79/17.08 new_show2(x0, x1) 33.79/17.08 new_primModNatS4(x0) 33.79/17.08 new_primIntToChar(x0, x1) 33.79/17.08 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.08 new_showsPrec(x0, x1, ty_Int) 33.79/17.08 new_show9(x0) 33.79/17.08 new_show11(x0) 33.79/17.08 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.08 new_show4(x0) 33.79/17.08 new_psPs0([], x0) 33.79/17.08 new_primDivNatS4(Zero, Zero) 33.79/17.08 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.08 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.08 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show0(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show13(x0) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_show3(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.08 new_showsPrec(x0, x1, ty_Char) 33.79/17.08 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_Double) 33.79/17.08 33.79/17.08 We have to consider all minimal (P,Q,R)-chains. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (120) DependencyGraphProof (EQUIVALENT) 33.79/17.08 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (121) 33.79/17.08 Obligation: 33.79/17.08 Q DP problem: 33.79/17.08 The TRS P consists of the following rules: 33.79/17.08 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 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) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.08 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) 33.79/17.08 33.79/17.08 The TRS R consists of the following rules: 33.79/17.08 33.79/17.08 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.08 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.08 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.08 new_psPs0([], ww60) -> ww60 33.79/17.08 new_show11(ww21) -> error([]) 33.79/17.08 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.08 new_show2(ww21, bb) -> error([]) 33.79/17.08 new_show12(ww21) -> error([]) 33.79/17.08 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.08 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_show1(ww21) -> error([]) 33.79/17.08 new_show5(ww21) -> error([]) 33.79/17.08 new_show3(ww21) -> error([]) 33.79/17.08 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.08 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))) 33.79/17.08 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)))))))))), [])) 33.79/17.08 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.08 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.08 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.08 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.08 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.08 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.08 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.08 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.08 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.08 new_primModNatS4(ww143) -> Zero 33.79/17.08 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.08 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.08 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.08 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.08 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS3(ww147) -> Zero 33.79/17.08 new_show(ww21, bf) -> error([]) 33.79/17.08 new_show9(ww21) -> error([]) 33.79/17.08 new_show8(ww21) -> error([]) 33.79/17.08 new_show10(ww21, ca, cb) -> error([]) 33.79/17.08 new_show14(ww21, cc) -> error([]) 33.79/17.08 new_show4(ww21) -> error([]) 33.79/17.08 new_show7(ww21, bd, be) -> error([]) 33.79/17.08 new_show6(ww21) -> error([]) 33.79/17.08 new_show0(ww21) -> error([]) 33.79/17.08 33.79/17.08 The set Q consists of the following terms: 33.79/17.08 33.79/17.08 new_primShowInt0(Pos(Succ(x0))) 33.79/17.08 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.08 new_primDivNatS4(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_IOError) 33.79/17.08 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.08 new_showsPrec(x0, x1, ty_Bool) 33.79/17.08 new_primShowInt0(Neg(x0)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, ty_@0) 33.79/17.08 new_primModNatS2(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_show10(x0, x1, x2) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.08 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS2(Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.08 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primShowInt0(Pos(Zero)) 33.79/17.08 new_show7(x0, x1, x2) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.08 new_primDivNatS02(x0, x1) 33.79/17.08 new_show1(x0) 33.79/17.08 new_psPs0(:(x0, x1), x2) 33.79/17.08 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.08 new_primModNatS02(x0, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.08 new_showsPrec(x0, x1, ty_Float) 33.79/17.08 new_show14(x0, x1) 33.79/17.08 new_div(x0, x1) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_show12(x0) 33.79/17.08 new_show8(x0) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_primModNatS3(Zero, Zero, x0) 33.79/17.08 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.08 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.08 new_primDivNatS2(Zero, Zero, x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.08 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_show6(x0) 33.79/17.08 new_show15(x0, x1, x2, x3) 33.79/17.08 new_primDivNatS3(x0) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.08 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.08 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(x0)) 33.79/17.08 new_show5(x0) 33.79/17.08 new_showsPrec(x0, x1, ty_Integer) 33.79/17.08 new_show(x0, x1) 33.79/17.08 new_show2(x0, x1) 33.79/17.08 new_primModNatS4(x0) 33.79/17.08 new_primIntToChar(x0, x1) 33.79/17.08 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.08 new_showsPrec(x0, x1, ty_Int) 33.79/17.08 new_show9(x0) 33.79/17.08 new_show11(x0) 33.79/17.08 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.08 new_show4(x0) 33.79/17.08 new_psPs0([], x0) 33.79/17.08 new_primDivNatS4(Zero, Zero) 33.79/17.08 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.08 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.08 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show0(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show13(x0) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_show3(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.08 new_showsPrec(x0, x1, ty_Char) 33.79/17.08 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_Double) 33.79/17.08 33.79/17.08 We have to consider all minimal (P,Q,R)-chains. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (122) TransformationProof (EQUIVALENT) 33.79/17.08 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.08 33.79/17.08 (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)) 33.79/17.08 33.79/17.08 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (123) 33.79/17.08 Obligation: 33.79/17.08 Q DP problem: 33.79/17.08 The TRS P consists of the following rules: 33.79/17.08 33.79/17.08 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 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) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.08 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) 33.79/17.08 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) 33.79/17.08 33.79/17.08 The TRS R consists of the following rules: 33.79/17.08 33.79/17.08 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.08 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.08 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.08 new_psPs0([], ww60) -> ww60 33.79/17.08 new_show11(ww21) -> error([]) 33.79/17.08 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.08 new_show2(ww21, bb) -> error([]) 33.79/17.08 new_show12(ww21) -> error([]) 33.79/17.08 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.08 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_show1(ww21) -> error([]) 33.79/17.08 new_show5(ww21) -> error([]) 33.79/17.08 new_show3(ww21) -> error([]) 33.79/17.08 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.08 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))) 33.79/17.08 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)))))))))), [])) 33.79/17.08 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.08 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.08 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.08 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.08 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.08 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.08 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.08 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.08 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.08 new_primModNatS4(ww143) -> Zero 33.79/17.08 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.08 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.08 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.08 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.08 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS3(ww147) -> Zero 33.79/17.08 new_show(ww21, bf) -> error([]) 33.79/17.08 new_show9(ww21) -> error([]) 33.79/17.08 new_show8(ww21) -> error([]) 33.79/17.08 new_show10(ww21, ca, cb) -> error([]) 33.79/17.08 new_show14(ww21, cc) -> error([]) 33.79/17.08 new_show4(ww21) -> error([]) 33.79/17.08 new_show7(ww21, bd, be) -> error([]) 33.79/17.08 new_show6(ww21) -> error([]) 33.79/17.08 new_show0(ww21) -> error([]) 33.79/17.08 33.79/17.08 The set Q consists of the following terms: 33.79/17.08 33.79/17.08 new_primShowInt0(Pos(Succ(x0))) 33.79/17.08 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.08 new_primDivNatS4(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_IOError) 33.79/17.08 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.08 new_showsPrec(x0, x1, ty_Bool) 33.79/17.08 new_primShowInt0(Neg(x0)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, ty_@0) 33.79/17.08 new_primModNatS2(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_show10(x0, x1, x2) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.08 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS2(Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.08 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primShowInt0(Pos(Zero)) 33.79/17.08 new_show7(x0, x1, x2) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.08 new_primDivNatS02(x0, x1) 33.79/17.08 new_show1(x0) 33.79/17.08 new_psPs0(:(x0, x1), x2) 33.79/17.08 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.08 new_primModNatS02(x0, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.08 new_showsPrec(x0, x1, ty_Float) 33.79/17.08 new_show14(x0, x1) 33.79/17.08 new_div(x0, x1) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_show12(x0) 33.79/17.08 new_show8(x0) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_primModNatS3(Zero, Zero, x0) 33.79/17.08 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.08 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.08 new_primDivNatS2(Zero, Zero, x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.08 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_show6(x0) 33.79/17.08 new_show15(x0, x1, x2, x3) 33.79/17.08 new_primDivNatS3(x0) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.08 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.08 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(x0)) 33.79/17.08 new_show5(x0) 33.79/17.08 new_showsPrec(x0, x1, ty_Integer) 33.79/17.08 new_show(x0, x1) 33.79/17.08 new_show2(x0, x1) 33.79/17.08 new_primModNatS4(x0) 33.79/17.08 new_primIntToChar(x0, x1) 33.79/17.08 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.08 new_showsPrec(x0, x1, ty_Int) 33.79/17.08 new_show9(x0) 33.79/17.08 new_show11(x0) 33.79/17.08 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.08 new_show4(x0) 33.79/17.08 new_psPs0([], x0) 33.79/17.08 new_primDivNatS4(Zero, Zero) 33.79/17.08 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.08 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.08 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show0(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show13(x0) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_show3(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.08 new_showsPrec(x0, x1, ty_Char) 33.79/17.08 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_Double) 33.79/17.08 33.79/17.08 We have to consider all minimal (P,Q,R)-chains. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (124) DependencyGraphProof (EQUIVALENT) 33.79/17.08 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (125) 33.79/17.08 Obligation: 33.79/17.08 Q DP problem: 33.79/17.08 The TRS P consists of the following rules: 33.79/17.08 33.79/17.08 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) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.08 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) 33.79/17.08 33.79/17.08 The TRS R consists of the following rules: 33.79/17.08 33.79/17.08 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.08 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.08 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.08 new_psPs0([], ww60) -> ww60 33.79/17.08 new_show11(ww21) -> error([]) 33.79/17.08 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.08 new_show2(ww21, bb) -> error([]) 33.79/17.08 new_show12(ww21) -> error([]) 33.79/17.08 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.08 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_show1(ww21) -> error([]) 33.79/17.08 new_show5(ww21) -> error([]) 33.79/17.08 new_show3(ww21) -> error([]) 33.79/17.08 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.08 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))) 33.79/17.08 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)))))))))), [])) 33.79/17.08 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.08 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.08 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.08 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.08 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.08 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.08 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.08 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.08 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.08 new_primModNatS4(ww143) -> Zero 33.79/17.08 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.08 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.08 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.08 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.08 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS3(ww147) -> Zero 33.79/17.08 new_show(ww21, bf) -> error([]) 33.79/17.08 new_show9(ww21) -> error([]) 33.79/17.08 new_show8(ww21) -> error([]) 33.79/17.08 new_show10(ww21, ca, cb) -> error([]) 33.79/17.08 new_show14(ww21, cc) -> error([]) 33.79/17.08 new_show4(ww21) -> error([]) 33.79/17.08 new_show7(ww21, bd, be) -> error([]) 33.79/17.08 new_show6(ww21) -> error([]) 33.79/17.08 new_show0(ww21) -> error([]) 33.79/17.08 33.79/17.08 The set Q consists of the following terms: 33.79/17.08 33.79/17.08 new_primShowInt0(Pos(Succ(x0))) 33.79/17.08 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.08 new_primDivNatS4(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_IOError) 33.79/17.08 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.08 new_showsPrec(x0, x1, ty_Bool) 33.79/17.08 new_primShowInt0(Neg(x0)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, ty_@0) 33.79/17.08 new_primModNatS2(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_show10(x0, x1, x2) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.08 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS2(Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.08 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primShowInt0(Pos(Zero)) 33.79/17.08 new_show7(x0, x1, x2) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.08 new_primDivNatS02(x0, x1) 33.79/17.08 new_show1(x0) 33.79/17.08 new_psPs0(:(x0, x1), x2) 33.79/17.08 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.08 new_primModNatS02(x0, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.08 new_showsPrec(x0, x1, ty_Float) 33.79/17.08 new_show14(x0, x1) 33.79/17.08 new_div(x0, x1) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_show12(x0) 33.79/17.08 new_show8(x0) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_primModNatS3(Zero, Zero, x0) 33.79/17.08 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.08 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.08 new_primDivNatS2(Zero, Zero, x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.08 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_show6(x0) 33.79/17.08 new_show15(x0, x1, x2, x3) 33.79/17.08 new_primDivNatS3(x0) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.08 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.08 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(x0)) 33.79/17.08 new_show5(x0) 33.79/17.08 new_showsPrec(x0, x1, ty_Integer) 33.79/17.08 new_show(x0, x1) 33.79/17.08 new_show2(x0, x1) 33.79/17.08 new_primModNatS4(x0) 33.79/17.08 new_primIntToChar(x0, x1) 33.79/17.08 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.08 new_showsPrec(x0, x1, ty_Int) 33.79/17.08 new_show9(x0) 33.79/17.08 new_show11(x0) 33.79/17.08 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.08 new_show4(x0) 33.79/17.08 new_psPs0([], x0) 33.79/17.08 new_primDivNatS4(Zero, Zero) 33.79/17.08 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.08 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.08 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show0(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show13(x0) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_show3(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.08 new_showsPrec(x0, x1, ty_Char) 33.79/17.08 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_Double) 33.79/17.08 33.79/17.08 We have to consider all minimal (P,Q,R)-chains. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (126) TransformationProof (EQUIVALENT) 33.79/17.08 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.08 33.79/17.08 (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)) 33.79/17.08 33.79/17.08 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (127) 33.79/17.08 Obligation: 33.79/17.08 Q DP problem: 33.79/17.08 The TRS P consists of the following rules: 33.79/17.08 33.79/17.08 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) 33.79/17.08 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.08 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) 33.79/17.08 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) 33.79/17.08 33.79/17.08 The TRS R consists of the following rules: 33.79/17.08 33.79/17.08 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.08 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.08 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.08 new_psPs0([], ww60) -> ww60 33.79/17.08 new_show11(ww21) -> error([]) 33.79/17.08 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.08 new_show2(ww21, bb) -> error([]) 33.79/17.08 new_show12(ww21) -> error([]) 33.79/17.08 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.08 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_show1(ww21) -> error([]) 33.79/17.08 new_show5(ww21) -> error([]) 33.79/17.08 new_show3(ww21) -> error([]) 33.79/17.08 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.08 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))) 33.79/17.08 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)))))))))), [])) 33.79/17.08 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.08 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.08 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.08 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.08 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.08 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.08 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.08 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.08 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.08 new_primModNatS4(ww143) -> Zero 33.79/17.08 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.08 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.08 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.08 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.08 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS3(ww147) -> Zero 33.79/17.08 new_show(ww21, bf) -> error([]) 33.79/17.08 new_show9(ww21) -> error([]) 33.79/17.08 new_show8(ww21) -> error([]) 33.79/17.08 new_show10(ww21, ca, cb) -> error([]) 33.79/17.08 new_show14(ww21, cc) -> error([]) 33.79/17.08 new_show4(ww21) -> error([]) 33.79/17.08 new_show7(ww21, bd, be) -> error([]) 33.79/17.08 new_show6(ww21) -> error([]) 33.79/17.08 new_show0(ww21) -> error([]) 33.79/17.08 33.79/17.08 The set Q consists of the following terms: 33.79/17.08 33.79/17.08 new_primShowInt0(Pos(Succ(x0))) 33.79/17.08 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.08 new_primDivNatS4(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_IOError) 33.79/17.08 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.08 new_showsPrec(x0, x1, ty_Bool) 33.79/17.08 new_primShowInt0(Neg(x0)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, ty_@0) 33.79/17.08 new_primModNatS2(Succ(x0), Zero) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_show10(x0, x1, x2) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.08 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS2(Zero, Zero) 33.79/17.08 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.08 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primShowInt0(Pos(Zero)) 33.79/17.08 new_show7(x0, x1, x2) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.08 new_primDivNatS02(x0, x1) 33.79/17.08 new_show1(x0) 33.79/17.08 new_psPs0(:(x0, x1), x2) 33.79/17.08 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.08 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.08 new_primModNatS02(x0, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.08 new_showsPrec(x0, x1, ty_Float) 33.79/17.08 new_show14(x0, x1) 33.79/17.08 new_div(x0, x1) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_show12(x0) 33.79/17.08 new_show8(x0) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.08 new_primModNatS3(Zero, Zero, x0) 33.79/17.08 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.08 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.08 new_primDivNatS2(Zero, Zero, x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.08 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_show6(x0) 33.79/17.08 new_show15(x0, x1, x2, x3) 33.79/17.08 new_primDivNatS3(x0) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.08 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.08 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.08 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.08 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(x0)) 33.79/17.08 new_show5(x0) 33.79/17.08 new_showsPrec(x0, x1, ty_Integer) 33.79/17.08 new_show(x0, x1) 33.79/17.08 new_show2(x0, x1) 33.79/17.08 new_primModNatS4(x0) 33.79/17.08 new_primIntToChar(x0, x1) 33.79/17.08 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.08 new_showsPrec(x0, x1, ty_Int) 33.79/17.08 new_show9(x0) 33.79/17.08 new_show11(x0) 33.79/17.08 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.08 new_show4(x0) 33.79/17.08 new_psPs0([], x0) 33.79/17.08 new_primDivNatS4(Zero, Zero) 33.79/17.08 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.08 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.08 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show0(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.08 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_show13(x0) 33.79/17.08 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.08 new_show3(x0) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.08 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.08 new_showsPrec(x0, x1, ty_Char) 33.79/17.08 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.08 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.08 new_showsPrec(x0, x1, ty_Double) 33.79/17.08 33.79/17.08 We have to consider all minimal (P,Q,R)-chains. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (128) DependencyGraphProof (EQUIVALENT) 33.79/17.08 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.08 ---------------------------------------- 33.79/17.08 33.79/17.08 (129) 33.79/17.08 Obligation: 33.79/17.08 Q DP problem: 33.79/17.08 The TRS P consists of the following rules: 33.79/17.08 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 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) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.08 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.08 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) 33.79/17.08 33.79/17.08 The TRS R consists of the following rules: 33.79/17.08 33.79/17.08 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.08 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.08 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.08 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.08 new_psPs0([], ww60) -> ww60 33.79/17.08 new_show11(ww21) -> error([]) 33.79/17.08 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.08 new_show2(ww21, bb) -> error([]) 33.79/17.08 new_show12(ww21) -> error([]) 33.79/17.08 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.08 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.08 new_show1(ww21) -> error([]) 33.79/17.08 new_show5(ww21) -> error([]) 33.79/17.08 new_show3(ww21) -> error([]) 33.79/17.08 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.08 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))) 33.79/17.08 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)))))))))), [])) 33.79/17.08 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.08 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.08 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.08 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.08 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.08 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.08 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.08 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.08 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.08 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.08 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.08 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.08 new_primModNatS4(ww143) -> Zero 33.79/17.08 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.08 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.08 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.08 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.08 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.08 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.08 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.08 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.08 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.08 new_primDivNatS3(ww147) -> Zero 33.79/17.08 new_show(ww21, bf) -> error([]) 33.79/17.08 new_show9(ww21) -> error([]) 33.79/17.08 new_show8(ww21) -> error([]) 33.79/17.08 new_show10(ww21, ca, cb) -> error([]) 33.79/17.08 new_show14(ww21, cc) -> error([]) 33.79/17.08 new_show4(ww21) -> error([]) 33.79/17.08 new_show7(ww21, bd, be) -> error([]) 33.79/17.08 new_show6(ww21) -> error([]) 33.79/17.08 new_show0(ww21) -> error([]) 33.79/17.08 33.79/17.08 The set Q consists of the following terms: 33.79/17.08 33.79/17.08 new_primShowInt0(Pos(Succ(x0))) 33.79/17.08 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.08 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.08 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.09 new_primDivNatS4(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_IOError) 33.79/17.09 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.09 new_showsPrec(x0, x1, ty_Bool) 33.79/17.09 new_primShowInt0(Neg(x0)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, ty_@0) 33.79/17.09 new_primModNatS2(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_show10(x0, x1, x2) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.09 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS2(Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.09 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primShowInt0(Pos(Zero)) 33.79/17.09 new_show7(x0, x1, x2) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.09 new_primDivNatS02(x0, x1) 33.79/17.09 new_show1(x0) 33.79/17.09 new_psPs0(:(x0, x1), x2) 33.79/17.09 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.09 new_primModNatS02(x0, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.09 new_showsPrec(x0, x1, ty_Float) 33.79/17.09 new_show14(x0, x1) 33.79/17.09 new_div(x0, x1) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_show12(x0) 33.79/17.09 new_show8(x0) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_primModNatS3(Zero, Zero, x0) 33.79/17.09 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.09 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.09 new_primDivNatS2(Zero, Zero, x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.09 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_show6(x0) 33.79/17.09 new_show15(x0, x1, x2, x3) 33.79/17.09 new_primDivNatS3(x0) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.09 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.09 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(x0)) 33.79/17.09 new_show5(x0) 33.79/17.09 new_showsPrec(x0, x1, ty_Integer) 33.79/17.09 new_show(x0, x1) 33.79/17.09 new_show2(x0, x1) 33.79/17.09 new_primModNatS4(x0) 33.79/17.09 new_primIntToChar(x0, x1) 33.79/17.09 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.09 new_showsPrec(x0, x1, ty_Int) 33.79/17.09 new_show9(x0) 33.79/17.09 new_show11(x0) 33.79/17.09 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.09 new_show4(x0) 33.79/17.09 new_psPs0([], x0) 33.79/17.09 new_primDivNatS4(Zero, Zero) 33.79/17.09 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.09 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.09 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show0(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show13(x0) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_show3(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.09 new_showsPrec(x0, x1, ty_Char) 33.79/17.09 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_Double) 33.79/17.09 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (130) TransformationProof (EQUIVALENT) 33.79/17.09 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.09 33.79/17.09 (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)) 33.79/17.09 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (131) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 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) 33.79/17.09 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.09 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.09 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.09 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) 33.79/17.09 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) 33.79/17.09 33.79/17.09 The TRS R consists of the following rules: 33.79/17.09 33.79/17.09 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.09 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.09 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.09 new_psPs0([], ww60) -> ww60 33.79/17.09 new_show11(ww21) -> error([]) 33.79/17.09 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.09 new_show2(ww21, bb) -> error([]) 33.79/17.09 new_show12(ww21) -> error([]) 33.79/17.09 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.09 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_show1(ww21) -> error([]) 33.79/17.09 new_show5(ww21) -> error([]) 33.79/17.09 new_show3(ww21) -> error([]) 33.79/17.09 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.09 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))) 33.79/17.09 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)))))))))), [])) 33.79/17.09 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.09 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.09 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.09 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.09 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.09 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.09 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.09 new_primModNatS4(ww143) -> Zero 33.79/17.09 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.09 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.09 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.09 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.09 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS3(ww147) -> Zero 33.79/17.09 new_show(ww21, bf) -> error([]) 33.79/17.09 new_show9(ww21) -> error([]) 33.79/17.09 new_show8(ww21) -> error([]) 33.79/17.09 new_show10(ww21, ca, cb) -> error([]) 33.79/17.09 new_show14(ww21, cc) -> error([]) 33.79/17.09 new_show4(ww21) -> error([]) 33.79/17.09 new_show7(ww21, bd, be) -> error([]) 33.79/17.09 new_show6(ww21) -> error([]) 33.79/17.09 new_show0(ww21) -> error([]) 33.79/17.09 33.79/17.09 The set Q consists of the following terms: 33.79/17.09 33.79/17.09 new_primShowInt0(Pos(Succ(x0))) 33.79/17.09 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.09 new_primDivNatS4(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_IOError) 33.79/17.09 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.09 new_showsPrec(x0, x1, ty_Bool) 33.79/17.09 new_primShowInt0(Neg(x0)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, ty_@0) 33.79/17.09 new_primModNatS2(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_show10(x0, x1, x2) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.09 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS2(Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.09 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primShowInt0(Pos(Zero)) 33.79/17.09 new_show7(x0, x1, x2) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.09 new_primDivNatS02(x0, x1) 33.79/17.09 new_show1(x0) 33.79/17.09 new_psPs0(:(x0, x1), x2) 33.79/17.09 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.09 new_primModNatS02(x0, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.09 new_showsPrec(x0, x1, ty_Float) 33.79/17.09 new_show14(x0, x1) 33.79/17.09 new_div(x0, x1) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_show12(x0) 33.79/17.09 new_show8(x0) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_primModNatS3(Zero, Zero, x0) 33.79/17.09 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.09 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.09 new_primDivNatS2(Zero, Zero, x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.09 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_show6(x0) 33.79/17.09 new_show15(x0, x1, x2, x3) 33.79/17.09 new_primDivNatS3(x0) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.09 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.09 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(x0)) 33.79/17.09 new_show5(x0) 33.79/17.09 new_showsPrec(x0, x1, ty_Integer) 33.79/17.09 new_show(x0, x1) 33.79/17.09 new_show2(x0, x1) 33.79/17.09 new_primModNatS4(x0) 33.79/17.09 new_primIntToChar(x0, x1) 33.79/17.09 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.09 new_showsPrec(x0, x1, ty_Int) 33.79/17.09 new_show9(x0) 33.79/17.09 new_show11(x0) 33.79/17.09 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.09 new_show4(x0) 33.79/17.09 new_psPs0([], x0) 33.79/17.09 new_primDivNatS4(Zero, Zero) 33.79/17.09 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.09 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.09 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show0(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show13(x0) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_show3(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.09 new_showsPrec(x0, x1, ty_Char) 33.79/17.09 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_Double) 33.79/17.09 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (132) DependencyGraphProof (EQUIVALENT) 33.79/17.09 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (133) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 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) 33.79/17.09 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.09 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.09 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.09 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) 33.79/17.09 33.79/17.09 The TRS R consists of the following rules: 33.79/17.09 33.79/17.09 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.09 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.09 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.09 new_psPs0([], ww60) -> ww60 33.79/17.09 new_show11(ww21) -> error([]) 33.79/17.09 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.09 new_show2(ww21, bb) -> error([]) 33.79/17.09 new_show12(ww21) -> error([]) 33.79/17.09 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.09 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_show1(ww21) -> error([]) 33.79/17.09 new_show5(ww21) -> error([]) 33.79/17.09 new_show3(ww21) -> error([]) 33.79/17.09 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.09 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))) 33.79/17.09 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)))))))))), [])) 33.79/17.09 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.09 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.09 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.09 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.09 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.09 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.09 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.09 new_primModNatS4(ww143) -> Zero 33.79/17.09 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.09 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.09 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.09 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.09 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS3(ww147) -> Zero 33.79/17.09 new_show(ww21, bf) -> error([]) 33.79/17.09 new_show9(ww21) -> error([]) 33.79/17.09 new_show8(ww21) -> error([]) 33.79/17.09 new_show10(ww21, ca, cb) -> error([]) 33.79/17.09 new_show14(ww21, cc) -> error([]) 33.79/17.09 new_show4(ww21) -> error([]) 33.79/17.09 new_show7(ww21, bd, be) -> error([]) 33.79/17.09 new_show6(ww21) -> error([]) 33.79/17.09 new_show0(ww21) -> error([]) 33.79/17.09 33.79/17.09 The set Q consists of the following terms: 33.79/17.09 33.79/17.09 new_primShowInt0(Pos(Succ(x0))) 33.79/17.09 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.09 new_primDivNatS4(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_IOError) 33.79/17.09 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.09 new_showsPrec(x0, x1, ty_Bool) 33.79/17.09 new_primShowInt0(Neg(x0)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, ty_@0) 33.79/17.09 new_primModNatS2(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_show10(x0, x1, x2) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.09 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS2(Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.09 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primShowInt0(Pos(Zero)) 33.79/17.09 new_show7(x0, x1, x2) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.09 new_primDivNatS02(x0, x1) 33.79/17.09 new_show1(x0) 33.79/17.09 new_psPs0(:(x0, x1), x2) 33.79/17.09 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.09 new_primModNatS02(x0, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.09 new_showsPrec(x0, x1, ty_Float) 33.79/17.09 new_show14(x0, x1) 33.79/17.09 new_div(x0, x1) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_show12(x0) 33.79/17.09 new_show8(x0) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_primModNatS3(Zero, Zero, x0) 33.79/17.09 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.09 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.09 new_primDivNatS2(Zero, Zero, x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.09 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_show6(x0) 33.79/17.09 new_show15(x0, x1, x2, x3) 33.79/17.09 new_primDivNatS3(x0) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.09 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.09 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(x0)) 33.79/17.09 new_show5(x0) 33.79/17.09 new_showsPrec(x0, x1, ty_Integer) 33.79/17.09 new_show(x0, x1) 33.79/17.09 new_show2(x0, x1) 33.79/17.09 new_primModNatS4(x0) 33.79/17.09 new_primIntToChar(x0, x1) 33.79/17.09 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.09 new_showsPrec(x0, x1, ty_Int) 33.79/17.09 new_show9(x0) 33.79/17.09 new_show11(x0) 33.79/17.09 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.09 new_show4(x0) 33.79/17.09 new_psPs0([], x0) 33.79/17.09 new_primDivNatS4(Zero, Zero) 33.79/17.09 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.09 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.09 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show0(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show13(x0) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_show3(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.09 new_showsPrec(x0, x1, ty_Char) 33.79/17.09 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_Double) 33.79/17.09 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (134) TransformationProof (EQUIVALENT) 33.79/17.09 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.09 33.79/17.09 (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)) 33.79/17.09 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (135) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 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) 33.79/17.09 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.09 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.09 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) 33.79/17.09 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) 33.79/17.09 33.79/17.09 The TRS R consists of the following rules: 33.79/17.09 33.79/17.09 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.09 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.09 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.09 new_psPs0([], ww60) -> ww60 33.79/17.09 new_show11(ww21) -> error([]) 33.79/17.09 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.09 new_show2(ww21, bb) -> error([]) 33.79/17.09 new_show12(ww21) -> error([]) 33.79/17.09 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.09 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_show1(ww21) -> error([]) 33.79/17.09 new_show5(ww21) -> error([]) 33.79/17.09 new_show3(ww21) -> error([]) 33.79/17.09 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.09 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))) 33.79/17.09 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)))))))))), [])) 33.79/17.09 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.09 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.09 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.09 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.09 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.09 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.09 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.09 new_primModNatS4(ww143) -> Zero 33.79/17.09 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.09 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.09 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.09 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.09 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS3(ww147) -> Zero 33.79/17.09 new_show(ww21, bf) -> error([]) 33.79/17.09 new_show9(ww21) -> error([]) 33.79/17.09 new_show8(ww21) -> error([]) 33.79/17.09 new_show10(ww21, ca, cb) -> error([]) 33.79/17.09 new_show14(ww21, cc) -> error([]) 33.79/17.09 new_show4(ww21) -> error([]) 33.79/17.09 new_show7(ww21, bd, be) -> error([]) 33.79/17.09 new_show6(ww21) -> error([]) 33.79/17.09 new_show0(ww21) -> error([]) 33.79/17.09 33.79/17.09 The set Q consists of the following terms: 33.79/17.09 33.79/17.09 new_primShowInt0(Pos(Succ(x0))) 33.79/17.09 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.09 new_primDivNatS4(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_IOError) 33.79/17.09 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.09 new_showsPrec(x0, x1, ty_Bool) 33.79/17.09 new_primShowInt0(Neg(x0)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, ty_@0) 33.79/17.09 new_primModNatS2(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_show10(x0, x1, x2) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.09 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS2(Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.09 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primShowInt0(Pos(Zero)) 33.79/17.09 new_show7(x0, x1, x2) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.09 new_primDivNatS02(x0, x1) 33.79/17.09 new_show1(x0) 33.79/17.09 new_psPs0(:(x0, x1), x2) 33.79/17.09 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.09 new_primModNatS02(x0, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.09 new_showsPrec(x0, x1, ty_Float) 33.79/17.09 new_show14(x0, x1) 33.79/17.09 new_div(x0, x1) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_show12(x0) 33.79/17.09 new_show8(x0) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_primModNatS3(Zero, Zero, x0) 33.79/17.09 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.09 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.09 new_primDivNatS2(Zero, Zero, x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.09 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_show6(x0) 33.79/17.09 new_show15(x0, x1, x2, x3) 33.79/17.09 new_primDivNatS3(x0) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.09 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.09 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(x0)) 33.79/17.09 new_show5(x0) 33.79/17.09 new_showsPrec(x0, x1, ty_Integer) 33.79/17.09 new_show(x0, x1) 33.79/17.09 new_show2(x0, x1) 33.79/17.09 new_primModNatS4(x0) 33.79/17.09 new_primIntToChar(x0, x1) 33.79/17.09 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.09 new_showsPrec(x0, x1, ty_Int) 33.79/17.09 new_show9(x0) 33.79/17.09 new_show11(x0) 33.79/17.09 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.09 new_show4(x0) 33.79/17.09 new_psPs0([], x0) 33.79/17.09 new_primDivNatS4(Zero, Zero) 33.79/17.09 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.09 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.09 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show0(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show13(x0) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_show3(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.09 new_showsPrec(x0, x1, ty_Char) 33.79/17.09 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_Double) 33.79/17.09 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (136) DependencyGraphProof (EQUIVALENT) 33.79/17.09 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (137) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) 33.79/17.09 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 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) 33.79/17.09 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.09 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) 33.79/17.09 33.79/17.09 The TRS R consists of the following rules: 33.79/17.09 33.79/17.09 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.09 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.09 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.09 new_psPs0([], ww60) -> ww60 33.79/17.09 new_show11(ww21) -> error([]) 33.79/17.09 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.09 new_show2(ww21, bb) -> error([]) 33.79/17.09 new_show12(ww21) -> error([]) 33.79/17.09 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.09 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_show1(ww21) -> error([]) 33.79/17.09 new_show5(ww21) -> error([]) 33.79/17.09 new_show3(ww21) -> error([]) 33.79/17.09 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.09 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))) 33.79/17.09 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)))))))))), [])) 33.79/17.09 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.09 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.09 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.09 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.09 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.09 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.09 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.09 new_primModNatS4(ww143) -> Zero 33.79/17.09 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.09 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.09 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.09 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.09 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS3(ww147) -> Zero 33.79/17.09 new_show(ww21, bf) -> error([]) 33.79/17.09 new_show9(ww21) -> error([]) 33.79/17.09 new_show8(ww21) -> error([]) 33.79/17.09 new_show10(ww21, ca, cb) -> error([]) 33.79/17.09 new_show14(ww21, cc) -> error([]) 33.79/17.09 new_show4(ww21) -> error([]) 33.79/17.09 new_show7(ww21, bd, be) -> error([]) 33.79/17.09 new_show6(ww21) -> error([]) 33.79/17.09 new_show0(ww21) -> error([]) 33.79/17.09 33.79/17.09 The set Q consists of the following terms: 33.79/17.09 33.79/17.09 new_primShowInt0(Pos(Succ(x0))) 33.79/17.09 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.09 new_primDivNatS4(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_IOError) 33.79/17.09 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.09 new_showsPrec(x0, x1, ty_Bool) 33.79/17.09 new_primShowInt0(Neg(x0)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, ty_@0) 33.79/17.09 new_primModNatS2(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_show10(x0, x1, x2) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.09 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS2(Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.09 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primShowInt0(Pos(Zero)) 33.79/17.09 new_show7(x0, x1, x2) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.09 new_primDivNatS02(x0, x1) 33.79/17.09 new_show1(x0) 33.79/17.09 new_psPs0(:(x0, x1), x2) 33.79/17.09 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.09 new_primModNatS02(x0, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.09 new_showsPrec(x0, x1, ty_Float) 33.79/17.09 new_show14(x0, x1) 33.79/17.09 new_div(x0, x1) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_show12(x0) 33.79/17.09 new_show8(x0) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_primModNatS3(Zero, Zero, x0) 33.79/17.09 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.09 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.09 new_primDivNatS2(Zero, Zero, x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.09 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_show6(x0) 33.79/17.09 new_show15(x0, x1, x2, x3) 33.79/17.09 new_primDivNatS3(x0) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.09 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.09 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(x0)) 33.79/17.09 new_show5(x0) 33.79/17.09 new_showsPrec(x0, x1, ty_Integer) 33.79/17.09 new_show(x0, x1) 33.79/17.09 new_show2(x0, x1) 33.79/17.09 new_primModNatS4(x0) 33.79/17.09 new_primIntToChar(x0, x1) 33.79/17.09 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.09 new_showsPrec(x0, x1, ty_Int) 33.79/17.09 new_show9(x0) 33.79/17.09 new_show11(x0) 33.79/17.09 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.09 new_show4(x0) 33.79/17.09 new_psPs0([], x0) 33.79/17.09 new_primDivNatS4(Zero, Zero) 33.79/17.09 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.09 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.09 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show0(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show13(x0) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_show3(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.09 new_showsPrec(x0, x1, ty_Char) 33.79/17.09 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_Double) 33.79/17.09 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (138) TransformationProof (EQUIVALENT) 33.79/17.09 By instantiating [LPAR04] the rule new_showParen00(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_pt1(ww22, ww23, ww24, ww25, ww26, bc) we obtained the following new rules [LPAR04]: 33.79/17.09 33.79/17.09 (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))) 33.79/17.09 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (139) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 new_pt1(ww22, ww23, ww24, :%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 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) 33.79/17.09 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.09 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) 33.79/17.09 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)) 33.79/17.09 33.79/17.09 The TRS R consists of the following rules: 33.79/17.09 33.79/17.09 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.09 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.09 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.09 new_psPs0([], ww60) -> ww60 33.79/17.09 new_show11(ww21) -> error([]) 33.79/17.09 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.09 new_show2(ww21, bb) -> error([]) 33.79/17.09 new_show12(ww21) -> error([]) 33.79/17.09 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.09 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_show1(ww21) -> error([]) 33.79/17.09 new_show5(ww21) -> error([]) 33.79/17.09 new_show3(ww21) -> error([]) 33.79/17.09 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.09 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))) 33.79/17.09 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)))))))))), [])) 33.79/17.09 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.09 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.09 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.09 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.09 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.09 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.09 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.09 new_primModNatS4(ww143) -> Zero 33.79/17.09 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.09 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.09 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.09 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.09 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS3(ww147) -> Zero 33.79/17.09 new_show(ww21, bf) -> error([]) 33.79/17.09 new_show9(ww21) -> error([]) 33.79/17.09 new_show8(ww21) -> error([]) 33.79/17.09 new_show10(ww21, ca, cb) -> error([]) 33.79/17.09 new_show14(ww21, cc) -> error([]) 33.79/17.09 new_show4(ww21) -> error([]) 33.79/17.09 new_show7(ww21, bd, be) -> error([]) 33.79/17.09 new_show6(ww21) -> error([]) 33.79/17.09 new_show0(ww21) -> error([]) 33.79/17.09 33.79/17.09 The set Q consists of the following terms: 33.79/17.09 33.79/17.09 new_primShowInt0(Pos(Succ(x0))) 33.79/17.09 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.09 new_primDivNatS4(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_IOError) 33.79/17.09 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.09 new_showsPrec(x0, x1, ty_Bool) 33.79/17.09 new_primShowInt0(Neg(x0)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, ty_@0) 33.79/17.09 new_primModNatS2(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_show10(x0, x1, x2) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.09 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS2(Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.09 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primShowInt0(Pos(Zero)) 33.79/17.09 new_show7(x0, x1, x2) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.09 new_primDivNatS02(x0, x1) 33.79/17.09 new_show1(x0) 33.79/17.09 new_psPs0(:(x0, x1), x2) 33.79/17.09 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.09 new_primModNatS02(x0, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.09 new_showsPrec(x0, x1, ty_Float) 33.79/17.09 new_show14(x0, x1) 33.79/17.09 new_div(x0, x1) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_show12(x0) 33.79/17.09 new_show8(x0) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_primModNatS3(Zero, Zero, x0) 33.79/17.09 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.09 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.09 new_primDivNatS2(Zero, Zero, x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.09 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_show6(x0) 33.79/17.09 new_show15(x0, x1, x2, x3) 33.79/17.09 new_primDivNatS3(x0) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.09 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.09 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(x0)) 33.79/17.09 new_show5(x0) 33.79/17.09 new_showsPrec(x0, x1, ty_Integer) 33.79/17.09 new_show(x0, x1) 33.79/17.09 new_show2(x0, x1) 33.79/17.09 new_primModNatS4(x0) 33.79/17.09 new_primIntToChar(x0, x1) 33.79/17.09 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.09 new_showsPrec(x0, x1, ty_Int) 33.79/17.09 new_show9(x0) 33.79/17.09 new_show11(x0) 33.79/17.09 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.09 new_show4(x0) 33.79/17.09 new_psPs0([], x0) 33.79/17.09 new_primDivNatS4(Zero, Zero) 33.79/17.09 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.09 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.09 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show0(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show13(x0) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_show3(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.09 new_showsPrec(x0, x1, ty_Char) 33.79/17.09 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_Double) 33.79/17.09 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (140) DependencyGraphProof (EQUIVALENT) 33.79/17.09 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (141) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) 33.79/17.09 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) 33.79/17.09 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) 33.79/17.09 33.79/17.09 The TRS R consists of the following rules: 33.79/17.09 33.79/17.09 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.09 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.09 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.09 new_psPs0([], ww60) -> ww60 33.79/17.09 new_show11(ww21) -> error([]) 33.79/17.09 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.09 new_show2(ww21, bb) -> error([]) 33.79/17.09 new_show12(ww21) -> error([]) 33.79/17.09 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.09 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_show1(ww21) -> error([]) 33.79/17.09 new_show5(ww21) -> error([]) 33.79/17.09 new_show3(ww21) -> error([]) 33.79/17.09 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.09 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))) 33.79/17.09 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)))))))))), [])) 33.79/17.09 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.09 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.09 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.09 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.09 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.09 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.09 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.09 new_primModNatS4(ww143) -> Zero 33.79/17.09 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.09 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.09 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.09 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.09 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS3(ww147) -> Zero 33.79/17.09 new_show(ww21, bf) -> error([]) 33.79/17.09 new_show9(ww21) -> error([]) 33.79/17.09 new_show8(ww21) -> error([]) 33.79/17.09 new_show10(ww21, ca, cb) -> error([]) 33.79/17.09 new_show14(ww21, cc) -> error([]) 33.79/17.09 new_show4(ww21) -> error([]) 33.79/17.09 new_show7(ww21, bd, be) -> error([]) 33.79/17.09 new_show6(ww21) -> error([]) 33.79/17.09 new_show0(ww21) -> error([]) 33.79/17.09 33.79/17.09 The set Q consists of the following terms: 33.79/17.09 33.79/17.09 new_primShowInt0(Pos(Succ(x0))) 33.79/17.09 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.09 new_primDivNatS4(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_IOError) 33.79/17.09 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.09 new_showsPrec(x0, x1, ty_Bool) 33.79/17.09 new_primShowInt0(Neg(x0)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, ty_@0) 33.79/17.09 new_primModNatS2(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_show10(x0, x1, x2) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.09 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS2(Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.09 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primShowInt0(Pos(Zero)) 33.79/17.09 new_show7(x0, x1, x2) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.09 new_primDivNatS02(x0, x1) 33.79/17.09 new_show1(x0) 33.79/17.09 new_psPs0(:(x0, x1), x2) 33.79/17.09 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.09 new_primModNatS02(x0, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.09 new_showsPrec(x0, x1, ty_Float) 33.79/17.09 new_show14(x0, x1) 33.79/17.09 new_div(x0, x1) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_show12(x0) 33.79/17.09 new_show8(x0) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_primModNatS3(Zero, Zero, x0) 33.79/17.09 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.09 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.09 new_primDivNatS2(Zero, Zero, x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.09 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_show6(x0) 33.79/17.09 new_show15(x0, x1, x2, x3) 33.79/17.09 new_primDivNatS3(x0) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.09 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.09 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(x0)) 33.79/17.09 new_show5(x0) 33.79/17.09 new_showsPrec(x0, x1, ty_Integer) 33.79/17.09 new_show(x0, x1) 33.79/17.09 new_show2(x0, x1) 33.79/17.09 new_primModNatS4(x0) 33.79/17.09 new_primIntToChar(x0, x1) 33.79/17.09 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.09 new_showsPrec(x0, x1, ty_Int) 33.79/17.09 new_show9(x0) 33.79/17.09 new_show11(x0) 33.79/17.09 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.09 new_show4(x0) 33.79/17.09 new_psPs0([], x0) 33.79/17.09 new_primDivNatS4(Zero, Zero) 33.79/17.09 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.09 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.09 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show0(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show13(x0) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_show3(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.09 new_showsPrec(x0, x1, ty_Char) 33.79/17.09 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_Double) 33.79/17.09 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (142) TransformationProof (EQUIVALENT) 33.79/17.09 By instantiating [LPAR04] the rule new_showParen00(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg)))), bg, bg) we obtained the following new rules [LPAR04]: 33.79/17.09 33.79/17.09 (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)) 33.79/17.09 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (143) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 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) 33.79/17.09 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) 33.79/17.09 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) 33.79/17.09 33.79/17.09 The TRS R consists of the following rules: 33.79/17.09 33.79/17.09 new_pt2(ww22, ww23, ww24, ww25, ww26, bc) -> new_psPs0(:(Char(Succ(ww22)), :(Char(Succ(ww23)), :(Char(Succ(ww24)), []))), new_showsPrec(ww25, ww26, bc)) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Bool) -> new_psPs0(new_show6(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_@0) -> new_psPs0(new_show3(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_IO, dd)) -> new_psPs0(new_show(ww25, dd), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_Maybe, dg)) -> new_psPs0(new_show14(ww25, dg), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_HugsException) -> new_psPs0(new_show4(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Float) -> new_psPs0(new_show5(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Char) -> new_psPs0(new_show1(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Double) -> new_psPs0(new_show0(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOError) -> new_psPs0(new_show8(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_IOErrorKind) -> new_psPs0(new_show9(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_@2, db), dc)) -> new_psPs0(new_show7(ww25, db, dc), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(ty_Either, de), df)) -> new_psPs0(new_show10(ww25, de, df), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Int) -> new_psPs0(new_show13(ww25), ww26) 33.79/17.09 new_showsPrec(:%(ww250, ww251), ww26, app(ty_Ratio, bh)) -> 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, bh, bh) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Ordering) -> new_psPs0(new_show12(ww25), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(ty_[], da)) -> new_psPs0(new_show2(ww25, da), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, app(app(app(ty_@3, dh), ea), eb)) -> new_psPs0(new_show15(ww25, dh, ea, eb), ww26) 33.79/17.09 new_showsPrec(ww25, ww26, ty_Integer) -> new_psPs0(new_show11(ww25), ww26) 33.79/17.09 new_psPs0(:(ww620, ww621), ww60) -> :(ww620, new_psPs0(ww621, ww60)) 33.79/17.09 new_psPs0([], ww60) -> ww60 33.79/17.09 new_show11(ww21) -> error([]) 33.79/17.09 new_show15(ww21, cd, ce, cf) -> error([]) 33.79/17.09 new_show2(ww21, bb) -> error([]) 33.79/17.09 new_show12(ww21) -> error([]) 33.79/17.09 new_pt3(:%(ww210, ww211), ww22, ww23, ww24, ww25, ww26, app(ty_Ratio, bg), bc) -> 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, bg), bg, bg) 33.79/17.09 new_showParen1(Pos(Zero), ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen02(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_showParen01(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) -> new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, cg, bc) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(app(ty_@3, cd), ce), cf), bc) -> new_psPs0(new_show15(ww21, cd, ce, cf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Double, bc) -> new_psPs0(new_show0(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Bool, bc) -> new_psPs0(new_show6(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww21, bd, be), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_HugsException, bc) -> new_psPs0(new_show4(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_Maybe, cc), bc) -> new_psPs0(new_show14(ww21, cc), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(app(ty_Either, ca), cb), bc) -> new_psPs0(new_show10(ww21, ca, cb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOError, bc) -> new_psPs0(new_show8(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_IOErrorKind, bc) -> new_psPs0(new_show9(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_IO, bf), bc) -> new_psPs0(new_show(ww21, bf), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, app(ty_[], bb), bc) -> new_psPs0(new_show2(ww21, bb), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Int, bc) -> new_psPs0(new_show13(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Integer, bc) -> new_psPs0(new_show11(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_@0, bc) -> new_psPs0(new_show3(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Ordering, bc) -> new_psPs0(new_show12(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Float, bc) -> new_psPs0(new_show5(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_pt3(ww21, ww22, ww23, ww24, ww25, ww26, ty_Char, bc) -> new_psPs0(new_show1(ww21), new_pt2(ww22, ww23, ww24, ww25, ww26, bc)) 33.79/17.09 new_show1(ww21) -> error([]) 33.79/17.09 new_show5(ww21) -> error([]) 33.79/17.09 new_show3(ww21) -> error([]) 33.79/17.09 new_show13(ww21) -> new_primShowInt0(ww21) 33.79/17.09 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))) 33.79/17.09 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)))))))))), [])) 33.79/17.09 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.79/17.09 new_div(ww81, ww82) -> Pos(new_primDivNatS4(ww81, ww82)) 33.79/17.09 new_primIntToChar(ww87, ww88) -> Char(new_primModNatS2(ww87, ww88)) 33.79/17.09 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(ww880)) -> Succ(Zero) 33.79/17.09 new_primModNatS3(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS3(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS3(Succ(ww1410), Zero, ww143) -> new_primModNatS2(ww1410, ww143) 33.79/17.09 new_primModNatS2(Succ(ww870), Zero) -> new_primModNatS3(Succ(ww870), Zero, Zero) 33.79/17.09 new_primModNatS2(Succ(ww870), Succ(ww880)) -> new_primModNatS01(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS02(ww136, ww137) -> new_primModNatS3(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS02(ww136, ww137) 33.79/17.09 new_primModNatS01(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS01(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS3(Zero, Succ(ww1420), ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS3(Zero, Zero, ww143) -> new_primModNatS4(ww143) 33.79/17.09 new_primModNatS01(ww136, ww137, Zero, Succ(ww1390)) -> Succ(Succ(ww136)) 33.79/17.09 new_primModNatS4(ww143) -> Zero 33.79/17.09 new_primDivNatS4(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.79/17.09 new_primDivNatS4(Succ(ww810), Succ(ww820)) -> new_primDivNatS01(ww810, ww820, ww810, ww820) 33.79/17.09 new_primDivNatS4(Zero, Succ(ww820)) -> Zero 33.79/17.09 new_primDivNatS4(Succ(ww810), Zero) -> Succ(new_primDivNatS2(Succ(ww810), Zero, Zero)) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Zero, ww147) -> new_primDivNatS4(ww1450, ww147) 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Succ(ww1340)) -> Zero 33.79/17.09 new_primDivNatS01(ww131, ww132, Succ(ww1330), Succ(ww1340)) -> new_primDivNatS01(ww131, ww132, ww1330, ww1340) 33.79/17.09 new_primDivNatS01(ww131, ww132, Zero, Zero) -> new_primDivNatS02(ww131, ww132) 33.79/17.09 new_primDivNatS02(ww131, ww132) -> Succ(new_primDivNatS2(Succ(ww131), Succ(ww132), Succ(ww132))) 33.79/17.09 new_primDivNatS2(Succ(ww1450), Succ(ww1460), ww147) -> new_primDivNatS2(ww1450, ww1460, ww147) 33.79/17.09 new_primDivNatS2(Zero, Zero, ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS2(Zero, Succ(ww1460), ww147) -> new_primDivNatS3(ww147) 33.79/17.09 new_primDivNatS3(ww147) -> Zero 33.79/17.09 new_show(ww21, bf) -> error([]) 33.79/17.09 new_show9(ww21) -> error([]) 33.79/17.09 new_show8(ww21) -> error([]) 33.79/17.09 new_show10(ww21, ca, cb) -> error([]) 33.79/17.09 new_show14(ww21, cc) -> error([]) 33.79/17.09 new_show4(ww21) -> error([]) 33.79/17.09 new_show7(ww21, bd, be) -> error([]) 33.79/17.09 new_show6(ww21) -> error([]) 33.79/17.09 new_show0(ww21) -> error([]) 33.79/17.09 33.79/17.09 The set Q consists of the following terms: 33.79/17.09 33.79/17.09 new_primShowInt0(Pos(Succ(x0))) 33.79/17.09 new_showParen1(Pos(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showParen1(Neg(Zero), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.79/17.09 new_primDivNatS4(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Zero))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_IOError) 33.79/17.09 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.79/17.09 new_showsPrec(x0, x1, ty_Bool) 33.79/17.09 new_primShowInt0(Neg(x0)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, ty_@0) 33.79/17.09 new_primModNatS2(Succ(x0), Zero) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Zero))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_show10(x0, x1, x2) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, ty_Ordering) 33.79/17.09 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS2(Zero, Zero) 33.79/17.09 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.79/17.09 new_showParen02(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primShowInt0(Pos(Zero)) 33.79/17.09 new_show7(x0, x1, x2) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.79/17.09 new_primDivNatS02(x0, x1) 33.79/17.09 new_show1(x0) 33.79/17.09 new_psPs0(:(x0, x1), x2) 33.79/17.09 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.79/17.09 new_primModNatS3(Zero, Succ(x0), x1) 33.79/17.09 new_primModNatS02(x0, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.79/17.09 new_showsPrec(x0, x1, ty_Float) 33.79/17.09 new_show14(x0, x1) 33.79/17.09 new_div(x0, x1) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_show12(x0) 33.79/17.09 new_show8(x0) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.79/17.09 new_primModNatS3(Zero, Zero, x0) 33.79/17.09 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.79/17.09 new_showParen1(Pos(Succ(Zero)), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.79/17.09 new_primDivNatS2(Zero, Zero, x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Zero)))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.79/17.09 new_showParen1(Neg(Succ(x0)), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_show6(x0) 33.79/17.09 new_show15(x0, x1, x2, x3) 33.79/17.09 new_primDivNatS3(x0) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_HugsException) 33.79/17.09 new_primModNatS3(Succ(x0), Zero, x1) 33.79/17.09 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.79/17.09 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_pt2(x0, x1, x2, x3, x4, x5) 33.79/17.09 new_primDivNatS01(x0, x1, Succ(x2), Zero) 33.79/17.09 new_primModNatS2(Zero, Succ(x0)) 33.79/17.09 new_show5(x0) 33.79/17.09 new_showsPrec(x0, x1, ty_Integer) 33.79/17.09 new_show(x0, x1) 33.79/17.09 new_show2(x0, x1) 33.79/17.09 new_primModNatS4(x0) 33.79/17.09 new_primIntToChar(x0, x1) 33.79/17.09 new_primDivNatS2(Zero, Succ(x0), x1) 33.79/17.09 new_showsPrec(x0, x1, ty_Int) 33.79/17.09 new_show9(x0) 33.79/17.09 new_show11(x0) 33.79/17.09 new_primModNatS2(Succ(x0), Succ(x1)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.79/17.09 new_show4(x0) 33.79/17.09 new_psPs0([], x0) 33.79/17.09 new_primDivNatS4(Zero, Zero) 33.79/17.09 new_primDivNatS4(Zero, Succ(x0)) 33.79/17.09 new_showsPrec(x0, x1, ty_IOErrorKind) 33.79/17.09 new_showParen01(x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show0(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.79/17.09 new_showsPrec(x0, x1, app(ty_[], x2)) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), x0, x1, x2, x3, x4, x5, x6, x7) 33.79/17.09 new_show13(x0) 33.79/17.09 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.79/17.09 new_show3(x0) 33.79/17.09 new_showParen1(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x0))))))))), x1, x2, x3, x4, x5, x6, x7, x8) 33.79/17.09 new_primDivNatS2(Succ(x0), Zero, x1) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.79/17.09 new_showsPrec(x0, x1, ty_Char) 33.79/17.09 new_primDivNatS4(Succ(x0), Succ(x1)) 33.79/17.09 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.79/17.09 new_pt3(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.79/17.09 new_showsPrec(x0, x1, ty_Double) 33.79/17.09 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (144) QDPSizeChangeProof (EQUIVALENT) 33.79/17.09 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. 33.79/17.09 33.79/17.09 From the DPs we obtained the following set of size-change graphs: 33.79/17.09 *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) 33.79/17.09 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 33.79/17.09 33.79/17.09 33.79/17.09 *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) 33.79/17.09 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 33.79/17.09 33.79/17.09 33.79/17.09 *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) 33.79/17.09 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 33.79/17.09 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (145) 33.79/17.09 YES 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (146) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 new_psPs(:(ww620, ww621), ww60) -> new_psPs(ww621, ww60) 33.79/17.09 33.79/17.09 R is empty. 33.79/17.09 Q is empty. 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (147) QDPSizeChangeProof (EQUIVALENT) 33.79/17.09 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. 33.79/17.09 33.79/17.09 From the DPs we obtained the following set of size-change graphs: 33.79/17.09 *new_psPs(:(ww620, ww621), ww60) -> new_psPs(ww621, ww60) 33.79/17.09 The graph contains the following edges 1 > 1, 2 >= 2 33.79/17.09 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (148) 33.79/17.09 YES 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (149) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 new_primModNatS(Succ(ww1410), Zero, ww143) -> new_primModNatS1(ww1410, ww143) 33.79/17.09 new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero) 33.79/17.09 new_primModNatS00(ww136, ww137) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS0(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS1(Succ(ww870), Succ(ww880)) -> new_primModNatS0(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS0(ww136, ww137, Zero, Zero) -> new_primModNatS00(ww136, ww137) 33.79/17.09 new_primModNatS1(Succ(ww870), Zero) -> new_primModNatS(Succ(ww870), Zero, Zero) 33.79/17.09 33.79/17.09 R is empty. 33.79/17.09 Q is empty. 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (150) DependencyGraphProof (EQUIVALENT) 33.79/17.09 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (151) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 new_primModNatS1(Succ(ww870), Succ(ww880)) -> new_primModNatS0(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS0(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS(Succ(ww1410), Zero, ww143) -> new_primModNatS1(ww1410, ww143) 33.79/17.09 new_primModNatS1(Succ(ww870), Zero) -> new_primModNatS(Succ(ww870), Zero, Zero) 33.79/17.09 new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS0(ww136, ww137, Zero, Zero) -> new_primModNatS00(ww136, ww137) 33.79/17.09 new_primModNatS00(ww136, ww137) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 33.79/17.09 R is empty. 33.79/17.09 Q is empty. 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (152) QDPOrderProof (EQUIVALENT) 33.79/17.09 We use the reduction pair processor [LPAR04,JAR06]. 33.79/17.09 33.79/17.09 33.79/17.09 The following pairs can be oriented strictly and are deleted. 33.79/17.09 33.79/17.09 new_primModNatS1(Succ(ww870), Succ(ww880)) -> new_primModNatS0(ww870, ww880, ww870, ww880) 33.79/17.09 new_primModNatS(Succ(ww1410), Succ(ww1420), ww143) -> new_primModNatS(ww1410, ww1420, ww143) 33.79/17.09 new_primModNatS1(Succ(ww870), Zero) -> new_primModNatS(Succ(ww870), Zero, Zero) 33.79/17.09 The remaining pairs can at least be oriented weakly. 33.79/17.09 Used ordering: Polynomial interpretation [POLO]: 33.79/17.09 33.79/17.09 POL(Succ(x_1)) = 1 + x_1 33.79/17.09 POL(Zero) = 0 33.79/17.09 POL(new_primModNatS(x_1, x_2, x_3)) = x_1 33.79/17.09 POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 33.79/17.09 POL(new_primModNatS00(x_1, x_2)) = 1 + x_1 33.79/17.09 POL(new_primModNatS1(x_1, x_2)) = 1 + x_1 33.79/17.09 33.79/17.09 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 33.79/17.09 none 33.79/17.09 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (153) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 new_primModNatS0(ww136, ww137, Succ(ww1380), Zero) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 new_primModNatS(Succ(ww1410), Zero, ww143) -> new_primModNatS1(ww1410, ww143) 33.79/17.09 new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) 33.79/17.09 new_primModNatS0(ww136, ww137, Zero, Zero) -> new_primModNatS00(ww136, ww137) 33.79/17.09 new_primModNatS00(ww136, ww137) -> new_primModNatS(Succ(ww136), Succ(ww137), Succ(ww137)) 33.79/17.09 33.79/17.09 R is empty. 33.79/17.09 Q is empty. 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (154) DependencyGraphProof (EQUIVALENT) 33.79/17.09 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (155) 33.79/17.09 Obligation: 33.79/17.09 Q DP problem: 33.79/17.09 The TRS P consists of the following rules: 33.79/17.09 33.79/17.09 new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) 33.79/17.09 33.79/17.09 R is empty. 33.79/17.09 Q is empty. 33.79/17.09 We have to consider all minimal (P,Q,R)-chains. 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (156) QDPSizeChangeProof (EQUIVALENT) 33.79/17.09 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. 33.79/17.09 33.79/17.09 From the DPs we obtained the following set of size-change graphs: 33.79/17.09 *new_primModNatS0(ww136, ww137, Succ(ww1380), Succ(ww1390)) -> new_primModNatS0(ww136, ww137, ww1380, ww1390) 33.79/17.09 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 33.79/17.09 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (157) 33.79/17.09 YES 33.79/17.09 33.79/17.09 ---------------------------------------- 33.79/17.09 33.79/17.09 (158) Narrow (COMPLETE) 33.79/17.09 Haskell To QDPs 33.79/17.09 33.79/17.09 digraph dp_graph { 33.79/17.09 node [outthreshold=100, inthreshold=100];1[label="showsPrec",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 33.79/17.10 3[label="showsPrec ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 33.79/17.10 4[label="showsPrec ww3 ww4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 33.79/17.10 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]; 33.79/17.10 1308 -> 6[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 6[label="showsPrec ww3 (ww40 :% ww41) ww5",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 33.79/17.10 7 -> 27[label="",style="dashed", color="red", weight=0]; 33.79/17.10 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]; 33.79/17.10 7 -> 29[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 7 -> 30[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 7 -> 31[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 7 -> 32[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 7 -> 33[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 7 -> 34[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 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 (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];29[label="ww5",fontsize=16,color="green",shape="box"];30[label="ww41",fontsize=16,color="green",shape="box"];31[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"];32[label="ww40",fontsize=16,color="green",shape="box"];33[label="ww3",fontsize=16,color="green",shape="box"];34[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"];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]; 33.79/17.10 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]; 33.79/17.10 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]; 33.79/17.10 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]; 33.79/17.10 1309 -> 45[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1310[label="ww20/Neg ww200",fontsize=10,color="white",style="solid",shape="box"];44 -> 1310[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1310 -> 46[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 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]; 33.79/17.10 1311 -> 47[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1312[label="ww200/Zero",fontsize=10,color="white",style="solid",shape="box"];45 -> 1312[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1312 -> 48[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 46[label="showParen0 ((shows ww21) . 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(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]; 33.79/17.10 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]; 33.79/17.10 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]; 33.79/17.10 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]; 33.79/17.10 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]; 33.79/17.10 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]; 33.79/17.10 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]; 33.79/17.10 54 -> 53[label="",style="dashed", color="red", weight=0]; 33.79/17.10 54[label="showParen0 ((shows ww21) . 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(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]; 33.79/17.10 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]; 33.79/17.10 61[label="showParen0 ((shows ww21) . 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33.79/17.10 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]; 33.79/17.10 97 -> 240[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 98 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 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]; 33.79/17.10 98 -> 242[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 99 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 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]; 33.79/17.10 99 -> 244[label="",style="dashed", color="magenta", weight=3]; 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33.79/17.10 105 -> 256[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 106 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 106[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]; 33.79/17.10 106 -> 258[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 107[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]; 33.79/17.10 1340 -> 127[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1341[label="ww2000000/Zero",fontsize=10,color="white",style="solid",shape="box"];107 -> 1341[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1341 -> 128[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 108 -> 53[label="",style="dashed", color="red", weight=0]; 33.79/17.10 108[label="showParen0 ((shows ww21) . (showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25) (LT == GT) ww26",fontsize=16,color="magenta"];225[label="show ww21",fontsize=16,color="black",shape="triangle"];225 -> 284[label="",style="solid", color="black", weight=3]; 33.79/17.10 226 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 226[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];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]; 33.79/17.10 1342 -> 285[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1343[label="ww62/[]",fontsize=10,color="white",style="solid",shape="box"];224 -> 1343[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1343 -> 286[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 227[label="show ww21",fontsize=16,color="black",shape="triangle"];227 -> 287[label="",style="solid", color="black", weight=3]; 33.79/17.10 228 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 228[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];229[label="show ww21",fontsize=16,color="black",shape="triangle"];229 -> 288[label="",style="solid", color="black", weight=3]; 33.79/17.10 230 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 230[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];231[label="show ww21",fontsize=16,color="black",shape="triangle"];231 -> 289[label="",style="solid", color="black", weight=3]; 33.79/17.10 232 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 232[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];233[label="show ww21",fontsize=16,color="black",shape="triangle"];233 -> 290[label="",style="solid", color="black", weight=3]; 33.79/17.10 234 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 234[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];235[label="show ww21",fontsize=16,color="black",shape="triangle"];235 -> 291[label="",style="solid", color="black", weight=3]; 33.79/17.10 236 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 236[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];237[label="show ww21",fontsize=16,color="black",shape="triangle"];237 -> 292[label="",style="solid", color="black", weight=3]; 33.79/17.10 238 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 238[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];116 -> 27[label="",style="dashed", color="red", weight=0]; 33.79/17.10 116[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"];116 -> 129[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 116 -> 130[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 116 -> 131[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 116 -> 132[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 116 -> 133[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 116 -> 134[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 116 -> 135[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 239[label="show ww21",fontsize=16,color="black",shape="triangle"];239 -> 293[label="",style="solid", color="black", weight=3]; 33.79/17.10 240 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 240[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];241[label="show ww21",fontsize=16,color="black",shape="triangle"];241 -> 294[label="",style="solid", color="black", weight=3]; 33.79/17.10 242 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 242[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];243[label="show ww21",fontsize=16,color="black",shape="triangle"];243 -> 295[label="",style="solid", color="black", weight=3]; 33.79/17.10 244 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 244[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];245[label="show ww21",fontsize=16,color="black",shape="triangle"];245 -> 296[label="",style="solid", color="black", weight=3]; 33.79/17.10 246 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 246[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];247[label="show ww21",fontsize=16,color="black",shape="triangle"];247 -> 297[label="",style="solid", color="black", weight=3]; 33.79/17.10 248 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 248[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];249[label="show ww21",fontsize=16,color="black",shape="triangle"];249 -> 298[label="",style="solid", color="black", weight=3]; 33.79/17.10 250 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 250[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];251[label="show ww21",fontsize=16,color="black",shape="triangle"];251 -> 299[label="",style="solid", color="black", weight=3]; 33.79/17.10 252 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 252[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];253[label="show ww21",fontsize=16,color="black",shape="triangle"];253 -> 300[label="",style="solid", color="black", weight=3]; 33.79/17.10 254 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 254[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];255[label="show ww21",fontsize=16,color="black",shape="triangle"];255 -> 301[label="",style="solid", color="black", weight=3]; 33.79/17.10 256 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 256[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];257[label="show ww21",fontsize=16,color="black",shape="triangle"];257 -> 302[label="",style="solid", color="black", weight=3]; 33.79/17.10 258 -> 130[label="",style="dashed", color="red", weight=0]; 33.79/17.10 258[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="magenta"];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]; 33.79/17.10 128[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]; 33.79/17.10 284[label="error []",fontsize=16,color="red",shape="box"];130[label="(showString (Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : [])) . shows ww25",fontsize=16,color="black",shape="triangle"];130 -> 140[label="",style="solid", color="black", weight=3]; 33.79/17.10 285[label="(ww620 : ww621) ++ ww60",fontsize=16,color="black",shape="box"];285 -> 306[label="",style="solid", color="black", weight=3]; 33.79/17.10 286[label="[] ++ ww60",fontsize=16,color="black",shape="box"];286 -> 307[label="",style="solid", color="black", weight=3]; 33.79/17.10 287[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"];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 (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];131[label="ww211",fontsize=16,color="green",shape="box"];132[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="ww210",fontsize=16,color="green",shape="box"];134[label="Pos Zero",fontsize=16,color="green",shape="box"];135[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"];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="primShowInt ww21",fontsize=16,color="burlywood",shape="triangle"];1344[label="ww21/Pos ww210",fontsize=10,color="white",style="solid",shape="box"];296 -> 1344[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1344 -> 308[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1345[label="ww21/Neg ww210",fontsize=10,color="white",style="solid",shape="box"];296 -> 1345[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1345 -> 309[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 297[label="error []",fontsize=16,color="red",shape="box"];298[label="error []",fontsize=16,color="red",shape="box"];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]; 33.79/17.10 1346 -> 144[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1347[label="ww20000000/Zero",fontsize=10,color="white",style="solid",shape="box"];138 -> 1347[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1347 -> 145[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 139 -> 53[label="",style="dashed", color="red", weight=0]; 33.79/17.10 139[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]; 33.79/17.10 306[label="ww620 : ww621 ++ ww60",fontsize=16,color="green",shape="box"];306 -> 330[label="",style="dashed", color="green", weight=3]; 33.79/17.10 307[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]; 33.79/17.10 1348 -> 331[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1349[label="ww210/Zero",fontsize=10,color="white",style="solid",shape="box"];308 -> 1349[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1349 -> 332[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 309[label="primShowInt (Neg ww210)",fontsize=16,color="black",shape="box"];309 -> 333[label="",style="solid", color="black", weight=3]; 33.79/17.10 144[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]; 33.79/17.10 145[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]; 33.79/17.10 146 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 146[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]; 33.79/17.10 146 -> 264[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 330 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 330[label="ww621 ++ ww60",fontsize=16,color="magenta"];330 -> 353[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 331[label="primShowInt (Pos (Succ ww2100))",fontsize=16,color="black",shape="box"];331 -> 354[label="",style="solid", color="black", weight=3]; 33.79/17.10 332[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];332 -> 355[label="",style="solid", color="black", weight=3]; 33.79/17.10 333[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]; 33.79/17.10 157[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]; 33.79/17.10 1350 -> 181[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1351[label="ww200000000/Zero",fontsize=10,color="white",style="solid",shape="box"];157 -> 1351[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1351 -> 182[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 158 -> 53[label="",style="dashed", color="red", weight=0]; 33.79/17.10 158[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="Char (Succ ww22) : Char (Succ ww23) : Char (Succ ww24) : []",fontsize=16,color="green",shape="box"];264[label="shows ww25 ww26",fontsize=16,color="black",shape="box"];264 -> 303[label="",style="solid", color="black", weight=3]; 33.79/17.10 353[label="ww621",fontsize=16,color="green",shape="box"];354 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 354[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]; 33.79/17.10 354 -> 401[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 355[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 -> 296[label="",style="dashed", color="red", weight=0]; 33.79/17.10 356[label="primShowInt (Pos ww210)",fontsize=16,color="magenta"];356 -> 402[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 181[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]; 33.79/17.10 182[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]; 33.79/17.10 303[label="showsPrec (Pos Zero) ww25 ww26",fontsize=16,color="blue",shape="box"];1352[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1352[label="",style="solid", color="blue", weight=9]; 33.79/17.10 1352 -> 310[label="",style="solid", color="blue", weight=3]; 33.79/17.10 1353[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1353[label="",style="solid", color="blue", weight=9]; 33.79/17.10 1353 -> 311[label="",style="solid", color="blue", weight=3]; 33.79/17.10 1354[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1354[label="",style="solid", color="blue", weight=9]; 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33.79/17.10 1366 -> 324[label="",style="solid", color="blue", weight=3]; 33.79/17.10 1367[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1367[label="",style="solid", color="blue", weight=9]; 33.79/17.10 1367 -> 325[label="",style="solid", color="blue", weight=3]; 33.79/17.10 1368[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1368[label="",style="solid", color="blue", weight=9]; 33.79/17.10 1368 -> 326[label="",style="solid", color="blue", weight=3]; 33.79/17.10 1369[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];303 -> 1369[label="",style="solid", color="blue", weight=9]; 33.79/17.10 1369 -> 327[label="",style="solid", color="blue", weight=3]; 33.79/17.10 400 -> 296[label="",style="dashed", color="red", weight=0]; 33.79/17.10 400[label="primShowInt (div Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];400 -> 443[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 401[label="toEnum (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];401 -> 444[label="",style="dashed", color="green", weight=3]; 33.79/17.10 402[label="Pos ww210",fontsize=16,color="green",shape="box"];214[label="showParen0 ((shows ww21) . 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(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]; 33.79/17.10 222[label="showParen0 ((shows ww21) . 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33.79/17.10 337 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 337[label="show ww25 ++ ww26",fontsize=16,color="magenta"];337 -> 363[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 337 -> 364[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 338 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 338[label="show ww25 ++ ww26",fontsize=16,color="magenta"];338 -> 365[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 338 -> 366[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 339 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 339[label="show ww25 ++ ww26",fontsize=16,color="magenta"];339 -> 367[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 339 -> 368[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 340 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 340[label="show ww25 ++ ww26",fontsize=16,color="magenta"];340 -> 369[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 340 -> 370[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 341[label="showsPrec (Pos Zero) (ww250 :% ww251) ww26",fontsize=16,color="black",shape="box"];341 -> 371[label="",style="solid", color="black", weight=3]; 33.79/17.10 342 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 342[label="show ww25 ++ ww26",fontsize=16,color="magenta"];342 -> 372[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 342 -> 373[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 343 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 343[label="show ww25 ++ ww26",fontsize=16,color="magenta"];343 -> 374[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 343 -> 375[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 344 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 344[label="show ww25 ++ ww26",fontsize=16,color="magenta"];344 -> 376[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 344 -> 377[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 345 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 345[label="show ww25 ++ ww26",fontsize=16,color="magenta"];345 -> 378[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 345 -> 379[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 346 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 346[label="show ww25 ++ ww26",fontsize=16,color="magenta"];346 -> 380[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 346 -> 381[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 347 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 347[label="show ww25 ++ ww26",fontsize=16,color="magenta"];347 -> 382[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 347 -> 383[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 348 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 348[label="show ww25 ++ ww26",fontsize=16,color="magenta"];348 -> 384[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 348 -> 385[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 349 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 349[label="show ww25 ++ ww26",fontsize=16,color="magenta"];349 -> 386[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 349 -> 387[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 350 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 350[label="show ww25 ++ ww26",fontsize=16,color="magenta"];350 -> 388[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 350 -> 389[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 351 -> 224[label="",style="dashed", color="red", weight=0]; 33.79/17.10 351[label="show ww25 ++ ww26",fontsize=16,color="magenta"];351 -> 390[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 351 -> 391[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 447[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];448[label="ww2100",fontsize=16,color="green",shape="box"];446[label="div Pos (Succ ww81) Pos (Succ ww82)",fontsize=16,color="black",shape="triangle"];446 -> 452[label="",style="solid", color="black", weight=3]; 33.79/17.10 464 -> 476[label="",style="dashed", color="red", weight=0]; 33.79/17.10 464[label="primIntToChar (mod Pos (Succ ww2100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];464 -> 477[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 464 -> 478[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 304[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]; 33.79/17.10 305[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]; 33.79/17.10 357 -> 225[label="",style="dashed", color="red", weight=0]; 33.79/17.10 357[label="show ww25",fontsize=16,color="magenta"];357 -> 403[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 358[label="ww26",fontsize=16,color="green",shape="box"];359 -> 227[label="",style="dashed", color="red", weight=0]; 33.79/17.10 359[label="show ww25",fontsize=16,color="magenta"];359 -> 404[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 360[label="ww26",fontsize=16,color="green",shape="box"];361 -> 229[label="",style="dashed", color="red", weight=0]; 33.79/17.10 361[label="show ww25",fontsize=16,color="magenta"];361 -> 405[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 362[label="ww26",fontsize=16,color="green",shape="box"];363 -> 231[label="",style="dashed", color="red", weight=0]; 33.79/17.10 363[label="show ww25",fontsize=16,color="magenta"];363 -> 406[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 364[label="ww26",fontsize=16,color="green",shape="box"];365 -> 233[label="",style="dashed", color="red", weight=0]; 33.79/17.10 365[label="show ww25",fontsize=16,color="magenta"];365 -> 407[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 366[label="ww26",fontsize=16,color="green",shape="box"];367 -> 235[label="",style="dashed", color="red", weight=0]; 33.79/17.10 367[label="show ww25",fontsize=16,color="magenta"];367 -> 408[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 368[label="ww26",fontsize=16,color="green",shape="box"];369 -> 237[label="",style="dashed", color="red", weight=0]; 33.79/17.10 369[label="show ww25",fontsize=16,color="magenta"];369 -> 409[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 370[label="ww26",fontsize=16,color="green",shape="box"];371 -> 27[label="",style="dashed", color="red", weight=0]; 33.79/17.10 371[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"];371 -> 410[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 371 -> 411[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 371 -> 412[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 371 -> 413[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 371 -> 414[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 371 -> 415[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 372 -> 239[label="",style="dashed", color="red", weight=0]; 33.79/17.10 372[label="show ww25",fontsize=16,color="magenta"];372 -> 416[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 373[label="ww26",fontsize=16,color="green",shape="box"];374 -> 241[label="",style="dashed", color="red", weight=0]; 33.79/17.10 374[label="show ww25",fontsize=16,color="magenta"];374 -> 417[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 375[label="ww26",fontsize=16,color="green",shape="box"];376 -> 243[label="",style="dashed", color="red", weight=0]; 33.79/17.10 376[label="show ww25",fontsize=16,color="magenta"];376 -> 418[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 377[label="ww26",fontsize=16,color="green",shape="box"];378 -> 245[label="",style="dashed", color="red", weight=0]; 33.79/17.10 378[label="show ww25",fontsize=16,color="magenta"];378 -> 419[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 379[label="ww26",fontsize=16,color="green",shape="box"];380 -> 247[label="",style="dashed", color="red", weight=0]; 33.79/17.10 380[label="show ww25",fontsize=16,color="magenta"];380 -> 420[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 381[label="ww26",fontsize=16,color="green",shape="box"];382 -> 249[label="",style="dashed", color="red", weight=0]; 33.79/17.10 382[label="show ww25",fontsize=16,color="magenta"];382 -> 421[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 383[label="ww26",fontsize=16,color="green",shape="box"];384 -> 251[label="",style="dashed", color="red", weight=0]; 33.79/17.10 384[label="show ww25",fontsize=16,color="magenta"];384 -> 422[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 385[label="ww26",fontsize=16,color="green",shape="box"];386 -> 253[label="",style="dashed", color="red", weight=0]; 33.79/17.10 386[label="show ww25",fontsize=16,color="magenta"];386 -> 423[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 387[label="ww26",fontsize=16,color="green",shape="box"];388 -> 255[label="",style="dashed", color="red", weight=0]; 33.79/17.10 388[label="show ww25",fontsize=16,color="magenta"];388 -> 424[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 389[label="ww26",fontsize=16,color="green",shape="box"];390 -> 257[label="",style="dashed", color="red", weight=0]; 33.79/17.10 390[label="show ww25",fontsize=16,color="magenta"];390 -> 425[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 391[label="ww26",fontsize=16,color="green",shape="box"];452[label="primDivInt (Pos (Succ ww81)) (Pos (Succ ww82))",fontsize=16,color="black",shape="box"];452 -> 463[label="",style="solid", color="black", weight=3]; 33.79/17.10 477[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];478[label="ww2100",fontsize=16,color="green",shape="box"];476[label="primIntToChar (mod Pos (Succ ww87) Pos (Succ ww88))",fontsize=16,color="black",shape="triangle"];476 -> 479[label="",style="solid", color="black", weight=3]; 33.79/17.10 328[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]; 33.79/17.10 329 -> 57[label="",style="dashed", color="red", weight=0]; 33.79/17.10 329[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="ww25",fontsize=16,color="green",shape="box"];405[label="ww25",fontsize=16,color="green",shape="box"];406[label="ww25",fontsize=16,color="green",shape="box"];407[label="ww25",fontsize=16,color="green",shape="box"];408[label="ww25",fontsize=16,color="green",shape="box"];409[label="ww25",fontsize=16,color="green",shape="box"];410[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"];411[label="ww251",fontsize=16,color="green",shape="box"];412[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"];413[label="ww250",fontsize=16,color="green",shape="box"];414[label="Pos Zero",fontsize=16,color="green",shape="box"];415[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"];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"];463[label="Pos (primDivNatS (Succ ww81) (Succ ww82))",fontsize=16,color="green",shape="box"];463 -> 475[label="",style="dashed", color="green", weight=3]; 33.79/17.10 479[label="primIntToChar (primModInt (Pos (Succ ww87)) (Pos (Succ ww88)))",fontsize=16,color="black",shape="box"];479 -> 482[label="",style="solid", color="black", weight=3]; 33.79/17.10 352 -> 426[label="",style="dashed", color="red", weight=0]; 33.79/17.10 352[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]; 33.79/17.10 352 -> 428[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 352 -> 429[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 352 -> 430[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 352 -> 431[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 352 -> 432[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 352 -> 433[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 352 -> 434[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 475[label="primDivNatS (Succ ww81) (Succ ww82)",fontsize=16,color="black",shape="triangle"];475 -> 480[label="",style="solid", color="black", weight=3]; 33.79/17.10 482[label="primIntToChar (Pos (primModNatS (Succ ww87) (Succ ww88)))",fontsize=16,color="black",shape="box"];482 -> 491[label="",style="solid", color="black", weight=3]; 33.79/17.10 427[label="ww22",fontsize=16,color="green",shape="box"];428[label="ww24",fontsize=16,color="green",shape="box"];429[label="ww21",fontsize=16,color="green",shape="box"];430[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"];431[label="ww25",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="ww26",fontsize=16,color="green",shape="box"];434[label="ww23",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]; 33.79/17.10 480[label="primDivNatS0 ww81 ww82 (primGEqNatS ww81 ww82)",fontsize=16,color="burlywood",shape="box"];1373[label="ww81/Succ ww810",fontsize=10,color="white",style="solid",shape="box"];480 -> 1373[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1373 -> 483[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1374[label="ww81/Zero",fontsize=10,color="white",style="solid",shape="box"];480 -> 1374[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1374 -> 484[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 491[label="Char (primModNatS (Succ ww87) (Succ ww88))",fontsize=16,color="green",shape="box"];491 -> 497[label="",style="dashed", color="green", weight=3]; 33.79/17.10 445[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]; 33.79/17.10 483[label="primDivNatS0 (Succ ww810) ww82 (primGEqNatS (Succ ww810) ww82)",fontsize=16,color="burlywood",shape="box"];1375[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];483 -> 1375[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1375 -> 492[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1376[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];483 -> 1376[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1376 -> 493[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 484[label="primDivNatS0 Zero ww82 (primGEqNatS Zero ww82)",fontsize=16,color="burlywood",shape="box"];1377[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];484 -> 1377[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1377 -> 494[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1378[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];484 -> 1378[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1378 -> 495[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 497[label="primModNatS (Succ ww87) (Succ ww88)",fontsize=16,color="black",shape="triangle"];497 -> 502[label="",style="solid", color="black", weight=3]; 33.79/17.10 462[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]; 33.79/17.10 492[label="primDivNatS0 (Succ ww810) (Succ ww820) (primGEqNatS (Succ ww810) (Succ ww820))",fontsize=16,color="black",shape="box"];492 -> 498[label="",style="solid", color="black", weight=3]; 33.79/17.10 493[label="primDivNatS0 (Succ ww810) Zero (primGEqNatS (Succ ww810) Zero)",fontsize=16,color="black",shape="box"];493 -> 499[label="",style="solid", color="black", weight=3]; 33.79/17.10 494[label="primDivNatS0 Zero (Succ ww820) (primGEqNatS Zero (Succ ww820))",fontsize=16,color="black",shape="box"];494 -> 500[label="",style="solid", color="black", weight=3]; 33.79/17.10 495[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];495 -> 501[label="",style="solid", color="black", weight=3]; 33.79/17.10 502[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"];502 -> 1379[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1379 -> 508[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1380[label="ww87/Zero",fontsize=10,color="white",style="solid",shape="box"];502 -> 1380[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1380 -> 509[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 474[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 -> 481[label="",style="solid", color="black", weight=3]; 33.79/17.10 498 -> 1014[label="",style="dashed", color="red", weight=0]; 33.79/17.10 498[label="primDivNatS0 (Succ ww810) (Succ ww820) (primGEqNatS ww810 ww820)",fontsize=16,color="magenta"];498 -> 1015[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 498 -> 1016[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 498 -> 1017[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 498 -> 1018[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 499[label="primDivNatS0 (Succ ww810) Zero True",fontsize=16,color="black",shape="box"];499 -> 505[label="",style="solid", color="black", weight=3]; 33.79/17.10 500[label="primDivNatS0 Zero (Succ ww820) False",fontsize=16,color="black",shape="box"];500 -> 506[label="",style="solid", color="black", weight=3]; 33.79/17.10 501[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];501 -> 507[label="",style="solid", color="black", weight=3]; 33.79/17.10 508[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"];508 -> 1381[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1381 -> 516[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1382[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];508 -> 1382[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1382 -> 517[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 509[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"];509 -> 1383[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1383 -> 518[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1384[label="ww88/Zero",fontsize=10,color="white",style="solid",shape="box"];509 -> 1384[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1384 -> 519[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 481 -> 60[label="",style="dashed", color="red", weight=0]; 33.79/17.10 481[label="(shows ww73) . (showString (Char (Succ ww74) : Char (Succ ww75) : Char (Succ ww76) : [])) . shows ww77",fontsize=16,color="magenta"];481 -> 485[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 481 -> 486[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 481 -> 487[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 481 -> 488[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 481 -> 489[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 481 -> 490[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1015[label="ww810",fontsize=16,color="green",shape="box"];1016[label="ww820",fontsize=16,color="green",shape="box"];1017[label="ww810",fontsize=16,color="green",shape="box"];1018[label="ww820",fontsize=16,color="green",shape="box"];1014[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"];1014 -> 1385[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1385 -> 1055[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1386[label="ww133/Zero",fontsize=10,color="white",style="solid",shape="box"];1014 -> 1386[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1386 -> 1056[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 505[label="Succ (primDivNatS (primMinusNatS (Succ ww810) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];505 -> 514[label="",style="dashed", color="green", weight=3]; 33.79/17.10 506[label="Zero",fontsize=16,color="green",shape="box"];507[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];507 -> 515[label="",style="dashed", color="green", weight=3]; 33.79/17.10 516[label="primModNatS0 (Succ ww870) (Succ ww880) (primGEqNatS (Succ ww870) (Succ ww880))",fontsize=16,color="black",shape="box"];516 -> 526[label="",style="solid", color="black", weight=3]; 33.79/17.10 517[label="primModNatS0 (Succ ww870) Zero (primGEqNatS (Succ ww870) Zero)",fontsize=16,color="black",shape="box"];517 -> 527[label="",style="solid", color="black", weight=3]; 33.79/17.10 518[label="primModNatS0 Zero (Succ ww880) (primGEqNatS Zero (Succ ww880))",fontsize=16,color="black",shape="box"];518 -> 528[label="",style="solid", color="black", weight=3]; 33.79/17.10 519[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];519 -> 529[label="",style="solid", color="black", weight=3]; 33.79/17.10 485[label="ww75",fontsize=16,color="green",shape="box"];486[label="showChar (Char (Succ ww78)) ww79",fontsize=16,color="black",shape="box"];486 -> 496[label="",style="solid", color="black", weight=3]; 33.79/17.10 487[label="ww77",fontsize=16,color="green",shape="box"];488[label="ww76",fontsize=16,color="green",shape="box"];489[label="ww73",fontsize=16,color="green",shape="box"];490[label="ww74",fontsize=16,color="green",shape="box"];1055[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"];1055 -> 1387[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1387 -> 1067[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1388[label="ww134/Zero",fontsize=10,color="white",style="solid",shape="box"];1055 -> 1388[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1388 -> 1068[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1056[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"];1056 -> 1389[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1389 -> 1069[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1390[label="ww134/Zero",fontsize=10,color="white",style="solid",shape="box"];1056 -> 1390[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1390 -> 1070[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 514 -> 1268[label="",style="dashed", color="red", weight=0]; 33.79/17.10 514[label="primDivNatS (primMinusNatS (Succ ww810) Zero) (Succ Zero)",fontsize=16,color="magenta"];514 -> 1269[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 514 -> 1270[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 514 -> 1271[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 515 -> 1268[label="",style="dashed", color="red", weight=0]; 33.79/17.10 515[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];515 -> 1272[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 515 -> 1273[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 515 -> 1274[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 526 -> 1089[label="",style="dashed", color="red", weight=0]; 33.79/17.10 526[label="primModNatS0 (Succ ww870) (Succ ww880) (primGEqNatS ww870 ww880)",fontsize=16,color="magenta"];526 -> 1090[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 526 -> 1091[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 526 -> 1092[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 526 -> 1093[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 527[label="primModNatS0 (Succ ww870) Zero True",fontsize=16,color="black",shape="box"];527 -> 540[label="",style="solid", color="black", weight=3]; 33.79/17.10 528[label="primModNatS0 Zero (Succ ww880) False",fontsize=16,color="black",shape="box"];528 -> 541[label="",style="solid", color="black", weight=3]; 33.79/17.10 529[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];529 -> 542[label="",style="solid", color="black", weight=3]; 33.79/17.10 496[label="(:) Char (Succ ww78) ww79",fontsize=16,color="green",shape="box"];1067[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) (Succ ww1340))",fontsize=16,color="black",shape="box"];1067 -> 1081[label="",style="solid", color="black", weight=3]; 33.79/17.10 1068[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS (Succ ww1330) Zero)",fontsize=16,color="black",shape="box"];1068 -> 1082[label="",style="solid", color="black", weight=3]; 33.79/17.10 1069[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero (Succ ww1340))",fontsize=16,color="black",shape="box"];1069 -> 1083[label="",style="solid", color="black", weight=3]; 33.79/17.10 1070[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1070 -> 1084[label="",style="solid", color="black", weight=3]; 33.79/17.10 1269[label="Zero",fontsize=16,color="green",shape="box"];1270[label="Succ ww810",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"];1391[label="ww145/Succ ww1450",fontsize=10,color="white",style="solid",shape="box"];1268 -> 1391[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1391 -> 1293[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1392[label="ww145/Zero",fontsize=10,color="white",style="solid",shape="box"];1268 -> 1392[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1392 -> 1294[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 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"];1090[label="ww870",fontsize=16,color="green",shape="box"];1091[label="ww880",fontsize=16,color="green",shape="box"];1092[label="ww880",fontsize=16,color="green",shape="box"];1093[label="ww870",fontsize=16,color="green",shape="box"];1089[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS ww138 ww139)",fontsize=16,color="burlywood",shape="triangle"];1393[label="ww138/Succ ww1380",fontsize=10,color="white",style="solid",shape="box"];1089 -> 1393[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1393 -> 1130[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1394[label="ww138/Zero",fontsize=10,color="white",style="solid",shape="box"];1089 -> 1394[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1394 -> 1131[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 540 -> 1176[label="",style="dashed", color="red", weight=0]; 33.79/17.10 540[label="primModNatS (primMinusNatS (Succ ww870) Zero) (Succ Zero)",fontsize=16,color="magenta"];540 -> 1177[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 540 -> 1178[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 540 -> 1179[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 541[label="Succ Zero",fontsize=16,color="green",shape="box"];542 -> 1176[label="",style="dashed", color="red", weight=0]; 33.79/17.10 542[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];542 -> 1180[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 542 -> 1181[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 542 -> 1182[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1081 -> 1014[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1081[label="primDivNatS0 (Succ ww131) (Succ ww132) (primGEqNatS ww1330 ww1340)",fontsize=16,color="magenta"];1081 -> 1132[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1081 -> 1133[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1082[label="primDivNatS0 (Succ ww131) (Succ ww132) True",fontsize=16,color="black",shape="triangle"];1082 -> 1134[label="",style="solid", color="black", weight=3]; 33.79/17.10 1083[label="primDivNatS0 (Succ ww131) (Succ ww132) False",fontsize=16,color="black",shape="box"];1083 -> 1135[label="",style="solid", color="black", weight=3]; 33.79/17.10 1084 -> 1082[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1084[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"];1395[label="ww146/Succ ww1460",fontsize=10,color="white",style="solid",shape="box"];1293 -> 1395[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1395 -> 1295[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1396[label="ww146/Zero",fontsize=10,color="white",style="solid",shape="box"];1293 -> 1396[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1396 -> 1296[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1294[label="primDivNatS (primMinusNatS Zero ww146) (Succ ww147)",fontsize=16,color="burlywood",shape="box"];1397[label="ww146/Succ ww1460",fontsize=10,color="white",style="solid",shape="box"];1294 -> 1397[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1397 -> 1297[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1398[label="ww146/Zero",fontsize=10,color="white",style="solid",shape="box"];1294 -> 1398[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1398 -> 1298[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1130[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) ww139)",fontsize=16,color="burlywood",shape="box"];1399[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1130 -> 1399[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1399 -> 1140[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1400[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1130 -> 1400[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1400 -> 1141[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1131[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero ww139)",fontsize=16,color="burlywood",shape="box"];1401[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1131 -> 1401[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1401 -> 1142[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1402[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1131 -> 1402[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1402 -> 1143[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1177[label="Succ ww870",fontsize=16,color="green",shape="box"];1178[label="Zero",fontsize=16,color="green",shape="box"];1179[label="Zero",fontsize=16,color="green",shape="box"];1176[label="primModNatS (primMinusNatS ww141 ww142) (Succ ww143)",fontsize=16,color="burlywood",shape="triangle"];1403[label="ww141/Succ ww1410",fontsize=10,color="white",style="solid",shape="box"];1176 -> 1403[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1403 -> 1207[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1404[label="ww141/Zero",fontsize=10,color="white",style="solid",shape="box"];1176 -> 1404[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1404 -> 1208[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1180[label="Zero",fontsize=16,color="green",shape="box"];1181[label="Zero",fontsize=16,color="green",shape="box"];1182[label="Zero",fontsize=16,color="green",shape="box"];1132[label="ww1340",fontsize=16,color="green",shape="box"];1133[label="ww1330",fontsize=16,color="green",shape="box"];1134[label="Succ (primDivNatS (primMinusNatS (Succ ww131) (Succ ww132)) (Succ (Succ ww132)))",fontsize=16,color="green",shape="box"];1134 -> 1144[label="",style="dashed", color="green", weight=3]; 33.79/17.10 1135[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]; 33.79/17.10 1296[label="primDivNatS (primMinusNatS (Succ ww1450) Zero) (Succ ww147)",fontsize=16,color="black",shape="box"];1296 -> 1300[label="",style="solid", color="black", weight=3]; 33.79/17.10 1297[label="primDivNatS (primMinusNatS Zero (Succ ww1460)) (Succ ww147)",fontsize=16,color="black",shape="box"];1297 -> 1301[label="",style="solid", color="black", weight=3]; 33.79/17.10 1298[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww147)",fontsize=16,color="black",shape="box"];1298 -> 1302[label="",style="solid", color="black", weight=3]; 33.79/17.10 1140[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) (Succ ww1390))",fontsize=16,color="black",shape="box"];1140 -> 1151[label="",style="solid", color="black", weight=3]; 33.79/17.10 1141[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS (Succ ww1380) Zero)",fontsize=16,color="black",shape="box"];1141 -> 1152[label="",style="solid", color="black", weight=3]; 33.79/17.10 1142[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero (Succ ww1390))",fontsize=16,color="black",shape="box"];1142 -> 1153[label="",style="solid", color="black", weight=3]; 33.79/17.10 1143[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1143 -> 1154[label="",style="solid", color="black", weight=3]; 33.79/17.10 1207[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"];1207 -> 1405[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1405 -> 1213[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1406[label="ww142/Zero",fontsize=10,color="white",style="solid",shape="box"];1207 -> 1406[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1406 -> 1214[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1208[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"];1208 -> 1407[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1407 -> 1215[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1408[label="ww142/Zero",fontsize=10,color="white",style="solid",shape="box"];1208 -> 1408[label="",style="solid", color="burlywood", weight=9]; 33.79/17.10 1408 -> 1216[label="",style="solid", color="burlywood", weight=3]; 33.79/17.10 1144 -> 1268[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1144[label="primDivNatS (primMinusNatS (Succ ww131) (Succ ww132)) (Succ (Succ ww132))",fontsize=16,color="magenta"];1144 -> 1275[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1144 -> 1276[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1144 -> 1277[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1299 -> 1268[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1299[label="primDivNatS (primMinusNatS ww1450 ww1460) (Succ ww147)",fontsize=16,color="magenta"];1299 -> 1303[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1299 -> 1304[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1300 -> 475[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1300[label="primDivNatS (Succ ww1450) (Succ ww147)",fontsize=16,color="magenta"];1300 -> 1305[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1300 -> 1306[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1301[label="primDivNatS Zero (Succ ww147)",fontsize=16,color="black",shape="triangle"];1301 -> 1307[label="",style="solid", color="black", weight=3]; 33.79/17.10 1302 -> 1301[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1302[label="primDivNatS Zero (Succ ww147)",fontsize=16,color="magenta"];1151 -> 1089[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1151[label="primModNatS0 (Succ ww136) (Succ ww137) (primGEqNatS ww1380 ww1390)",fontsize=16,color="magenta"];1151 -> 1160[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1151 -> 1161[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1152[label="primModNatS0 (Succ ww136) (Succ ww137) True",fontsize=16,color="black",shape="triangle"];1152 -> 1162[label="",style="solid", color="black", weight=3]; 33.79/17.10 1153[label="primModNatS0 (Succ ww136) (Succ ww137) False",fontsize=16,color="black",shape="box"];1153 -> 1163[label="",style="solid", color="black", weight=3]; 33.79/17.10 1154 -> 1152[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1154[label="primModNatS0 (Succ ww136) (Succ ww137) True",fontsize=16,color="magenta"];1213[label="primModNatS (primMinusNatS (Succ ww1410) (Succ ww1420)) (Succ ww143)",fontsize=16,color="black",shape="box"];1213 -> 1223[label="",style="solid", color="black", weight=3]; 33.79/17.10 1214[label="primModNatS (primMinusNatS (Succ ww1410) Zero) (Succ ww143)",fontsize=16,color="black",shape="box"];1214 -> 1224[label="",style="solid", color="black", weight=3]; 33.79/17.10 1215[label="primModNatS (primMinusNatS Zero (Succ ww1420)) (Succ ww143)",fontsize=16,color="black",shape="box"];1215 -> 1225[label="",style="solid", color="black", weight=3]; 33.79/17.10 1216[label="primModNatS (primMinusNatS Zero Zero) (Succ ww143)",fontsize=16,color="black",shape="box"];1216 -> 1226[label="",style="solid", color="black", weight=3]; 33.79/17.10 1275[label="Succ ww132",fontsize=16,color="green",shape="box"];1276[label="Succ ww131",fontsize=16,color="green",shape="box"];1277[label="Succ ww132",fontsize=16,color="green",shape="box"];1303[label="ww1460",fontsize=16,color="green",shape="box"];1304[label="ww1450",fontsize=16,color="green",shape="box"];1305[label="ww147",fontsize=16,color="green",shape="box"];1306[label="ww1450",fontsize=16,color="green",shape="box"];1307[label="Zero",fontsize=16,color="green",shape="box"];1160[label="ww1390",fontsize=16,color="green",shape="box"];1161[label="ww1380",fontsize=16,color="green",shape="box"];1162 -> 1176[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1162[label="primModNatS (primMinusNatS (Succ ww136) (Succ ww137)) (Succ (Succ ww137))",fontsize=16,color="magenta"];1162 -> 1189[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1162 -> 1190[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1162 -> 1191[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1163[label="Succ (Succ ww136)",fontsize=16,color="green",shape="box"];1223 -> 1176[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1223[label="primModNatS (primMinusNatS ww1410 ww1420) (Succ ww143)",fontsize=16,color="magenta"];1223 -> 1231[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1223 -> 1232[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1224 -> 497[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1224[label="primModNatS (Succ ww1410) (Succ ww143)",fontsize=16,color="magenta"];1224 -> 1233[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1224 -> 1234[label="",style="dashed", color="magenta", weight=3]; 33.79/17.10 1225[label="primModNatS Zero (Succ ww143)",fontsize=16,color="black",shape="triangle"];1225 -> 1235[label="",style="solid", color="black", weight=3]; 33.79/17.10 1226 -> 1225[label="",style="dashed", color="red", weight=0]; 33.79/17.10 1226[label="primModNatS Zero (Succ ww143)",fontsize=16,color="magenta"];1189[label="Succ ww136",fontsize=16,color="green",shape="box"];1190[label="Succ ww137",fontsize=16,color="green",shape="box"];1191[label="Succ ww137",fontsize=16,color="green",shape="box"];1231[label="ww1410",fontsize=16,color="green",shape="box"];1232[label="ww1420",fontsize=16,color="green",shape="box"];1233[label="ww143",fontsize=16,color="green",shape="box"];1234[label="ww1410",fontsize=16,color="green",shape="box"];1235[label="Zero",fontsize=16,color="green",shape="box"];} 33.79/17.10 33.79/17.10 ---------------------------------------- 33.79/17.10 33.79/17.10 (159) 33.79/17.10 TRUE 33.96/17.13 EOF