31.76/17.35 MAYBE 33.93/17.96 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 33.93/17.96 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 33.93/17.96 33.93/17.96 33.93/17.96 H-Termination with start terms of the given HASKELL could not be shown: 33.93/17.96 33.93/17.96 (0) HASKELL 33.93/17.96 (1) IFR [EQUIVALENT, 0 ms] 33.93/17.96 (2) HASKELL 33.93/17.96 (3) BR [EQUIVALENT, 0 ms] 33.93/17.96 (4) HASKELL 33.93/17.96 (5) COR [EQUIVALENT, 0 ms] 33.93/17.96 (6) HASKELL 33.93/17.96 (7) LetRed [EQUIVALENT, 0 ms] 33.93/17.96 (8) HASKELL 33.93/17.96 (9) NumRed [SOUND, 0 ms] 33.93/17.96 (10) HASKELL 33.93/17.96 (11) Narrow [SOUND, 0 ms] 33.93/17.96 (12) AND 33.93/17.96 (13) QDP 33.93/17.96 (14) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (15) QDP 33.93/17.96 (16) QDPOrderProof [EQUIVALENT, 18 ms] 33.93/17.96 (17) QDP 33.93/17.96 (18) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (19) QDP 33.93/17.96 (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.93/17.96 (21) YES 33.93/17.96 (22) QDP 33.93/17.96 (23) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (24) QDP 33.93/17.96 (25) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (26) QDP 33.93/17.96 (27) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (28) QDP 33.93/17.96 (29) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (30) QDP 33.93/17.96 (31) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (32) QDP 33.93/17.96 (33) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (34) QDP 33.93/17.96 (35) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (36) QDP 33.93/17.96 (37) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (38) QDP 33.93/17.96 (39) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (40) QDP 33.93/17.96 (41) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (42) QDP 33.93/17.96 (43) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (44) QDP 33.93/17.96 (45) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (46) QDP 33.93/17.96 (47) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (48) QDP 33.93/17.96 (49) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (50) QDP 33.93/17.96 (51) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (52) QDP 33.93/17.96 (53) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (54) QDP 33.93/17.96 (55) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (56) QDP 33.93/17.96 (57) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (58) QDP 33.93/17.96 (59) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.93/17.96 (60) YES 33.93/17.96 (61) QDP 33.93/17.96 (62) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (63) QDP 33.93/17.96 (64) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (65) QDP 33.93/17.96 (66) UsableRulesProof [EQUIVALENT, 0 ms] 33.93/17.96 (67) QDP 33.93/17.96 (68) QReductionProof [EQUIVALENT, 0 ms] 33.93/17.96 (69) QDP 33.93/17.96 (70) MNOCProof [EQUIVALENT, 0 ms] 33.93/17.96 (71) QDP 33.93/17.96 (72) InductionCalculusProof [EQUIVALENT, 0 ms] 33.93/17.96 (73) QDP 33.93/17.96 (74) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (75) QDP 33.93/17.96 (76) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (77) QDP 33.93/17.96 (78) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (79) QDP 33.93/17.96 (80) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (81) QDP 33.93/17.96 (82) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (83) QDP 33.93/17.96 (84) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (85) QDP 33.93/17.96 (86) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (87) QDP 33.93/17.96 (88) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (89) QDP 33.93/17.96 (90) MNOCProof [EQUIVALENT, 0 ms] 33.93/17.96 (91) QDP 33.93/17.96 (92) InductionCalculusProof [EQUIVALENT, 0 ms] 33.93/17.96 (93) QDP 33.93/17.96 (94) QDP 33.93/17.96 (95) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.93/17.96 (96) YES 33.93/17.96 (97) QDP 33.93/17.96 (98) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (99) QDP 33.93/17.96 (100) QDPOrderProof [EQUIVALENT, 6 ms] 33.93/17.96 (101) QDP 33.93/17.96 (102) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (103) QDP 33.93/17.96 (104) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.93/17.96 (105) YES 33.93/17.96 (106) QDP 33.93/17.96 (107) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (108) QDP 33.93/17.96 (109) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (110) QDP 33.93/17.96 (111) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (112) QDP 33.93/17.96 (113) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (114) QDP 33.93/17.96 (115) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (116) QDP 33.93/17.96 (117) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (118) QDP 33.93/17.96 (119) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (120) QDP 33.93/17.96 (121) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (122) QDP 33.93/17.96 (123) TransformationProof [EQUIVALENT, 1 ms] 33.93/17.96 (124) QDP 33.93/17.96 (125) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (126) QDP 33.93/17.96 (127) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (128) QDP 33.93/17.96 (129) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (130) QDP 33.93/17.96 (131) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (132) QDP 33.93/17.96 (133) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (134) QDP 33.93/17.96 (135) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (136) QDP 33.93/17.96 (137) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (138) QDP 33.93/17.96 (139) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (140) QDP 33.93/17.96 (141) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (142) QDP 33.93/17.96 (143) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (144) QDP 33.93/17.96 (145) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (146) QDP 33.93/17.96 (147) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (148) QDP 33.93/17.96 (149) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (150) QDP 33.93/17.96 (151) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (152) QDP 33.93/17.96 (153) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (154) QDP 33.93/17.96 (155) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (156) QDP 33.93/17.96 (157) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (158) QDP 33.93/17.96 (159) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (160) QDP 33.93/17.96 (161) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (162) QDP 33.93/17.96 (163) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (164) QDP 33.93/17.96 (165) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (166) QDP 33.93/17.96 (167) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (168) QDP 33.93/17.96 (169) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (170) QDP 33.93/17.96 (171) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (172) QDP 33.93/17.96 (173) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (174) QDP 33.93/17.96 (175) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (176) QDP 33.93/17.96 (177) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (178) QDP 33.93/17.96 (179) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (180) QDP 33.93/17.96 (181) TransformationProof [EQUIVALENT, 0 ms] 33.93/17.96 (182) QDP 33.93/17.96 (183) DependencyGraphProof [EQUIVALENT, 0 ms] 33.93/17.96 (184) QDP 33.93/17.96 (185) TransformationProof [EQUIVALENT, 6 ms] 33.93/17.96 (186) QDP 33.93/17.96 (187) QDPSizeChangeProof [EQUIVALENT, 0 ms] 33.93/17.96 (188) YES 33.93/17.96 (189) Narrow [COMPLETE, 0 ms] 33.93/17.96 (190) TRUE 33.93/17.96 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (0) 33.93/17.96 Obligation: 33.93/17.96 mainModule Main 33.93/17.96 module Main where { 33.93/17.96 import qualified Prelude; 33.93/17.96 } 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (1) IFR (EQUIVALENT) 33.93/17.96 If Reductions: 33.93/17.96 The following If expression 33.93/17.96 "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" 33.93/17.96 is transformed to 33.93/17.96 "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); 33.93/17.96 primDivNatS0 x y False = Zero; 33.93/17.96 " 33.93/17.96 The following If expression 33.93/17.96 "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" 33.93/17.96 is transformed to 33.93/17.96 "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); 33.93/17.96 primModNatS0 x y False = Succ x; 33.93/17.96 " 33.93/17.96 The following If expression 33.93/17.96 "if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x" 33.93/17.96 is transformed to 33.93/17.96 "primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y); 33.93/17.96 primModNatP0 x y False = primMinusNatS y x; 33.93/17.96 " 33.93/17.96 The following If expression 33.93/17.96 "if b then (showChar '(') . p . showChar ')' else p" 33.93/17.96 is transformed to 33.93/17.96 "showParen0 p True = (showChar '(') . p . showChar ')'; 33.93/17.96 showParen0 p False = p; 33.93/17.96 " 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (2) 33.93/17.96 Obligation: 33.93/17.96 mainModule Main 33.93/17.96 module Main where { 33.93/17.96 import qualified Prelude; 33.93/17.96 } 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (3) BR (EQUIVALENT) 33.93/17.96 Replaced joker patterns by fresh variables and removed binding patterns. 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (4) 33.93/17.96 Obligation: 33.93/17.96 mainModule Main 33.93/17.96 module Main where { 33.93/17.96 import qualified Prelude; 33.93/17.96 } 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (5) COR (EQUIVALENT) 33.93/17.96 Cond Reductions: 33.93/17.96 The following Function with conditions 33.93/17.96 "undefined |Falseundefined; 33.93/17.96 " 33.93/17.96 is transformed to 33.93/17.96 "undefined = undefined1; 33.93/17.96 " 33.93/17.96 "undefined0 True = undefined; 33.93/17.96 " 33.93/17.96 "undefined1 = undefined0 False; 33.93/17.96 " 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (6) 33.93/17.96 Obligation: 33.93/17.96 mainModule Main 33.93/17.96 module Main where { 33.93/17.96 import qualified Prelude; 33.93/17.96 } 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (7) LetRed (EQUIVALENT) 33.93/17.96 Let/Where Reductions: 33.93/17.96 The bindings of the following Let/Where expression 33.93/17.96 "(showChar '[') . (shows x) . showl xs where { 33.93/17.96 showl [] = showChar ']'; 33.93/17.96 showl (x : xs) = (showChar ',') . (shows x) . showl xs; 33.93/17.96 } 33.93/17.96 " 33.93/17.96 are unpacked to the following functions on top level 33.93/17.96 "showListShowl [] = showChar ']'; 33.93/17.96 showListShowl (x : xs) = (showChar ',') . (shows x) . showListShowl xs; 33.93/17.96 " 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (8) 33.93/17.96 Obligation: 33.93/17.96 mainModule Main 33.93/17.96 module Main where { 33.93/17.96 import qualified Prelude; 33.93/17.96 } 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (9) NumRed (SOUND) 33.93/17.96 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (10) 33.93/17.96 Obligation: 33.93/17.96 mainModule Main 33.93/17.96 module Main where { 33.93/17.96 import qualified Prelude; 33.93/17.96 } 33.93/17.96 33.93/17.96 ---------------------------------------- 33.93/17.96 33.93/17.96 (11) Narrow (SOUND) 33.93/17.96 Haskell To QDPs 33.93/17.96 33.93/17.96 digraph dp_graph { 33.93/17.96 node [outthreshold=100, inthreshold=100];1[label="showList",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 33.93/17.96 3[label="showList ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 33.93/17.96 4[label="showList ww3 ww4",fontsize=16,color="burlywood",shape="triangle"];1766[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 1766[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1766 -> 5[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 1767[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 1767[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1767 -> 6[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 5[label="showList (ww30 : ww31) ww4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 33.93/17.96 6[label="showList [] ww4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 33.93/17.96 7 -> 9[label="",style="dashed", color="red", weight=0]; 33.93/17.96 7[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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 ww30) . showListShowl ww31",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 7 -> 11[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 7 -> 12[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 7 -> 13[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 8 -> 18[label="",style="dashed", color="red", weight=0]; 33.93/17.96 8[label="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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) : []) ww4",fontsize=16,color="magenta"];8 -> 19[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 8 -> 20[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 8 -> 21[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 10[label="ww31",fontsize=16,color="green",shape="box"];11[label="ww4",fontsize=16,color="green",shape="box"];12[label="ww30",fontsize=16,color="green",shape="box"];13[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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"];9[label="(showChar (Char (Succ ww6))) . (shows ww7) . showListShowl ww8",fontsize=16,color="black",shape="triangle"];9 -> 17[label="",style="solid", color="black", weight=3]; 33.93/17.96 19[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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"];20[label="ww4",fontsize=16,color="green",shape="box"];21[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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"];18[label="showString (Char (Succ ww14) : Char (Succ ww15) : []) ww16",fontsize=16,color="black",shape="triangle"];18 -> 25[label="",style="solid", color="black", weight=3]; 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33.93/17.96 450[label="ww16",fontsize=16,color="green",shape="box"];451[label="Char (Succ ww14) : Char (Succ ww15) : []",fontsize=16,color="green",shape="box"];449[label="ww117 ++ ww106",fontsize=16,color="burlywood",shape="triangle"];1768[label="ww117/ww1170 : ww1171",fontsize=10,color="white",style="solid",shape="box"];449 -> 1768[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1768 -> 589[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 1769[label="ww117/[]",fontsize=10,color="white",style="solid",shape="box"];449 -> 1769[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1769 -> 590[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 184[label="shows ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];184 -> 186[label="",style="solid", color="black", weight=3]; 33.93/17.96 185[label="(:) Char (Succ ww57) ww58",fontsize=16,color="green",shape="box"];589[label="(ww1170 : ww1171) ++ ww106",fontsize=16,color="black",shape="box"];589 -> 632[label="",style="solid", color="black", weight=3]; 33.93/17.96 590[label="[] ++ ww106",fontsize=16,color="black",shape="box"];590 -> 633[label="",style="solid", color="black", weight=3]; 33.93/17.96 186[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="blue",shape="box"];1770[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1770[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1770 -> 187[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1771[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1771[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1771 -> 188[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1772[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1772[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1772 -> 189[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1773[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1773[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1773 -> 190[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1774[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1774[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1774 -> 191[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1775[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1775[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1775 -> 192[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1776[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1776[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1776 -> 193[label="",style="solid", color="blue", weight=3]; 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33.93/17.96 1781[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1781[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1781 -> 198[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1782[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1782[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1782 -> 199[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1783[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1783[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1783 -> 200[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1784[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1784[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1784 -> 201[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1785[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1785[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1785 -> 202[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1786[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1786[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1786 -> 203[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1787[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1787[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1787 -> 204[label="",style="solid", color="blue", weight=3]; 33.93/17.96 632[label="ww1170 : ww1171 ++ ww106",fontsize=16,color="green",shape="box"];632 -> 659[label="",style="dashed", color="green", weight=3]; 33.93/17.96 633[label="ww106",fontsize=16,color="green",shape="box"];187[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];187 -> 205[label="",style="solid", color="black", weight=3]; 33.93/17.96 188[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];188 -> 206[label="",style="solid", color="black", weight=3]; 33.93/17.96 189[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];189 -> 207[label="",style="solid", color="black", weight=3]; 33.93/17.96 190[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];190 -> 208[label="",style="solid", color="black", weight=3]; 33.93/17.96 191[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];191 -> 209[label="",style="solid", color="black", weight=3]; 33.93/17.96 192[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];192 -> 210[label="",style="solid", color="black", weight=3]; 33.93/17.96 193[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];193 -> 211[label="",style="solid", color="black", weight=3]; 33.93/17.96 194[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];194 -> 212[label="",style="solid", color="black", weight=3]; 33.93/17.96 195[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];195 -> 213[label="",style="solid", color="black", weight=3]; 33.93/17.96 196[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];196 -> 214[label="",style="solid", color="black", weight=3]; 33.93/17.96 197[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];197 -> 215[label="",style="solid", color="black", weight=3]; 33.93/17.96 198[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];198 -> 216[label="",style="solid", color="black", weight=3]; 33.93/17.96 199[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];199 -> 217[label="",style="solid", color="black", weight=3]; 33.93/17.96 200[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];200 -> 218[label="",style="solid", color="black", weight=3]; 33.93/17.96 201[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="burlywood",shape="box"];1788[label="ww7/ww70 :% ww71",fontsize=10,color="white",style="solid",shape="box"];201 -> 1788[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1788 -> 219[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 202[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];202 -> 220[label="",style="solid", color="black", weight=3]; 33.93/17.96 203[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];203 -> 221[label="",style="solid", color="black", weight=3]; 33.93/17.96 204[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];204 -> 222[label="",style="solid", color="black", weight=3]; 33.93/17.96 659 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 659[label="ww1171 ++ ww106",fontsize=16,color="magenta"];659 -> 684[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 205 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 205[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];205 -> 456[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 205 -> 457[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 206 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 206[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];206 -> 458[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 206 -> 459[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 207 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 207[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];207 -> 460[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 207 -> 461[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 208 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 208[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];208 -> 462[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 208 -> 463[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 209 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 209[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];209 -> 464[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 209 -> 465[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 210 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 210[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];210 -> 466[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 210 -> 467[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 211 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 211[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];211 -> 468[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 211 -> 469[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 212 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 212[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];212 -> 470[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 212 -> 471[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 213 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 213[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];213 -> 472[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 213 -> 473[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 214 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 214[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];214 -> 474[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 214 -> 475[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 215 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 215[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];215 -> 476[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 215 -> 477[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 216 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 216[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];216 -> 478[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 216 -> 479[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 217 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 217[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];217 -> 480[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 217 -> 481[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 218 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 218[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];218 -> 482[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 218 -> 483[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 219[label="showsPrec (Pos Zero) (ww70 :% ww71) (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];219 -> 237[label="",style="solid", color="black", weight=3]; 33.93/17.96 220 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 220[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];220 -> 484[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 220 -> 485[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 221 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 221[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];221 -> 486[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 221 -> 487[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 222 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 222[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];222 -> 488[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 222 -> 489[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 684[label="ww1171",fontsize=16,color="green",shape="box"];456 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 456[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];457[label="show ww7",fontsize=16,color="black",shape="triangle"];457 -> 591[label="",style="solid", color="black", weight=3]; 33.93/17.96 458 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 458[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];459[label="show ww7",fontsize=16,color="black",shape="triangle"];459 -> 592[label="",style="solid", color="black", weight=3]; 33.93/17.96 460 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 460[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];461[label="show ww7",fontsize=16,color="black",shape="triangle"];461 -> 593[label="",style="solid", color="black", weight=3]; 33.93/17.96 462 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 462[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];463[label="show ww7",fontsize=16,color="black",shape="triangle"];463 -> 594[label="",style="solid", color="black", weight=3]; 33.93/17.96 464 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 464[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];465[label="show ww7",fontsize=16,color="black",shape="triangle"];465 -> 595[label="",style="solid", color="black", weight=3]; 33.93/17.96 466 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 466[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];467[label="show ww7",fontsize=16,color="black",shape="triangle"];467 -> 596[label="",style="solid", color="black", weight=3]; 33.93/17.96 468 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 468[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];469[label="show ww7",fontsize=16,color="black",shape="triangle"];469 -> 597[label="",style="solid", color="black", weight=3]; 33.93/17.96 470 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 470[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];471[label="show ww7",fontsize=16,color="black",shape="triangle"];471 -> 598[label="",style="solid", color="black", weight=3]; 33.93/17.96 472 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 472[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];473[label="show ww7",fontsize=16,color="black",shape="triangle"];473 -> 599[label="",style="solid", color="black", weight=3]; 33.93/17.96 474 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 474[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];475[label="show ww7",fontsize=16,color="black",shape="triangle"];475 -> 600[label="",style="solid", color="black", weight=3]; 33.93/17.96 476 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 476[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];477[label="show ww7",fontsize=16,color="black",shape="triangle"];477 -> 601[label="",style="solid", color="black", weight=3]; 33.93/17.96 478 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 478[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];479[label="show ww7",fontsize=16,color="black",shape="triangle"];479 -> 602[label="",style="solid", color="black", weight=3]; 33.93/17.96 480 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 480[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];481[label="show ww7",fontsize=16,color="black",shape="triangle"];481 -> 603[label="",style="solid", color="black", weight=3]; 33.93/17.96 482 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 482[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];483[label="show ww7",fontsize=16,color="black",shape="triangle"];483 -> 604[label="",style="solid", color="black", weight=3]; 33.93/17.96 237 -> 688[label="",style="dashed", color="red", weight=0]; 33.93/17.96 237[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww70) . (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 ww71) (showListShowl ww8 ww9)",fontsize=16,color="magenta"];237 -> 689[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 237 -> 690[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 237 -> 691[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 237 -> 692[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 237 -> 693[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 237 -> 694[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 484 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 484[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];485[label="show ww7",fontsize=16,color="black",shape="triangle"];485 -> 605[label="",style="solid", color="black", weight=3]; 33.93/17.96 486 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 486[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];487[label="show ww7",fontsize=16,color="black",shape="triangle"];487 -> 606[label="",style="solid", color="black", weight=3]; 33.93/17.96 488 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 488[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];489[label="show ww7",fontsize=16,color="black",shape="triangle"];489 -> 607[label="",style="solid", color="black", weight=3]; 33.93/17.96 294[label="showListShowl ww8 ww9",fontsize=16,color="burlywood",shape="triangle"];1789[label="ww8/ww80 : ww81",fontsize=10,color="white",style="solid",shape="box"];294 -> 1789[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1789 -> 310[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 1790[label="ww8/[]",fontsize=10,color="white",style="solid",shape="box"];294 -> 1790[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1790 -> 311[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 591[label="error []",fontsize=16,color="red",shape="box"];592[label="error []",fontsize=16,color="red",shape="box"];593[label="error []",fontsize=16,color="red",shape="box"];594[label="error []",fontsize=16,color="red",shape="box"];595[label="error []",fontsize=16,color="red",shape="box"];596[label="error []",fontsize=16,color="red",shape="box"];597[label="error []",fontsize=16,color="red",shape="box"];598[label="error []",fontsize=16,color="red",shape="box"];599[label="error []",fontsize=16,color="red",shape="box"];600[label="error []",fontsize=16,color="red",shape="box"];601[label="error []",fontsize=16,color="red",shape="box"];602[label="primShowInt ww7",fontsize=16,color="burlywood",shape="triangle"];1791[label="ww7/Pos ww70",fontsize=10,color="white",style="solid",shape="box"];602 -> 1791[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1791 -> 634[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 1792[label="ww7/Neg ww70",fontsize=10,color="white",style="solid",shape="box"];602 -> 1792[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1792 -> 635[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 603[label="error []",fontsize=16,color="red",shape="box"];604[label="error []",fontsize=16,color="red",shape="box"];689 -> 294[label="",style="dashed", color="red", weight=0]; 33.93/17.96 689[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];690[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"];691[label="ww70",fontsize=16,color="green",shape="box"];692[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"];693[label="ww71",fontsize=16,color="green",shape="box"];694[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"];688[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww138) . 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(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww148",fontsize=16,color="black",shape="box"];708 -> 712[label="",style="solid", color="black", weight=3]; 33.93/17.96 317 -> 9[label="",style="dashed", color="red", weight=0]; 33.93/17.96 317[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 (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))) . (shows ww80) . showListShowl ww81",fontsize=16,color="magenta"];317 -> 328[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 317 -> 329[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 317 -> 330[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 318 -> 179[label="",style="dashed", color="red", weight=0]; 33.93/17.96 318[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ww9",fontsize=16,color="magenta"];318 -> 331[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 318 -> 332[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 660[label="primShowInt (Pos (Succ ww700))",fontsize=16,color="black",shape="box"];660 -> 685[label="",style="solid", color="black", weight=3]; 33.93/17.96 661[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];661 -> 686[label="",style="solid", color="black", weight=3]; 33.93/17.96 662[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 ww70)",fontsize=16,color="green",shape="box"];662 -> 687[label="",style="dashed", color="green", weight=3]; 33.93/17.96 712[label="showParen0 ((shows ww138) . 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(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) False ww148",fontsize=16,color="black",shape="box"];734 -> 746[label="",style="solid", color="black", weight=3]; 33.93/17.96 748[label="ww700",fontsize=16,color="green",shape="box"];749[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];747[label="primIntToChar (mod Pos (Succ ww156) Pos (Succ ww157))",fontsize=16,color="black",shape="triangle"];747 -> 750[label="",style="solid", color="black", weight=3]; 33.93/17.96 733[label="primDivInt (Pos (Succ ww153)) (Pos (Succ ww154))",fontsize=16,color="black",shape="box"];733 -> 745[label="",style="solid", color="black", weight=3]; 33.93/17.96 746[label="(shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="black",shape="box"];746 -> 751[label="",style="solid", color="black", weight=3]; 33.93/17.96 750[label="primIntToChar (primModInt (Pos (Succ ww156)) (Pos (Succ ww157)))",fontsize=16,color="black",shape="box"];750 -> 753[label="",style="solid", color="black", weight=3]; 33.93/17.96 745[label="Pos (primDivNatS (Succ ww153) (Succ ww154))",fontsize=16,color="green",shape="box"];745 -> 752[label="",style="dashed", color="green", weight=3]; 33.93/17.96 751[label="shows ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];751 -> 754[label="",style="solid", color="black", weight=3]; 33.93/17.96 753[label="primIntToChar (Pos (primModNatS (Succ ww156) (Succ ww157)))",fontsize=16,color="black",shape="box"];753 -> 756[label="",style="solid", color="black", weight=3]; 33.93/17.96 752[label="primDivNatS (Succ ww153) (Succ ww154)",fontsize=16,color="black",shape="triangle"];752 -> 755[label="",style="solid", color="black", weight=3]; 33.93/17.96 754[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="blue",shape="box"];1795[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1795[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1795 -> 757[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1796[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1796[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1796 -> 758[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1797[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1797[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1797 -> 759[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1798[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1798[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1798 -> 760[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1799[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1799[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1799 -> 761[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1800[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1800[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1800 -> 762[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1801[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1801[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1801 -> 763[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1802[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1802[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1802 -> 764[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1803[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1803[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1803 -> 765[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1804[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1804[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1804 -> 766[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1805[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1805[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1805 -> 767[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1806[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1806[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1806 -> 768[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1807[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1807[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1807 -> 769[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1808[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1808[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1808 -> 770[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1809[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1809[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1809 -> 771[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1810[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1810[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1810 -> 772[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1811[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1811[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1811 -> 773[label="",style="solid", color="blue", weight=3]; 33.93/17.96 1812[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1812[label="",style="solid", color="blue", weight=9]; 33.93/17.96 1812 -> 774[label="",style="solid", color="blue", weight=3]; 33.93/17.96 756[label="Char (primModNatS (Succ ww156) (Succ ww157))",fontsize=16,color="green",shape="box"];756 -> 777[label="",style="dashed", color="green", weight=3]; 33.93/17.96 755[label="primDivNatS0 ww153 ww154 (primGEqNatS ww153 ww154)",fontsize=16,color="burlywood",shape="box"];1813[label="ww153/Succ ww1530",fontsize=10,color="white",style="solid",shape="box"];755 -> 1813[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1813 -> 775[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 1814[label="ww153/Zero",fontsize=10,color="white",style="solid",shape="box"];755 -> 1814[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1814 -> 776[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 757[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];757 -> 778[label="",style="solid", color="black", weight=3]; 33.93/17.96 758[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];758 -> 779[label="",style="solid", color="black", weight=3]; 33.93/17.96 759[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];759 -> 780[label="",style="solid", color="black", weight=3]; 33.93/17.96 760[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];760 -> 781[label="",style="solid", color="black", weight=3]; 33.93/17.96 761[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];761 -> 782[label="",style="solid", color="black", weight=3]; 33.93/17.96 762[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];762 -> 783[label="",style="solid", color="black", weight=3]; 33.93/17.96 763[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];763 -> 784[label="",style="solid", color="black", weight=3]; 33.93/17.96 764[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];764 -> 785[label="",style="solid", color="black", weight=3]; 33.93/17.96 765[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];765 -> 786[label="",style="solid", color="black", weight=3]; 33.93/17.96 766[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];766 -> 787[label="",style="solid", color="black", weight=3]; 33.93/17.96 767[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];767 -> 788[label="",style="solid", color="black", weight=3]; 33.93/17.96 768[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];768 -> 789[label="",style="solid", color="black", weight=3]; 33.93/17.96 769[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];769 -> 790[label="",style="solid", color="black", weight=3]; 33.93/17.96 770[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];770 -> 791[label="",style="solid", color="black", weight=3]; 33.93/17.96 771[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="burlywood",shape="box"];1815[label="ww138/ww1380 :% ww1381",fontsize=10,color="white",style="solid",shape="box"];771 -> 1815[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1815 -> 792[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 772[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];772 -> 793[label="",style="solid", color="black", weight=3]; 33.93/17.96 773[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];773 -> 794[label="",style="solid", color="black", weight=3]; 33.93/17.96 774[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];774 -> 795[label="",style="solid", color="black", weight=3]; 33.93/17.96 777[label="primModNatS (Succ ww156) (Succ ww157)",fontsize=16,color="black",shape="triangle"];777 -> 800[label="",style="solid", color="black", weight=3]; 33.93/17.96 775[label="primDivNatS0 (Succ ww1530) ww154 (primGEqNatS (Succ ww1530) ww154)",fontsize=16,color="burlywood",shape="box"];1816[label="ww154/Succ ww1540",fontsize=10,color="white",style="solid",shape="box"];775 -> 1816[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1816 -> 796[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 1817[label="ww154/Zero",fontsize=10,color="white",style="solid",shape="box"];775 -> 1817[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1817 -> 797[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 776[label="primDivNatS0 Zero ww154 (primGEqNatS Zero ww154)",fontsize=16,color="burlywood",shape="box"];1818[label="ww154/Succ ww1540",fontsize=10,color="white",style="solid",shape="box"];776 -> 1818[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1818 -> 798[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 1819[label="ww154/Zero",fontsize=10,color="white",style="solid",shape="box"];776 -> 1819[label="",style="solid", color="burlywood", weight=9]; 33.93/17.96 1819 -> 799[label="",style="solid", color="burlywood", weight=3]; 33.93/17.96 778 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 778[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];778 -> 801[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 778 -> 802[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 779 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 779[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];779 -> 803[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 779 -> 804[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 780 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 780[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];780 -> 805[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 780 -> 806[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 781 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 781[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];781 -> 807[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 781 -> 808[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 782 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 782[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];782 -> 809[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 782 -> 810[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 783 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 783[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];783 -> 811[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 783 -> 812[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 784 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 784[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];784 -> 813[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 784 -> 814[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 785 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 785[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];785 -> 815[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 785 -> 816[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 786 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 786[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];786 -> 817[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 786 -> 818[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 787 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 787[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];787 -> 819[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 787 -> 820[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 788 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 788[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];788 -> 821[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 788 -> 822[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 789 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 789[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];789 -> 823[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 789 -> 824[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 790 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 790[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];790 -> 825[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 790 -> 826[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 791 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.96 791[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];791 -> 827[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 791 -> 828[label="",style="dashed", color="magenta", weight=3]; 33.93/17.96 792[label="showsPrec (Pos Zero) (ww1380 :% ww1381) ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];792 -> 829[label="",style="solid", color="black", weight=3]; 33.93/17.97 793 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.97 793[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];793 -> 830[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 793 -> 831[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 794 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.97 794[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];794 -> 832[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 794 -> 833[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 795 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.97 795[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];795 -> 834[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 795 -> 835[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 800[label="primModNatS0 ww156 ww157 (primGEqNatS ww156 ww157)",fontsize=16,color="burlywood",shape="box"];1820[label="ww156/Succ ww1560",fontsize=10,color="white",style="solid",shape="box"];800 -> 1820[label="",style="solid", color="burlywood", weight=9]; 33.93/17.97 1820 -> 840[label="",style="solid", color="burlywood", weight=3]; 33.93/17.97 1821[label="ww156/Zero",fontsize=10,color="white",style="solid",shape="box"];800 -> 1821[label="",style="solid", color="burlywood", weight=9]; 33.93/17.97 1821 -> 841[label="",style="solid", color="burlywood", weight=3]; 33.93/17.97 796[label="primDivNatS0 (Succ ww1530) (Succ ww1540) (primGEqNatS (Succ ww1530) (Succ ww1540))",fontsize=16,color="black",shape="box"];796 -> 836[label="",style="solid", color="black", weight=3]; 33.93/17.97 797[label="primDivNatS0 (Succ ww1530) Zero (primGEqNatS (Succ ww1530) Zero)",fontsize=16,color="black",shape="box"];797 -> 837[label="",style="solid", color="black", weight=3]; 33.93/17.97 798[label="primDivNatS0 Zero (Succ ww1540) (primGEqNatS Zero (Succ ww1540))",fontsize=16,color="black",shape="box"];798 -> 838[label="",style="solid", color="black", weight=3]; 33.93/17.97 799[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];799 -> 839[label="",style="solid", color="black", weight=3]; 33.93/17.97 801[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="black",shape="triangle"];801 -> 842[label="",style="solid", color="black", weight=3]; 33.93/17.97 802 -> 457[label="",style="dashed", color="red", weight=0]; 33.93/17.97 802[label="show ww138",fontsize=16,color="magenta"];802 -> 843[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 803 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.97 803[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];804 -> 459[label="",style="dashed", color="red", weight=0]; 33.93/17.97 804[label="show ww138",fontsize=16,color="magenta"];804 -> 844[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 805 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.97 805[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];806 -> 461[label="",style="dashed", color="red", weight=0]; 33.93/17.97 806[label="show ww138",fontsize=16,color="magenta"];806 -> 845[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 807 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.97 807[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];808 -> 463[label="",style="dashed", color="red", weight=0]; 33.93/17.97 808[label="show ww138",fontsize=16,color="magenta"];808 -> 846[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 809 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.97 809[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];810 -> 465[label="",style="dashed", color="red", weight=0]; 33.93/17.97 810[label="show ww138",fontsize=16,color="magenta"];810 -> 847[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 811 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.97 811[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];812 -> 467[label="",style="dashed", color="red", weight=0]; 33.93/17.97 812[label="show ww138",fontsize=16,color="magenta"];812 -> 848[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 813 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.97 813[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];814 -> 469[label="",style="dashed", color="red", weight=0]; 33.93/17.97 814[label="show ww138",fontsize=16,color="magenta"];814 -> 849[label="",style="dashed", color="magenta", weight=3]; 33.93/17.97 815 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.97 815[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];816 -> 471[label="",style="dashed", color="red", weight=0]; 33.93/17.98 816[label="show ww138",fontsize=16,color="magenta"];816 -> 850[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 817 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 817[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];818 -> 473[label="",style="dashed", color="red", weight=0]; 33.93/17.98 818[label="show ww138",fontsize=16,color="magenta"];818 -> 851[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 819 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 819[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];820 -> 475[label="",style="dashed", color="red", weight=0]; 33.93/17.98 820[label="show ww138",fontsize=16,color="magenta"];820 -> 852[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 821 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 821[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];822 -> 477[label="",style="dashed", color="red", weight=0]; 33.93/17.98 822[label="show ww138",fontsize=16,color="magenta"];822 -> 853[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 823 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 823[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];824 -> 479[label="",style="dashed", color="red", weight=0]; 33.93/17.98 824[label="show ww138",fontsize=16,color="magenta"];824 -> 854[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 825 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 825[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];826 -> 481[label="",style="dashed", color="red", weight=0]; 33.93/17.98 826[label="show ww138",fontsize=16,color="magenta"];826 -> 855[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 827 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 827[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];828 -> 483[label="",style="dashed", color="red", weight=0]; 33.93/17.98 828[label="show ww138",fontsize=16,color="magenta"];828 -> 856[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 829 -> 688[label="",style="dashed", color="red", weight=0]; 33.93/17.98 829[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1380) . (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 ww1381) ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="magenta"];829 -> 857[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 829 -> 858[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 829 -> 859[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 829 -> 860[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 829 -> 861[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 829 -> 862[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 830 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 830[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];831 -> 485[label="",style="dashed", color="red", weight=0]; 33.93/17.98 831[label="show ww138",fontsize=16,color="magenta"];831 -> 863[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 832 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 832[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];833 -> 487[label="",style="dashed", color="red", weight=0]; 33.93/17.98 833[label="show ww138",fontsize=16,color="magenta"];833 -> 864[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 834 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 834[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];835 -> 489[label="",style="dashed", color="red", weight=0]; 33.93/17.98 835[label="show ww138",fontsize=16,color="magenta"];835 -> 865[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 840[label="primModNatS0 (Succ ww1560) ww157 (primGEqNatS (Succ ww1560) ww157)",fontsize=16,color="burlywood",shape="box"];1822[label="ww157/Succ ww1570",fontsize=10,color="white",style="solid",shape="box"];840 -> 1822[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1822 -> 871[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1823[label="ww157/Zero",fontsize=10,color="white",style="solid",shape="box"];840 -> 1823[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1823 -> 872[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 841[label="primModNatS0 Zero ww157 (primGEqNatS Zero ww157)",fontsize=16,color="burlywood",shape="box"];1824[label="ww157/Succ ww1570",fontsize=10,color="white",style="solid",shape="box"];841 -> 1824[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1824 -> 873[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1825[label="ww157/Zero",fontsize=10,color="white",style="solid",shape="box"];841 -> 1825[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1825 -> 874[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 836 -> 1482[label="",style="dashed", color="red", weight=0]; 33.93/17.98 836[label="primDivNatS0 (Succ ww1530) (Succ ww1540) (primGEqNatS ww1530 ww1540)",fontsize=16,color="magenta"];836 -> 1483[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 836 -> 1484[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 836 -> 1485[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 836 -> 1486[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 837[label="primDivNatS0 (Succ ww1530) Zero True",fontsize=16,color="black",shape="box"];837 -> 868[label="",style="solid", color="black", weight=3]; 33.93/17.98 838[label="primDivNatS0 Zero (Succ ww1540) False",fontsize=16,color="black",shape="box"];838 -> 869[label="",style="solid", color="black", weight=3]; 33.93/17.98 839[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];839 -> 870[label="",style="solid", color="black", weight=3]; 33.93/17.98 842[label="showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []) (shows ww142 ww148)",fontsize=16,color="black",shape="box"];842 -> 875[label="",style="solid", color="black", weight=3]; 33.93/17.98 843[label="ww138",fontsize=16,color="green",shape="box"];844[label="ww138",fontsize=16,color="green",shape="box"];845[label="ww138",fontsize=16,color="green",shape="box"];846[label="ww138",fontsize=16,color="green",shape="box"];847[label="ww138",fontsize=16,color="green",shape="box"];848[label="ww138",fontsize=16,color="green",shape="box"];849[label="ww138",fontsize=16,color="green",shape="box"];850[label="ww138",fontsize=16,color="green",shape="box"];851[label="ww138",fontsize=16,color="green",shape="box"];852[label="ww138",fontsize=16,color="green",shape="box"];853[label="ww138",fontsize=16,color="green",shape="box"];854[label="ww138",fontsize=16,color="green",shape="box"];855[label="ww138",fontsize=16,color="green",shape="box"];856[label="ww138",fontsize=16,color="green",shape="box"];857 -> 801[label="",style="dashed", color="red", weight=0]; 33.93/17.98 857[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];858[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"];859[label="ww1380",fontsize=16,color="green",shape="box"];860[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"];861[label="ww1381",fontsize=16,color="green",shape="box"];862[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"];863[label="ww138",fontsize=16,color="green",shape="box"];864[label="ww138",fontsize=16,color="green",shape="box"];865[label="ww138",fontsize=16,color="green",shape="box"];871[label="primModNatS0 (Succ ww1560) (Succ ww1570) (primGEqNatS (Succ ww1560) (Succ ww1570))",fontsize=16,color="black",shape="box"];871 -> 882[label="",style="solid", color="black", weight=3]; 33.93/17.98 872[label="primModNatS0 (Succ ww1560) Zero (primGEqNatS (Succ ww1560) Zero)",fontsize=16,color="black",shape="box"];872 -> 883[label="",style="solid", color="black", weight=3]; 33.93/17.98 873[label="primModNatS0 Zero (Succ ww1570) (primGEqNatS Zero (Succ ww1570))",fontsize=16,color="black",shape="box"];873 -> 884[label="",style="solid", color="black", weight=3]; 33.93/17.98 874[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];874 -> 885[label="",style="solid", color="black", weight=3]; 33.93/17.98 1483[label="ww1530",fontsize=16,color="green",shape="box"];1484[label="ww1530",fontsize=16,color="green",shape="box"];1485[label="ww1540",fontsize=16,color="green",shape="box"];1486[label="ww1540",fontsize=16,color="green",shape="box"];1482[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS ww202 ww203)",fontsize=16,color="burlywood",shape="triangle"];1826[label="ww202/Succ ww2020",fontsize=10,color="white",style="solid",shape="box"];1482 -> 1826[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1826 -> 1523[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1827[label="ww202/Zero",fontsize=10,color="white",style="solid",shape="box"];1482 -> 1827[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1827 -> 1524[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 868[label="Succ (primDivNatS (primMinusNatS (Succ ww1530) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];868 -> 880[label="",style="dashed", color="green", weight=3]; 33.93/17.98 869[label="Zero",fontsize=16,color="green",shape="box"];870[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];870 -> 881[label="",style="dashed", color="green", weight=3]; 33.93/17.98 875 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 875[label="(++) (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []) shows ww142 ww148",fontsize=16,color="magenta"];875 -> 886[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 875 -> 887[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 882 -> 1543[label="",style="dashed", color="red", weight=0]; 33.93/17.98 882[label="primModNatS0 (Succ ww1560) (Succ ww1570) (primGEqNatS ww1560 ww1570)",fontsize=16,color="magenta"];882 -> 1544[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 882 -> 1545[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 882 -> 1546[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 882 -> 1547[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 883[label="primModNatS0 (Succ ww1560) Zero True",fontsize=16,color="black",shape="box"];883 -> 896[label="",style="solid", color="black", weight=3]; 33.93/17.98 884[label="primModNatS0 Zero (Succ ww1570) False",fontsize=16,color="black",shape="box"];884 -> 897[label="",style="solid", color="black", weight=3]; 33.93/17.98 885[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];885 -> 898[label="",style="solid", color="black", weight=3]; 33.93/17.98 1523[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) ww203)",fontsize=16,color="burlywood",shape="box"];1828[label="ww203/Succ ww2030",fontsize=10,color="white",style="solid",shape="box"];1523 -> 1828[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1828 -> 1535[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1829[label="ww203/Zero",fontsize=10,color="white",style="solid",shape="box"];1523 -> 1829[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1829 -> 1536[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1524[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero ww203)",fontsize=16,color="burlywood",shape="box"];1830[label="ww203/Succ ww2030",fontsize=10,color="white",style="solid",shape="box"];1524 -> 1830[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1830 -> 1537[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1831[label="ww203/Zero",fontsize=10,color="white",style="solid",shape="box"];1524 -> 1831[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1831 -> 1538[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 880 -> 1726[label="",style="dashed", color="red", weight=0]; 33.93/17.98 880[label="primDivNatS (primMinusNatS (Succ ww1530) Zero) (Succ Zero)",fontsize=16,color="magenta"];880 -> 1727[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 880 -> 1728[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 880 -> 1729[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 881 -> 1726[label="",style="dashed", color="red", weight=0]; 33.93/17.98 881[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];881 -> 1730[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 881 -> 1731[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 881 -> 1732[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 886[label="shows ww142 ww148",fontsize=16,color="black",shape="box"];886 -> 899[label="",style="solid", color="black", weight=3]; 33.93/17.98 887[label="Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []",fontsize=16,color="green",shape="box"];1544[label="ww1570",fontsize=16,color="green",shape="box"];1545[label="ww1560",fontsize=16,color="green",shape="box"];1546[label="ww1570",fontsize=16,color="green",shape="box"];1547[label="ww1560",fontsize=16,color="green",shape="box"];1543[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS ww207 ww208)",fontsize=16,color="burlywood",shape="triangle"];1832[label="ww207/Succ ww2070",fontsize=10,color="white",style="solid",shape="box"];1543 -> 1832[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1832 -> 1584[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1833[label="ww207/Zero",fontsize=10,color="white",style="solid",shape="box"];1543 -> 1833[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1833 -> 1585[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 896 -> 1630[label="",style="dashed", color="red", weight=0]; 33.93/17.98 896[label="primModNatS (primMinusNatS (Succ ww1560) Zero) (Succ Zero)",fontsize=16,color="magenta"];896 -> 1631[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 896 -> 1632[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 896 -> 1633[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 897[label="Succ Zero",fontsize=16,color="green",shape="box"];898 -> 1630[label="",style="dashed", color="red", weight=0]; 33.93/17.98 898[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];898 -> 1634[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 898 -> 1635[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 898 -> 1636[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1535[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) (Succ ww2030))",fontsize=16,color="black",shape="box"];1535 -> 1586[label="",style="solid", color="black", weight=3]; 33.93/17.98 1536[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) Zero)",fontsize=16,color="black",shape="box"];1536 -> 1587[label="",style="solid", color="black", weight=3]; 33.93/17.98 1537[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero (Succ ww2030))",fontsize=16,color="black",shape="box"];1537 -> 1588[label="",style="solid", color="black", weight=3]; 33.93/17.98 1538[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1538 -> 1589[label="",style="solid", color="black", weight=3]; 33.93/17.98 1727[label="Succ ww1530",fontsize=16,color="green",shape="box"];1728[label="Zero",fontsize=16,color="green",shape="box"];1729[label="Zero",fontsize=16,color="green",shape="box"];1726[label="primDivNatS (primMinusNatS ww214 ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="triangle"];1834[label="ww214/Succ ww2140",fontsize=10,color="white",style="solid",shape="box"];1726 -> 1834[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1834 -> 1751[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1835[label="ww214/Zero",fontsize=10,color="white",style="solid",shape="box"];1726 -> 1835[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1835 -> 1752[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1730[label="Zero",fontsize=16,color="green",shape="box"];1731[label="Zero",fontsize=16,color="green",shape="box"];1732[label="Zero",fontsize=16,color="green",shape="box"];899[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="blue",shape="box"];1836[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1836[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1836 -> 914[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1837[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1837[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1837 -> 915[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1838[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1838[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1838 -> 916[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1839[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1839[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1839 -> 917[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1840[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1840[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1840 -> 918[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1841[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1841[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1841 -> 919[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1842[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1842[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1842 -> 920[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1843[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1843[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1843 -> 921[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1844[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1844[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1844 -> 922[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1845[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1845[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1845 -> 923[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1846[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1846[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1846 -> 924[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1847[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1847[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1847 -> 925[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1848[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1848[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1848 -> 926[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1849[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1849[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1849 -> 927[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1850[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1850[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1850 -> 928[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1851[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1851[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1851 -> 929[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1852[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1852[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1852 -> 930[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1853[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1853[label="",style="solid", color="blue", weight=9]; 33.93/17.98 1853 -> 931[label="",style="solid", color="blue", weight=3]; 33.93/17.98 1584[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) ww208)",fontsize=16,color="burlywood",shape="box"];1854[label="ww208/Succ ww2080",fontsize=10,color="white",style="solid",shape="box"];1584 -> 1854[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1854 -> 1594[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1855[label="ww208/Zero",fontsize=10,color="white",style="solid",shape="box"];1584 -> 1855[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1855 -> 1595[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1585[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero ww208)",fontsize=16,color="burlywood",shape="box"];1856[label="ww208/Succ ww2080",fontsize=10,color="white",style="solid",shape="box"];1585 -> 1856[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1856 -> 1596[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1857[label="ww208/Zero",fontsize=10,color="white",style="solid",shape="box"];1585 -> 1857[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1857 -> 1597[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1631[label="Zero",fontsize=16,color="green",shape="box"];1632[label="Zero",fontsize=16,color="green",shape="box"];1633[label="Succ ww1560",fontsize=16,color="green",shape="box"];1630[label="primModNatS (primMinusNatS ww210 ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="triangle"];1858[label="ww210/Succ ww2100",fontsize=10,color="white",style="solid",shape="box"];1630 -> 1858[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1858 -> 1661[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1859[label="ww210/Zero",fontsize=10,color="white",style="solid",shape="box"];1630 -> 1859[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1859 -> 1662[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1634[label="Zero",fontsize=16,color="green",shape="box"];1635[label="Zero",fontsize=16,color="green",shape="box"];1636[label="Zero",fontsize=16,color="green",shape="box"];1586 -> 1482[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1586[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS ww2020 ww2030)",fontsize=16,color="magenta"];1586 -> 1598[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1586 -> 1599[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1587[label="primDivNatS0 (Succ ww200) (Succ ww201) True",fontsize=16,color="black",shape="triangle"];1587 -> 1600[label="",style="solid", color="black", weight=3]; 33.93/17.98 1588[label="primDivNatS0 (Succ ww200) (Succ ww201) False",fontsize=16,color="black",shape="box"];1588 -> 1601[label="",style="solid", color="black", weight=3]; 33.93/17.98 1589 -> 1587[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1589[label="primDivNatS0 (Succ ww200) (Succ ww201) True",fontsize=16,color="magenta"];1751[label="primDivNatS (primMinusNatS (Succ ww2140) ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="box"];1860[label="ww215/Succ ww2150",fontsize=10,color="white",style="solid",shape="box"];1751 -> 1860[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1860 -> 1753[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1861[label="ww215/Zero",fontsize=10,color="white",style="solid",shape="box"];1751 -> 1861[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1861 -> 1754[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1752[label="primDivNatS (primMinusNatS Zero ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="box"];1862[label="ww215/Succ ww2150",fontsize=10,color="white",style="solid",shape="box"];1752 -> 1862[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1862 -> 1755[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1863[label="ww215/Zero",fontsize=10,color="white",style="solid",shape="box"];1752 -> 1863[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1863 -> 1756[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 914[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];914 -> 945[label="",style="solid", color="black", weight=3]; 33.93/17.98 915[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];915 -> 946[label="",style="solid", color="black", weight=3]; 33.93/17.98 916[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];916 -> 947[label="",style="solid", color="black", weight=3]; 33.93/17.98 917[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];917 -> 948[label="",style="solid", color="black", weight=3]; 33.93/17.98 918[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];918 -> 949[label="",style="solid", color="black", weight=3]; 33.93/17.98 919[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];919 -> 950[label="",style="solid", color="black", weight=3]; 33.93/17.98 920[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];920 -> 951[label="",style="solid", color="black", weight=3]; 33.93/17.98 921[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];921 -> 952[label="",style="solid", color="black", weight=3]; 33.93/17.98 922[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];922 -> 953[label="",style="solid", color="black", weight=3]; 33.93/17.98 923[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];923 -> 954[label="",style="solid", color="black", weight=3]; 33.93/17.98 924[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];924 -> 955[label="",style="solid", color="black", weight=3]; 33.93/17.98 925[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];925 -> 956[label="",style="solid", color="black", weight=3]; 33.93/17.98 926[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];926 -> 957[label="",style="solid", color="black", weight=3]; 33.93/17.98 927[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];927 -> 958[label="",style="solid", color="black", weight=3]; 33.93/17.98 928[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="burlywood",shape="box"];1864[label="ww142/ww1420 :% ww1421",fontsize=10,color="white",style="solid",shape="box"];928 -> 1864[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1864 -> 959[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 929[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];929 -> 960[label="",style="solid", color="black", weight=3]; 33.93/17.98 930[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];930 -> 961[label="",style="solid", color="black", weight=3]; 33.93/17.98 931[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];931 -> 962[label="",style="solid", color="black", weight=3]; 33.93/17.98 1594[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) (Succ ww2080))",fontsize=16,color="black",shape="box"];1594 -> 1608[label="",style="solid", color="black", weight=3]; 33.93/17.98 1595[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) Zero)",fontsize=16,color="black",shape="box"];1595 -> 1609[label="",style="solid", color="black", weight=3]; 33.93/17.98 1596[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero (Succ ww2080))",fontsize=16,color="black",shape="box"];1596 -> 1610[label="",style="solid", color="black", weight=3]; 33.93/17.98 1597[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1597 -> 1611[label="",style="solid", color="black", weight=3]; 33.93/17.98 1661[label="primModNatS (primMinusNatS (Succ ww2100) ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="box"];1865[label="ww211/Succ ww2110",fontsize=10,color="white",style="solid",shape="box"];1661 -> 1865[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1865 -> 1667[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1866[label="ww211/Zero",fontsize=10,color="white",style="solid",shape="box"];1661 -> 1866[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1866 -> 1668[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1662[label="primModNatS (primMinusNatS Zero ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="box"];1867[label="ww211/Succ ww2110",fontsize=10,color="white",style="solid",shape="box"];1662 -> 1867[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1867 -> 1669[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1868[label="ww211/Zero",fontsize=10,color="white",style="solid",shape="box"];1662 -> 1868[label="",style="solid", color="burlywood", weight=9]; 33.93/17.98 1868 -> 1670[label="",style="solid", color="burlywood", weight=3]; 33.93/17.98 1598[label="ww2020",fontsize=16,color="green",shape="box"];1599[label="ww2030",fontsize=16,color="green",shape="box"];1600[label="Succ (primDivNatS (primMinusNatS (Succ ww200) (Succ ww201)) (Succ (Succ ww201)))",fontsize=16,color="green",shape="box"];1600 -> 1612[label="",style="dashed", color="green", weight=3]; 33.93/17.98 1601[label="Zero",fontsize=16,color="green",shape="box"];1753[label="primDivNatS (primMinusNatS (Succ ww2140) (Succ ww2150)) (Succ ww216)",fontsize=16,color="black",shape="box"];1753 -> 1757[label="",style="solid", color="black", weight=3]; 33.93/17.98 1754[label="primDivNatS (primMinusNatS (Succ ww2140) Zero) (Succ ww216)",fontsize=16,color="black",shape="box"];1754 -> 1758[label="",style="solid", color="black", weight=3]; 33.93/17.98 1755[label="primDivNatS (primMinusNatS Zero (Succ ww2150)) (Succ ww216)",fontsize=16,color="black",shape="box"];1755 -> 1759[label="",style="solid", color="black", weight=3]; 33.93/17.98 1756[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww216)",fontsize=16,color="black",shape="box"];1756 -> 1760[label="",style="solid", color="black", weight=3]; 33.93/17.98 945 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 945[label="show ww142 ++ ww148",fontsize=16,color="magenta"];945 -> 974[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 945 -> 975[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 946 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 946[label="show ww142 ++ ww148",fontsize=16,color="magenta"];946 -> 976[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 946 -> 977[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 947 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 947[label="show ww142 ++ ww148",fontsize=16,color="magenta"];947 -> 978[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 947 -> 979[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 948 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 948[label="show ww142 ++ ww148",fontsize=16,color="magenta"];948 -> 980[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 948 -> 981[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 949 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 949[label="show ww142 ++ ww148",fontsize=16,color="magenta"];949 -> 982[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 949 -> 983[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 950 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 950[label="show ww142 ++ ww148",fontsize=16,color="magenta"];950 -> 984[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 950 -> 985[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 951 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 951[label="show ww142 ++ ww148",fontsize=16,color="magenta"];951 -> 986[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 951 -> 987[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 952 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 952[label="show ww142 ++ ww148",fontsize=16,color="magenta"];952 -> 988[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 952 -> 989[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 953 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 953[label="show ww142 ++ ww148",fontsize=16,color="magenta"];953 -> 990[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 953 -> 991[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 954 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 954[label="show ww142 ++ ww148",fontsize=16,color="magenta"];954 -> 992[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 954 -> 993[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 955 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 955[label="show ww142 ++ ww148",fontsize=16,color="magenta"];955 -> 994[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 955 -> 995[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 956 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 956[label="show ww142 ++ ww148",fontsize=16,color="magenta"];956 -> 996[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 956 -> 997[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 957 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 957[label="show ww142 ++ ww148",fontsize=16,color="magenta"];957 -> 998[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 957 -> 999[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 958 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 958[label="show ww142 ++ ww148",fontsize=16,color="magenta"];958 -> 1000[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 958 -> 1001[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 959[label="showsPrec (Pos Zero) (ww1420 :% ww1421) ww148",fontsize=16,color="black",shape="box"];959 -> 1002[label="",style="solid", color="black", weight=3]; 33.93/17.98 960 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 960[label="show ww142 ++ ww148",fontsize=16,color="magenta"];960 -> 1003[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 960 -> 1004[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 961 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 961[label="show ww142 ++ ww148",fontsize=16,color="magenta"];961 -> 1005[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 961 -> 1006[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 962 -> 449[label="",style="dashed", color="red", weight=0]; 33.93/17.98 962[label="show ww142 ++ ww148",fontsize=16,color="magenta"];962 -> 1007[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 962 -> 1008[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1608 -> 1543[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1608[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS ww2070 ww2080)",fontsize=16,color="magenta"];1608 -> 1617[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1608 -> 1618[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1609[label="primModNatS0 (Succ ww205) (Succ ww206) True",fontsize=16,color="black",shape="triangle"];1609 -> 1619[label="",style="solid", color="black", weight=3]; 33.93/17.98 1610[label="primModNatS0 (Succ ww205) (Succ ww206) False",fontsize=16,color="black",shape="box"];1610 -> 1620[label="",style="solid", color="black", weight=3]; 33.93/17.98 1611 -> 1609[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1611[label="primModNatS0 (Succ ww205) (Succ ww206) True",fontsize=16,color="magenta"];1667[label="primModNatS (primMinusNatS (Succ ww2100) (Succ ww2110)) (Succ ww212)",fontsize=16,color="black",shape="box"];1667 -> 1675[label="",style="solid", color="black", weight=3]; 33.93/17.98 1668[label="primModNatS (primMinusNatS (Succ ww2100) Zero) (Succ ww212)",fontsize=16,color="black",shape="box"];1668 -> 1676[label="",style="solid", color="black", weight=3]; 33.93/17.98 1669[label="primModNatS (primMinusNatS Zero (Succ ww2110)) (Succ ww212)",fontsize=16,color="black",shape="box"];1669 -> 1677[label="",style="solid", color="black", weight=3]; 33.93/17.98 1670[label="primModNatS (primMinusNatS Zero Zero) (Succ ww212)",fontsize=16,color="black",shape="box"];1670 -> 1678[label="",style="solid", color="black", weight=3]; 33.93/17.98 1612 -> 1726[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1612[label="primDivNatS (primMinusNatS (Succ ww200) (Succ ww201)) (Succ (Succ ww201))",fontsize=16,color="magenta"];1612 -> 1733[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1612 -> 1734[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1612 -> 1735[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1757 -> 1726[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1757[label="primDivNatS (primMinusNatS ww2140 ww2150) (Succ ww216)",fontsize=16,color="magenta"];1757 -> 1761[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1757 -> 1762[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1758 -> 752[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1758[label="primDivNatS (Succ ww2140) (Succ ww216)",fontsize=16,color="magenta"];1758 -> 1763[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1758 -> 1764[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1759[label="primDivNatS Zero (Succ ww216)",fontsize=16,color="black",shape="triangle"];1759 -> 1765[label="",style="solid", color="black", weight=3]; 33.93/17.98 1760 -> 1759[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1760[label="primDivNatS Zero (Succ ww216)",fontsize=16,color="magenta"];974[label="ww148",fontsize=16,color="green",shape="box"];975 -> 457[label="",style="dashed", color="red", weight=0]; 33.93/17.98 975[label="show ww142",fontsize=16,color="magenta"];975 -> 1022[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 976[label="ww148",fontsize=16,color="green",shape="box"];977 -> 459[label="",style="dashed", color="red", weight=0]; 33.93/17.98 977[label="show ww142",fontsize=16,color="magenta"];977 -> 1023[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 978[label="ww148",fontsize=16,color="green",shape="box"];979 -> 461[label="",style="dashed", color="red", weight=0]; 33.93/17.98 979[label="show ww142",fontsize=16,color="magenta"];979 -> 1024[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 980[label="ww148",fontsize=16,color="green",shape="box"];981 -> 463[label="",style="dashed", color="red", weight=0]; 33.93/17.98 981[label="show ww142",fontsize=16,color="magenta"];981 -> 1025[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 982[label="ww148",fontsize=16,color="green",shape="box"];983 -> 465[label="",style="dashed", color="red", weight=0]; 33.93/17.98 983[label="show ww142",fontsize=16,color="magenta"];983 -> 1026[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 984[label="ww148",fontsize=16,color="green",shape="box"];985 -> 467[label="",style="dashed", color="red", weight=0]; 33.93/17.98 985[label="show ww142",fontsize=16,color="magenta"];985 -> 1027[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 986[label="ww148",fontsize=16,color="green",shape="box"];987 -> 469[label="",style="dashed", color="red", weight=0]; 33.93/17.98 987[label="show ww142",fontsize=16,color="magenta"];987 -> 1028[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 988[label="ww148",fontsize=16,color="green",shape="box"];989 -> 471[label="",style="dashed", color="red", weight=0]; 33.93/17.98 989[label="show ww142",fontsize=16,color="magenta"];989 -> 1029[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 990[label="ww148",fontsize=16,color="green",shape="box"];991 -> 473[label="",style="dashed", color="red", weight=0]; 33.93/17.98 991[label="show ww142",fontsize=16,color="magenta"];991 -> 1030[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 992[label="ww148",fontsize=16,color="green",shape="box"];993 -> 475[label="",style="dashed", color="red", weight=0]; 33.93/17.98 993[label="show ww142",fontsize=16,color="magenta"];993 -> 1031[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 994[label="ww148",fontsize=16,color="green",shape="box"];995 -> 477[label="",style="dashed", color="red", weight=0]; 33.93/17.98 995[label="show ww142",fontsize=16,color="magenta"];995 -> 1032[label="",style="dashed", color="magenta", weight=3]; 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33.93/17.98 1617[label="ww2070",fontsize=16,color="green",shape="box"];1618[label="ww2080",fontsize=16,color="green",shape="box"];1619 -> 1630[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1619[label="primModNatS (primMinusNatS (Succ ww205) (Succ ww206)) (Succ (Succ ww206))",fontsize=16,color="magenta"];1619 -> 1643[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1619 -> 1644[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1619 -> 1645[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1620[label="Succ (Succ ww205)",fontsize=16,color="green",shape="box"];1675 -> 1630[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1675[label="primModNatS (primMinusNatS ww2100 ww2110) (Succ ww212)",fontsize=16,color="magenta"];1675 -> 1685[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1675 -> 1686[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1676 -> 777[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1676[label="primModNatS (Succ ww2100) (Succ ww212)",fontsize=16,color="magenta"];1676 -> 1687[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1676 -> 1688[label="",style="dashed", color="magenta", weight=3]; 33.93/17.98 1677[label="primModNatS Zero (Succ ww212)",fontsize=16,color="black",shape="triangle"];1677 -> 1689[label="",style="solid", color="black", weight=3]; 33.93/17.98 1678 -> 1677[label="",style="dashed", color="red", weight=0]; 33.93/17.98 1678[label="primModNatS Zero (Succ ww212)",fontsize=16,color="magenta"];1733[label="Succ ww200",fontsize=16,color="green",shape="box"];1734[label="Succ ww201",fontsize=16,color="green",shape="box"];1735[label="Succ ww201",fontsize=16,color="green",shape="box"];1761[label="ww2140",fontsize=16,color="green",shape="box"];1762[label="ww2150",fontsize=16,color="green",shape="box"];1763[label="ww2140",fontsize=16,color="green",shape="box"];1764[label="ww216",fontsize=16,color="green",shape="box"];1765[label="Zero",fontsize=16,color="green",shape="box"];1022[label="ww142",fontsize=16,color="green",shape="box"];1023[label="ww142",fontsize=16,color="green",shape="box"];1024[label="ww142",fontsize=16,color="green",shape="box"];1025[label="ww142",fontsize=16,color="green",shape="box"];1026[label="ww142",fontsize=16,color="green",shape="box"];1027[label="ww142",fontsize=16,color="green",shape="box"];1028[label="ww142",fontsize=16,color="green",shape="box"];1029[label="ww142",fontsize=16,color="green",shape="box"];1030[label="ww142",fontsize=16,color="green",shape="box"];1031[label="ww142",fontsize=16,color="green",shape="box"];1032[label="ww142",fontsize=16,color="green",shape="box"];1033[label="ww142",fontsize=16,color="green",shape="box"];1034[label="ww142",fontsize=16,color="green",shape="box"];1035[label="ww142",fontsize=16,color="green",shape="box"];1036[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"];1037[label="ww1420",fontsize=16,color="green",shape="box"];1038[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"];1039[label="ww1421",fontsize=16,color="green",shape="box"];1040[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"];1041[label="ww142",fontsize=16,color="green",shape="box"];1042[label="ww142",fontsize=16,color="green",shape="box"];1043[label="ww142",fontsize=16,color="green",shape="box"];1643[label="Succ ww206",fontsize=16,color="green",shape="box"];1644[label="Succ ww206",fontsize=16,color="green",shape="box"];1645[label="Succ ww205",fontsize=16,color="green",shape="box"];1685[label="ww2110",fontsize=16,color="green",shape="box"];1686[label="ww2100",fontsize=16,color="green",shape="box"];1687[label="ww2100",fontsize=16,color="green",shape="box"];1688[label="ww212",fontsize=16,color="green",shape="box"];1689[label="Zero",fontsize=16,color="green",shape="box"];} 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (12) 33.93/17.98 Complex Obligation (AND) 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (13) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS0(ww200, ww201, Zero, Zero) -> new_primDivNatS00(ww200, ww201) 33.93/17.98 new_primDivNatS00(ww200, ww201) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) 33.93/17.98 new_primDivNatS(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS1(Succ(ww1530), Zero) -> new_primDivNatS(Succ(ww1530), Zero, Zero) 33.93/17.98 new_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS0(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) 33.93/17.98 new_primDivNatS1(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS0(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) 33.93/17.98 new_primDivNatS(Succ(ww2140), Zero, ww216) -> new_primDivNatS1(ww2140, ww216) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (14) DependencyGraphProof (EQUIVALENT) 33.93/17.98 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (15) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS00(ww200, ww201) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) 33.93/17.98 new_primDivNatS(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS(Succ(ww2140), Zero, ww216) -> new_primDivNatS1(ww2140, ww216) 33.93/17.98 new_primDivNatS1(Succ(ww1530), Zero) -> new_primDivNatS(Succ(ww1530), Zero, Zero) 33.93/17.98 new_primDivNatS1(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS0(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS0(ww200, ww201, Zero, Zero) -> new_primDivNatS00(ww200, ww201) 33.93/17.98 new_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS0(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (16) QDPOrderProof (EQUIVALENT) 33.93/17.98 We use the reduction pair processor [LPAR04,JAR06]. 33.93/17.98 33.93/17.98 33.93/17.98 The following pairs can be oriented strictly and are deleted. 33.93/17.98 33.93/17.98 new_primDivNatS(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS1(Succ(ww1530), Zero) -> new_primDivNatS(Succ(ww1530), Zero, Zero) 33.93/17.98 new_primDivNatS1(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS0(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 The remaining pairs can at least be oriented weakly. 33.93/17.98 Used ordering: Polynomial interpretation [POLO]: 33.93/17.98 33.93/17.98 POL(Succ(x_1)) = 1 + x_1 33.93/17.98 POL(Zero) = 0 33.93/17.98 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 33.93/17.98 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 33.93/17.98 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 33.93/17.98 POL(new_primDivNatS1(x_1, x_2)) = 1 + x_1 33.93/17.98 33.93/17.98 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 33.93/17.98 none 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (17) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS00(ww200, ww201) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) 33.93/17.98 new_primDivNatS(Succ(ww2140), Zero, ww216) -> new_primDivNatS1(ww2140, ww216) 33.93/17.98 new_primDivNatS0(ww200, ww201, Zero, Zero) -> new_primDivNatS00(ww200, ww201) 33.93/17.98 new_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS0(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (18) DependencyGraphProof (EQUIVALENT) 33.93/17.98 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (19) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (20) QDPSizeChangeProof (EQUIVALENT) 33.93/17.98 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. 33.93/17.98 33.93/17.98 From the DPs we obtained the following set of size-change graphs: 33.93/17.98 *new_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) 33.93/17.98 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (21) 33.93/17.98 YES 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (22) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_HugsException, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_Maybe, bg), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, :%(ww70, ww71), ww8, ww9, app(ty_Ratio, cc), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (23) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_HugsException, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (24) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_Maybe, bg), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, :%(ww70, ww71), ww8, ww9, app(ty_Ratio, cc), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (25) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(ty_Maybe, bg), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)),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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4))) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (26) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_pt1(ww6, :%(ww70, ww71), ww8, ww9, app(ty_Ratio, cc), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (27) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, :%(ww70, ww71), ww8, ww9, app(ty_Ratio, cc), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)),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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5))) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (28) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (29) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (30) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (31) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6))) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (32) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (33) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (34) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (35) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (36) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (37) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (38) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (39) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)),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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5))) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (40) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (41) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (42) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (43) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(ty_[], bf), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)),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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4))) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (44) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (45) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (46) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (47) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (48) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (49) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (50) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (51) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, ba), bb), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)),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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5))) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (52) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (53) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, be), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)),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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4))) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (54) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (55) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (56) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (57) TransformationProof (EQUIVALENT) 33.93/17.98 By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError)) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (58) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int) 33.93/17.98 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 33.93/17.98 33.93/17.98 R is empty. 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (59) QDPSizeChangeProof (EQUIVALENT) 33.93/17.98 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. 33.93/17.98 33.93/17.98 From the DPs we obtained the following set of size-change graphs: 33.93/17.98 *new_showListShowl(:(ww80, ww81), ww9, h) -> 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 33.93/17.98 The graph contains the following edges 1 > 2, 1 > 3, 2 >= 4, 3 >= 5, 3 >= 6 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 *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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 33.93/17.98 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (60) 33.93/17.98 YES 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (61) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primShowInt(Neg(ww70)) -> new_primShowInt(Pos(ww70)) 33.93/17.98 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.93/17.98 33.93/17.98 The TRS R consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.98 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/17.98 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.98 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.98 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.98 new_primDivNatS4(ww216) -> Zero 33.93/17.98 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.98 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.98 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.98 33.93/17.98 The set Q consists of the following terms: 33.93/17.98 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.98 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.98 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.98 new_primDivNatS01(x0, x1) 33.93/17.98 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.98 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.98 new_primDivNatS2(Zero, Zero, x0) 33.93/17.98 new_div(x0, x1) 33.93/17.98 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.98 new_primDivNatS4(x0) 33.93/17.98 new_primDivNatS3(Succ(x0), Zero) 33.93/17.98 new_primDivNatS3(Zero, Zero) 33.93/17.98 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (62) DependencyGraphProof (EQUIVALENT) 33.93/17.98 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (63) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.93/17.98 33.93/17.98 The TRS R consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.98 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/17.98 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.98 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.98 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.98 new_primDivNatS4(ww216) -> Zero 33.93/17.98 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.98 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.98 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.98 33.93/17.98 The set Q consists of the following terms: 33.93/17.98 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.98 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.98 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.98 new_primDivNatS01(x0, x1) 33.93/17.98 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.98 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.98 new_primDivNatS2(Zero, Zero, x0) 33.93/17.98 new_div(x0, x1) 33.93/17.98 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.98 new_primDivNatS4(x0) 33.93/17.98 new_primDivNatS3(Succ(x0), Zero) 33.93/17.98 new_primDivNatS3(Zero, Zero) 33.93/17.98 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (64) TransformationProof (EQUIVALENT) 33.93/17.98 By rewriting [LPAR04] the rule new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (65) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.93/17.98 33.93/17.98 The TRS R consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.98 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/17.98 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.98 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.98 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.98 new_primDivNatS4(ww216) -> Zero 33.93/17.98 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.98 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.98 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.98 33.93/17.98 The set Q consists of the following terms: 33.93/17.98 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.98 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.98 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.98 new_primDivNatS01(x0, x1) 33.93/17.98 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.98 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.98 new_primDivNatS2(Zero, Zero, x0) 33.93/17.98 new_div(x0, x1) 33.93/17.98 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.98 new_primDivNatS4(x0) 33.93/17.98 new_primDivNatS3(Succ(x0), Zero) 33.93/17.98 new_primDivNatS3(Zero, Zero) 33.93/17.98 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (66) UsableRulesProof (EQUIVALENT) 33.93/17.98 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. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (67) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.93/17.98 33.93/17.98 The TRS R consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.98 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.98 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS4(ww216) -> Zero 33.93/17.98 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.98 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.98 33.93/17.98 The set Q consists of the following terms: 33.93/17.98 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.98 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.98 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.98 new_primDivNatS01(x0, x1) 33.93/17.98 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.98 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.98 new_primDivNatS2(Zero, Zero, x0) 33.93/17.98 new_div(x0, x1) 33.93/17.98 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.98 new_primDivNatS4(x0) 33.93/17.98 new_primDivNatS3(Succ(x0), Zero) 33.93/17.98 new_primDivNatS3(Zero, Zero) 33.93/17.98 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (68) QReductionProof (EQUIVALENT) 33.93/17.98 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 33.93/17.98 33.93/17.98 new_div(x0, x1) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (69) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.93/17.98 33.93/17.98 The TRS R consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.98 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.98 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS4(ww216) -> Zero 33.93/17.98 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.98 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.98 33.93/17.98 The set Q consists of the following terms: 33.93/17.98 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.98 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.98 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.98 new_primDivNatS01(x0, x1) 33.93/17.98 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.98 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.98 new_primDivNatS2(Zero, Zero, x0) 33.93/17.98 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.98 new_primDivNatS4(x0) 33.93/17.98 new_primDivNatS3(Succ(x0), Zero) 33.93/17.98 new_primDivNatS3(Zero, Zero) 33.93/17.98 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (70) MNOCProof (EQUIVALENT) 33.93/17.98 We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (71) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.93/17.98 33.93/17.98 The TRS R consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.98 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.98 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS4(ww216) -> Zero 33.93/17.98 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.98 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.98 33.93/17.98 Q is empty. 33.93/17.98 We have to consider all (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (72) InductionCalculusProof (EQUIVALENT) 33.93/17.98 Note that final constraints are written in bold face. 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 For Pair new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) the following chains were created: 33.93/17.98 *We consider the chain new_primShowInt(Pos(Succ(x0))) -> new_primShowInt(Pos(new_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), new_primShowInt(Pos(Succ(x1))) -> new_primShowInt(Pos(new_primDivNatS3(x1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) which results in the following constraint: 33.93/17.98 33.93/17.98 (1) (new_primShowInt(Pos(new_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))=new_primShowInt(Pos(Succ(x1))) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: 33.93/17.98 33.93/17.98 (2) (Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=x2 & new_primDivNatS3(x0, x2)=Succ(x1) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS3(x0, x2)=Succ(x1) which results in the following new constraints: 33.93/17.98 33.93/17.98 (3) (new_primDivNatS02(x4, x3, x4, x3)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Succ(x3) ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 (4) (Succ(new_primDivNatS2(Succ(x6), Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero ==> new_primShowInt(Pos(Succ(Succ(x6))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x6), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 (5) (Succ(new_primDivNatS2(Zero, Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero ==> new_primShowInt(Pos(Succ(Zero)))_>=_new_primShowInt(Pos(new_primDivNatS3(Zero, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint: 33.93/17.98 33.93/17.98 (6) (x4=x7 & x3=x8 & new_primDivNatS02(x4, x3, x7, x8)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS02(x4, x3, x7, x8)=Succ(x1) which results in the following new constraints: 33.93/17.98 33.93/17.98 (7) (new_primDivNatS02(x12, x11, x10, x9)=Succ(x1) & x12=Succ(x10) & x11=Succ(x9) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 & (\/x13:new_primDivNatS02(x12, x11, x10, x9)=Succ(x13) & x12=x10 & x11=x9 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 ==> new_primShowInt(Pos(Succ(Succ(x12))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x12), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ==> new_primShowInt(Pos(Succ(Succ(x12))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x12), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 (8) (new_primDivNatS01(x16, x15)=Succ(x1) & x16=Succ(x14) & x15=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 ==> new_primShowInt(Pos(Succ(Succ(x16))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x16), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 (9) (new_primDivNatS01(x18, x17)=Succ(x1) & x18=Zero & x17=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x17 ==> new_primShowInt(Pos(Succ(Succ(x18))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x18), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 We simplified constraint (7) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint: 33.93/17.98 33.93/17.98 (10) (new_primShowInt(Pos(Succ(Succ(Succ(x10)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x10)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 We solved constraint (8) using rules (I), (II), (III).We solved constraint (9) using rules (I), (II), (III). 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 To summarize, we get the following constraints P__>=_ for the following pairs. 33.93/17.98 33.93/17.98 *new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.93/17.98 33.93/17.98 *(new_primShowInt(Pos(Succ(Succ(Succ(x10)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x10)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 33.93/17.98 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. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (73) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.93/17.98 33.93/17.98 The TRS R consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.98 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.98 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS4(ww216) -> Zero 33.93/17.98 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.98 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.98 33.93/17.98 The set Q consists of the following terms: 33.93/17.98 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.98 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.98 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.98 new_primDivNatS01(x0, x1) 33.93/17.98 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.98 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.98 new_primDivNatS2(Zero, Zero, x0) 33.93/17.98 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.98 new_primDivNatS4(x0) 33.93/17.98 new_primDivNatS3(Succ(x0), Zero) 33.93/17.98 new_primDivNatS3(Zero, Zero) 33.93/17.98 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (74) TransformationProof (EQUIVALENT) 33.93/17.98 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 33.93/17.98 33.93/17.98 (new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))),new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 33.93/17.98 (new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero))) 33.93/17.98 33.93/17.98 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (75) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.93/17.98 new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)) 33.93/17.98 33.93/17.98 The TRS R consists of the following rules: 33.93/17.98 33.93/17.98 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.98 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.98 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.98 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.98 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.98 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.98 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.98 new_primDivNatS4(ww216) -> Zero 33.93/17.98 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.98 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.98 33.93/17.98 The set Q consists of the following terms: 33.93/17.98 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.98 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.98 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.98 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.98 new_primDivNatS01(x0, x1) 33.93/17.98 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.98 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.98 new_primDivNatS2(Zero, Zero, x0) 33.93/17.98 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.98 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.98 new_primDivNatS4(x0) 33.93/17.98 new_primDivNatS3(Succ(x0), Zero) 33.93/17.98 new_primDivNatS3(Zero, Zero) 33.93/17.98 33.93/17.98 We have to consider all minimal (P,Q,R)-chains. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (76) DependencyGraphProof (EQUIVALENT) 33.93/17.98 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.93/17.98 ---------------------------------------- 33.93/17.98 33.93/17.98 (77) 33.93/17.98 Obligation: 33.93/17.98 Q DP problem: 33.93/17.98 The TRS P consists of the following rules: 33.93/17.98 33.93/17.98 new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (78) TransformationProof (EQUIVALENT) 33.93/17.99 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 33.93/17.99 33.93/17.99 (new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))),new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 33.93/17.99 (new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero))) 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (79) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (80) DependencyGraphProof (EQUIVALENT) 33.93/17.99 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (81) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (82) TransformationProof (EQUIVALENT) 33.93/17.99 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 33.93/17.99 33.93/17.99 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 33.93/17.99 (new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero))) 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (83) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (84) DependencyGraphProof (EQUIVALENT) 33.93/17.99 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (85) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (86) TransformationProof (EQUIVALENT) 33.93/17.99 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 33.93/17.99 33.93/17.99 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero))) 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (87) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (88) DependencyGraphProof (EQUIVALENT) 33.93/17.99 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (89) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (90) MNOCProof (EQUIVALENT) 33.93/17.99 We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (91) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 33.93/17.99 Q is empty. 33.93/17.99 We have to consider all (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (92) InductionCalculusProof (EQUIVALENT) 33.93/17.99 Note that final constraints are written in bold face. 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 For Pair new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) the following chains were created: 33.93/17.99 *We consider the chain new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))), new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x1))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x1, Succ(Succ(Succ(Succ(Succ(Zero)))))))) which results in the following constraint: 33.93/17.99 33.93/17.99 (1) (new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))=new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: 33.93/17.99 33.93/17.99 (2) (Succ(Succ(Succ(x0)))=x2 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x4 & new_primDivNatS02(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS02(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: 33.93/17.99 33.93/17.99 (3) (new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x6))))=x8 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x7 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Succ(x5) & (\/x9:new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x9))))) & Succ(Succ(Succ(x6)))=x8 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x7 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x5 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x6)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x6, Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x6))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x6)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x6), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 (4) (new_primDivNatS01(x12, x11)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x10))))=x12 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x10))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x10)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x10), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 (5) (new_primDivNatS01(x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Zero)))=x14 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x13 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Zero, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint: 33.93/17.99 33.93/17.99 (6) (new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x6))))=x8 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x7 & Succ(Succ(Succ(Succ(Zero))))=x5 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x6))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x6)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x6), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: 33.93/17.99 33.93/17.99 (7) (new_primDivNatS02(x21, x20, x19, x18)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x19)))))=x21 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x20 & Succ(Succ(Succ(Succ(Zero))))=Succ(x18) & (\/x22:new_primDivNatS02(x21, x20, x19, x18)=Succ(Succ(Succ(Succ(Succ(x22))))) & Succ(Succ(Succ(Succ(x19))))=x21 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x20 & Succ(Succ(Succ(Succ(Zero))))=x18 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x19))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x19)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x19), Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x19)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x19))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x19)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 (8) (new_primDivNatS01(x25, x24)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x23)))))=x25 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x24 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x23)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x23))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x23)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 (9) (new_primDivNatS01(x27, x26)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Zero))))=x27 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x26 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 We simplified constraint (7) using rules (I), (II), (III), (IV) which results in the following new constraint: 33.93/17.99 33.93/17.99 (10) (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x19)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x19))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x19)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 We solved constraint (8) using rules (I), (II).We solved constraint (9) using rules (I), (II). 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 To summarize, we get the following constraints P__>=_ for the following pairs. 33.93/17.99 33.93/17.99 *new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.93/17.99 33.93/17.99 *(new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x19)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x19))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x19)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 33.93/17.99 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. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (93) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (94) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_psPs(:(ww1170, ww1171), ww106) -> new_psPs(ww1171, ww106) 33.93/17.99 33.93/17.99 R is empty. 33.93/17.99 Q is empty. 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (95) QDPSizeChangeProof (EQUIVALENT) 33.93/17.99 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. 33.93/17.99 33.93/17.99 From the DPs we obtained the following set of size-change graphs: 33.93/17.99 *new_psPs(:(ww1170, ww1171), ww106) -> new_psPs(ww1171, ww106) 33.93/17.99 The graph contains the following edges 1 > 1, 2 >= 2 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (96) 33.93/17.99 YES 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (97) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primModNatS(Succ(ww2100), Zero, ww212) -> new_primModNatS1(ww2100, ww212) 33.93/17.99 new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero) 33.93/17.99 new_primModNatS00(ww205, ww206) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 new_primModNatS0(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 new_primModNatS(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS(ww2100, ww2110, ww212) 33.93/17.99 new_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) 33.93/17.99 new_primModNatS1(Succ(ww1560), Succ(ww1570)) -> new_primModNatS0(ww1560, ww1570, ww1560, ww1570) 33.93/17.99 new_primModNatS0(ww205, ww206, Zero, Zero) -> new_primModNatS00(ww205, ww206) 33.93/17.99 new_primModNatS1(Succ(ww1560), Zero) -> new_primModNatS(Succ(ww1560), Zero, Zero) 33.93/17.99 33.93/17.99 R is empty. 33.93/17.99 Q is empty. 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (98) DependencyGraphProof (EQUIVALENT) 33.93/17.99 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (99) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primModNatS1(Succ(ww1560), Succ(ww1570)) -> new_primModNatS0(ww1560, ww1570, ww1560, ww1570) 33.93/17.99 new_primModNatS0(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 new_primModNatS(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS(ww2100, ww2110, ww212) 33.93/17.99 new_primModNatS(Succ(ww2100), Zero, ww212) -> new_primModNatS1(ww2100, ww212) 33.93/17.99 new_primModNatS1(Succ(ww1560), Zero) -> new_primModNatS(Succ(ww1560), Zero, Zero) 33.93/17.99 new_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) 33.93/17.99 new_primModNatS0(ww205, ww206, Zero, Zero) -> new_primModNatS00(ww205, ww206) 33.93/17.99 new_primModNatS00(ww205, ww206) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 33.93/17.99 R is empty. 33.93/17.99 Q is empty. 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (100) QDPOrderProof (EQUIVALENT) 33.93/17.99 We use the reduction pair processor [LPAR04,JAR06]. 33.93/17.99 33.93/17.99 33.93/17.99 The following pairs can be oriented strictly and are deleted. 33.93/17.99 33.93/17.99 new_primModNatS1(Succ(ww1560), Succ(ww1570)) -> new_primModNatS0(ww1560, ww1570, ww1560, ww1570) 33.93/17.99 new_primModNatS(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS(ww2100, ww2110, ww212) 33.93/17.99 new_primModNatS1(Succ(ww1560), Zero) -> new_primModNatS(Succ(ww1560), Zero, Zero) 33.93/17.99 The remaining pairs can at least be oriented weakly. 33.93/17.99 Used ordering: Polynomial interpretation [POLO]: 33.93/17.99 33.93/17.99 POL(Succ(x_1)) = 1 + x_1 33.93/17.99 POL(Zero) = 0 33.93/17.99 POL(new_primModNatS(x_1, x_2, x_3)) = x_1 33.93/17.99 POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 33.93/17.99 POL(new_primModNatS00(x_1, x_2)) = 1 + x_1 33.93/17.99 POL(new_primModNatS1(x_1, x_2)) = 1 + x_1 33.93/17.99 33.93/17.99 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 33.93/17.99 none 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (101) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primModNatS0(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 new_primModNatS(Succ(ww2100), Zero, ww212) -> new_primModNatS1(ww2100, ww212) 33.93/17.99 new_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) 33.93/17.99 new_primModNatS0(ww205, ww206, Zero, Zero) -> new_primModNatS00(ww205, ww206) 33.93/17.99 new_primModNatS00(ww205, ww206) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 33.93/17.99 R is empty. 33.93/17.99 Q is empty. 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (102) DependencyGraphProof (EQUIVALENT) 33.93/17.99 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (103) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) 33.93/17.99 33.93/17.99 R is empty. 33.93/17.99 Q is empty. 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (104) QDPSizeChangeProof (EQUIVALENT) 33.93/17.99 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. 33.93/17.99 33.93/17.99 From the DPs we obtained the following set of size-change graphs: 33.93/17.99 *new_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) 33.93/17.99 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (105) 33.93/17.99 YES 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (106) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(app(ty_Either, h), ba), app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_show10(ww7) -> error([]) 33.93/17.99 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/17.99 new_show(ww7) -> error([]) 33.93/17.99 new_show7(ww7, dc, dd) -> error([]) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_show14(ww7) -> error([]) 33.93/17.99 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/17.99 new_show3(ww7) -> error([]) 33.93/17.99 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/17.99 new_show8(ww7) -> error([]) 33.93/17.99 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/17.99 new_primModNatS4(ww212) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/17.99 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_show4(ww7) -> error([]) 33.93/17.99 new_show13(ww7, fa) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/17.99 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/17.99 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/17.99 new_psPs0([], ww106) -> ww106 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_show12(ww7) -> error([]) 33.93/17.99 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/17.99 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_show9(ww7, de, df) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/17.99 new_show5(ww7, db) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/17.99 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/17.99 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/17.99 new_show1(ww7, da) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/17.99 new_show6(ww7) -> error([]) 33.93/17.99 new_show11(ww7) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/17.99 new_show15(ww7) -> error([]) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_show0(x0, x1, x2, x3) 33.93/17.99 new_show4(x0) 33.93/17.99 new_show1(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/17.99 new_showsPrec(x0, x1, ty_Ordering) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/17.99 new_primShowInt0(Neg(x0)) 33.93/17.99 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_show3(x0) 33.93/17.99 new_show5(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_IOError) 33.93/17.99 new_show15(x0) 33.93/17.99 new_primModNatS2(Zero, Succ(x0)) 33.93/17.99 new_show10(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/17.99 new_primModNatS2(Succ(x0), Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/17.99 new_show6(x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Int) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primModNatS2(Zero, Zero) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/17.99 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/17.99 new_primModNatS02(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/17.99 new_primIntToChar(x0, x1) 33.93/17.99 new_show(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/17.99 new_showsPrec(x0, x1, ty_HugsException) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/17.99 new_show12(x0) 33.93/17.99 new_show13(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_@0) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primShowInt0(Pos(Zero)) 33.93/17.99 new_primModNatS3(Zero, Zero, x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Char) 33.93/17.99 new_show11(x0) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_div(x0, x1) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/17.99 new_primModNatS3(Zero, Succ(x0), x1) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_show8(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/17.99 new_showsPrec(x0, x1, ty_Float) 33.93/17.99 new_primShowInt0(Pos(Succ(x0))) 33.93/17.99 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/17.99 new_psPs0([], x0) 33.93/17.99 new_show9(x0, x1, x2) 33.93/17.99 new_showsPrec(x0, x1, ty_Bool) 33.93/17.99 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/17.99 new_show2(x0) 33.93/17.99 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/17.99 new_showsPrec(x0, x1, ty_Double) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/17.99 new_show14(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_Integer) 33.93/17.99 new_primModNatS3(Succ(x0), Zero, x1) 33.93/17.99 new_psPs0(:(x0, x1), x2) 33.93/17.99 new_primModNatS4(x0) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_show7(x0, x1, x2) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (107) DependencyGraphProof (EQUIVALENT) 33.93/17.99 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (108) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_show10(ww7) -> error([]) 33.93/17.99 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/17.99 new_show(ww7) -> error([]) 33.93/17.99 new_show7(ww7, dc, dd) -> error([]) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_show14(ww7) -> error([]) 33.93/17.99 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/17.99 new_show3(ww7) -> error([]) 33.93/17.99 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/17.99 new_show8(ww7) -> error([]) 33.93/17.99 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/17.99 new_primModNatS4(ww212) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/17.99 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_show4(ww7) -> error([]) 33.93/17.99 new_show13(ww7, fa) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/17.99 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/17.99 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/17.99 new_psPs0([], ww106) -> ww106 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_show12(ww7) -> error([]) 33.93/17.99 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/17.99 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_show9(ww7, de, df) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/17.99 new_show5(ww7, db) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/17.99 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/17.99 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/17.99 new_show1(ww7, da) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/17.99 new_show6(ww7) -> error([]) 33.93/17.99 new_show11(ww7) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/17.99 new_show15(ww7) -> error([]) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_show0(x0, x1, x2, x3) 33.93/17.99 new_show4(x0) 33.93/17.99 new_show1(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/17.99 new_showsPrec(x0, x1, ty_Ordering) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/17.99 new_primShowInt0(Neg(x0)) 33.93/17.99 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_show3(x0) 33.93/17.99 new_show5(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_IOError) 33.93/17.99 new_show15(x0) 33.93/17.99 new_primModNatS2(Zero, Succ(x0)) 33.93/17.99 new_show10(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/17.99 new_primModNatS2(Succ(x0), Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/17.99 new_show6(x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Int) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primModNatS2(Zero, Zero) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/17.99 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/17.99 new_primModNatS02(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/17.99 new_primIntToChar(x0, x1) 33.93/17.99 new_show(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/17.99 new_showsPrec(x0, x1, ty_HugsException) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/17.99 new_show12(x0) 33.93/17.99 new_show13(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_@0) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primShowInt0(Pos(Zero)) 33.93/17.99 new_primModNatS3(Zero, Zero, x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Char) 33.93/17.99 new_show11(x0) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_div(x0, x1) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/17.99 new_primModNatS3(Zero, Succ(x0), x1) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_show8(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/17.99 new_showsPrec(x0, x1, ty_Float) 33.93/17.99 new_primShowInt0(Pos(Succ(x0))) 33.93/17.99 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/17.99 new_psPs0([], x0) 33.93/17.99 new_show9(x0, x1, x2) 33.93/17.99 new_showsPrec(x0, x1, ty_Bool) 33.93/17.99 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/17.99 new_show2(x0) 33.93/17.99 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/17.99 new_showsPrec(x0, x1, ty_Double) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/17.99 new_show14(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_Integer) 33.93/17.99 new_primModNatS3(Succ(x0), Zero, x1) 33.93/17.99 new_psPs0(:(x0, x1), x2) 33.93/17.99 new_primModNatS4(x0) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_show7(x0, x1, x2) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (109) TransformationProof (EQUIVALENT) 33.93/17.99 By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) at position [5] we obtained the following new rules [LPAR04]: 33.93/17.99 33.93/17.99 (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, cd)), cd, cd),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, cd)), cd, cd)) 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (110) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, cd)), cd, cd) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_show10(ww7) -> error([]) 33.93/17.99 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/17.99 new_show(ww7) -> error([]) 33.93/17.99 new_show7(ww7, dc, dd) -> error([]) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_show14(ww7) -> error([]) 33.93/17.99 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/17.99 new_show3(ww7) -> error([]) 33.93/17.99 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/17.99 new_show8(ww7) -> error([]) 33.93/17.99 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/17.99 new_primModNatS4(ww212) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/17.99 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_show4(ww7) -> error([]) 33.93/17.99 new_show13(ww7, fa) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/17.99 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/17.99 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/17.99 new_psPs0([], ww106) -> ww106 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_show12(ww7) -> error([]) 33.93/17.99 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/17.99 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_show9(ww7, de, df) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/17.99 new_show5(ww7, db) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/17.99 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/17.99 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/17.99 new_show1(ww7, da) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/17.99 new_show6(ww7) -> error([]) 33.93/17.99 new_show11(ww7) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/17.99 new_show15(ww7) -> error([]) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_show0(x0, x1, x2, x3) 33.93/17.99 new_show4(x0) 33.93/17.99 new_show1(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/17.99 new_showsPrec(x0, x1, ty_Ordering) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/17.99 new_primShowInt0(Neg(x0)) 33.93/17.99 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_show3(x0) 33.93/17.99 new_show5(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_IOError) 33.93/17.99 new_show15(x0) 33.93/17.99 new_primModNatS2(Zero, Succ(x0)) 33.93/17.99 new_show10(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/17.99 new_primModNatS2(Succ(x0), Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/17.99 new_show6(x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Int) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primModNatS2(Zero, Zero) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/17.99 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/17.99 new_primModNatS02(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/17.99 new_primIntToChar(x0, x1) 33.93/17.99 new_show(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/17.99 new_showsPrec(x0, x1, ty_HugsException) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/17.99 new_show12(x0) 33.93/17.99 new_show13(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_@0) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primShowInt0(Pos(Zero)) 33.93/17.99 new_primModNatS3(Zero, Zero, x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Char) 33.93/17.99 new_show11(x0) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_div(x0, x1) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/17.99 new_primModNatS3(Zero, Succ(x0), x1) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_show8(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/17.99 new_showsPrec(x0, x1, ty_Float) 33.93/17.99 new_primShowInt0(Pos(Succ(x0))) 33.93/17.99 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/17.99 new_psPs0([], x0) 33.93/17.99 new_show9(x0, x1, x2) 33.93/17.99 new_showsPrec(x0, x1, ty_Bool) 33.93/17.99 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/17.99 new_show2(x0) 33.93/17.99 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/17.99 new_showsPrec(x0, x1, ty_Double) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/17.99 new_show14(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_Integer) 33.93/17.99 new_primModNatS3(Succ(x0), Zero, x1) 33.93/17.99 new_psPs0(:(x0, x1), x2) 33.93/17.99 new_primModNatS4(x0) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_show7(x0, x1, x2) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (111) TransformationProof (EQUIVALENT) 33.93/17.99 By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, cd)), cd, cd) at position [5] we obtained the following new rules [LPAR04]: 33.93/17.99 33.93/17.99 (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), new_psPs0(:(Char(Succ(ww140)), :(Char(Succ(ww141)), [])), new_showsPrec(ww142, ww148, cd))), cd, cd),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), new_psPs0(:(Char(Succ(ww140)), :(Char(Succ(ww141)), [])), new_showsPrec(ww142, ww148, cd))), cd, cd)) 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (112) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), new_psPs0(:(Char(Succ(ww140)), :(Char(Succ(ww141)), [])), new_showsPrec(ww142, ww148, cd))), cd, cd) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_show10(ww7) -> error([]) 33.93/17.99 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/17.99 new_show(ww7) -> error([]) 33.93/17.99 new_show7(ww7, dc, dd) -> error([]) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_show14(ww7) -> error([]) 33.93/17.99 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/17.99 new_show3(ww7) -> error([]) 33.93/17.99 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/17.99 new_show8(ww7) -> error([]) 33.93/17.99 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/17.99 new_primModNatS4(ww212) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/17.99 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_show4(ww7) -> error([]) 33.93/17.99 new_show13(ww7, fa) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/17.99 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/17.99 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/17.99 new_psPs0([], ww106) -> ww106 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_show12(ww7) -> error([]) 33.93/17.99 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/17.99 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_show9(ww7, de, df) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/17.99 new_show5(ww7, db) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/17.99 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/17.99 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/17.99 new_show1(ww7, da) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/17.99 new_show6(ww7) -> error([]) 33.93/17.99 new_show11(ww7) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/17.99 new_show15(ww7) -> error([]) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_show0(x0, x1, x2, x3) 33.93/17.99 new_show4(x0) 33.93/17.99 new_show1(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/17.99 new_showsPrec(x0, x1, ty_Ordering) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/17.99 new_primShowInt0(Neg(x0)) 33.93/17.99 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_show3(x0) 33.93/17.99 new_show5(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_IOError) 33.93/17.99 new_show15(x0) 33.93/17.99 new_primModNatS2(Zero, Succ(x0)) 33.93/17.99 new_show10(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/17.99 new_primModNatS2(Succ(x0), Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/17.99 new_show6(x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Int) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primModNatS2(Zero, Zero) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/17.99 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/17.99 new_primModNatS02(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/17.99 new_primIntToChar(x0, x1) 33.93/17.99 new_show(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/17.99 new_showsPrec(x0, x1, ty_HugsException) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/17.99 new_show12(x0) 33.93/17.99 new_show13(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_@0) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primShowInt0(Pos(Zero)) 33.93/17.99 new_primModNatS3(Zero, Zero, x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Char) 33.93/17.99 new_show11(x0) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_div(x0, x1) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/17.99 new_primModNatS3(Zero, Succ(x0), x1) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_show8(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/17.99 new_showsPrec(x0, x1, ty_Float) 33.93/17.99 new_primShowInt0(Pos(Succ(x0))) 33.93/17.99 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/17.99 new_psPs0([], x0) 33.93/17.99 new_show9(x0, x1, x2) 33.93/17.99 new_showsPrec(x0, x1, ty_Bool) 33.93/17.99 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/17.99 new_show2(x0) 33.93/17.99 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/17.99 new_showsPrec(x0, x1, ty_Double) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/17.99 new_show14(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_Integer) 33.93/17.99 new_primModNatS3(Succ(x0), Zero, x1) 33.93/17.99 new_psPs0(:(x0, x1), x2) 33.93/17.99 new_primModNatS4(x0) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_show7(x0, x1, x2) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (113) TransformationProof (EQUIVALENT) 33.93/17.99 By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), new_psPs0(:(Char(Succ(ww140)), :(Char(Succ(ww141)), [])), new_showsPrec(ww142, ww148, cd))), cd, cd) at position [5,1] we obtained the following new rules [LPAR04]: 33.93/17.99 33.93/17.99 (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), new_psPs0(:(Char(Succ(ww141)), []), new_showsPrec(ww142, ww148, cd)))), cd, cd),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), new_psPs0(:(Char(Succ(ww141)), []), new_showsPrec(ww142, ww148, cd)))), cd, cd)) 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (114) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), new_psPs0(:(Char(Succ(ww141)), []), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/17.99 33.93/17.99 The TRS R consists of the following rules: 33.93/17.99 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/17.99 new_show10(ww7) -> error([]) 33.93/17.99 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/17.99 new_show(ww7) -> error([]) 33.93/17.99 new_show7(ww7, dc, dd) -> error([]) 33.93/17.99 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/17.99 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/17.99 new_show14(ww7) -> error([]) 33.93/17.99 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/17.99 new_show3(ww7) -> error([]) 33.93/17.99 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/17.99 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/17.99 new_show8(ww7) -> error([]) 33.93/17.99 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/17.99 new_primModNatS4(ww212) -> Zero 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/17.99 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/17.99 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_show4(ww7) -> error([]) 33.93/17.99 new_show13(ww7, fa) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/17.99 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/17.99 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/17.99 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/17.99 new_psPs0([], ww106) -> ww106 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/17.99 new_show12(ww7) -> error([]) 33.93/17.99 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/17.99 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/17.99 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/17.99 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/17.99 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/17.99 new_show9(ww7, de, df) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/17.99 new_show5(ww7, db) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/17.99 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/17.99 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/17.99 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/17.99 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/17.99 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/17.99 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/17.99 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/17.99 new_show1(ww7, da) -> error([]) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/17.99 new_show6(ww7) -> error([]) 33.93/17.99 new_show11(ww7) -> error([]) 33.93/17.99 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/17.99 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/17.99 new_show15(ww7) -> error([]) 33.93/17.99 new_primDivNatS4(ww216) -> Zero 33.93/17.99 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/17.99 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/17.99 33.93/17.99 The set Q consists of the following terms: 33.93/17.99 33.93/17.99 new_show0(x0, x1, x2, x3) 33.93/17.99 new_show4(x0) 33.93/17.99 new_show1(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/17.99 new_showsPrec(x0, x1, ty_Ordering) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/17.99 new_primShowInt0(Neg(x0)) 33.93/17.99 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Zero, Succ(x0)) 33.93/17.99 new_show3(x0) 33.93/17.99 new_show5(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_IOError) 33.93/17.99 new_show15(x0) 33.93/17.99 new_primModNatS2(Zero, Succ(x0)) 33.93/17.99 new_show10(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/17.99 new_primModNatS2(Succ(x0), Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/17.99 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/17.99 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/17.99 new_show6(x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Int) 33.93/17.99 new_primDivNatS4(x0) 33.93/17.99 new_primModNatS2(Zero, Zero) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/17.99 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/17.99 new_primModNatS02(x0, x1) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/17.99 new_primIntToChar(x0, x1) 33.93/17.99 new_show(x0) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/17.99 new_showsPrec(x0, x1, ty_HugsException) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/17.99 new_show12(x0) 33.93/17.99 new_show13(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_@0) 33.93/17.99 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/17.99 new_primShowInt0(Pos(Zero)) 33.93/17.99 new_primModNatS3(Zero, Zero, x0) 33.93/17.99 new_showsPrec(x0, x1, ty_Char) 33.93/17.99 new_show11(x0) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/17.99 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/17.99 new_primDivNatS2(Zero, Zero, x0) 33.93/17.99 new_div(x0, x1) 33.93/17.99 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/17.99 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/17.99 new_primModNatS3(Zero, Succ(x0), x1) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/17.99 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/17.99 new_show8(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/17.99 new_showsPrec(x0, x1, ty_Float) 33.93/17.99 new_primShowInt0(Pos(Succ(x0))) 33.93/17.99 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/17.99 new_psPs0([], x0) 33.93/17.99 new_show9(x0, x1, x2) 33.93/17.99 new_showsPrec(x0, x1, ty_Bool) 33.93/17.99 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/17.99 new_show2(x0) 33.93/17.99 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/17.99 new_showsPrec(x0, x1, ty_Double) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Zero) 33.93/17.99 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/17.99 new_show14(x0) 33.93/17.99 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/17.99 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/17.99 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/17.99 new_primDivNatS01(x0, x1) 33.93/17.99 new_showsPrec(x0, x1, ty_Integer) 33.93/17.99 new_primModNatS3(Succ(x0), Zero, x1) 33.93/17.99 new_psPs0(:(x0, x1), x2) 33.93/17.99 new_primModNatS4(x0) 33.93/17.99 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/17.99 new_primDivNatS3(Succ(x0), Zero) 33.93/17.99 new_show7(x0, x1, x2) 33.93/17.99 new_primDivNatS3(Zero, Zero) 33.93/17.99 33.93/17.99 We have to consider all minimal (P,Q,R)-chains. 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (115) TransformationProof (EQUIVALENT) 33.93/17.99 By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), new_psPs0(:(Char(Succ(ww141)), []), new_showsPrec(ww142, ww148, cd)))), cd, cd) at position [5,1,1] we obtained the following new rules [LPAR04]: 33.93/17.99 33.93/17.99 (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_psPs0([], new_showsPrec(ww142, ww148, cd))))), cd, cd),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_psPs0([], new_showsPrec(ww142, ww148, cd))))), cd, cd)) 33.93/17.99 33.93/17.99 33.93/17.99 ---------------------------------------- 33.93/17.99 33.93/17.99 (116) 33.93/17.99 Obligation: 33.93/17.99 Q DP problem: 33.93/17.99 The TRS P consists of the following rules: 33.93/17.99 33.93/17.99 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/17.99 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_psPs0([], new_showsPrec(ww142, ww148, cd))))), cd, cd) 33.93/18.00 33.93/18.00 The TRS R consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.00 new_show10(ww7) -> error([]) 33.93/18.00 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.00 new_show(ww7) -> error([]) 33.93/18.00 new_show7(ww7, dc, dd) -> error([]) 33.93/18.00 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.00 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.00 new_show14(ww7) -> error([]) 33.93/18.00 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.00 new_show3(ww7) -> error([]) 33.93/18.00 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.00 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.00 new_show8(ww7) -> error([]) 33.93/18.00 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.00 new_primModNatS4(ww212) -> Zero 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.00 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_show4(ww7) -> error([]) 33.93/18.00 new_show13(ww7, fa) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.00 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.00 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.00 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.00 new_psPs0([], ww106) -> ww106 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.00 new_show12(ww7) -> error([]) 33.93/18.00 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.00 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.00 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.00 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.00 new_show9(ww7, de, df) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.00 new_show5(ww7, db) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.00 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.00 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.00 new_show1(ww7, da) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.00 new_show6(ww7) -> error([]) 33.93/18.00 new_show11(ww7) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.00 new_show15(ww7) -> error([]) 33.93/18.00 new_primDivNatS4(ww216) -> Zero 33.93/18.00 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 33.93/18.00 The set Q consists of the following terms: 33.93/18.00 33.93/18.00 new_show0(x0, x1, x2, x3) 33.93/18.00 new_show4(x0) 33.93/18.00 new_show1(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.00 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.00 new_primShowInt0(Neg(x0)) 33.93/18.00 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.00 new_show3(x0) 33.93/18.00 new_show5(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_IOError) 33.93/18.00 new_show15(x0) 33.93/18.00 new_primModNatS2(Zero, Succ(x0)) 33.93/18.00 new_show10(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.00 new_primModNatS2(Succ(x0), Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.00 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.00 new_show6(x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Int) 33.93/18.00 new_primDivNatS4(x0) 33.93/18.00 new_primModNatS2(Zero, Zero) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.00 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.00 new_primModNatS02(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.00 new_primIntToChar(x0, x1) 33.93/18.00 new_show(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.00 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.00 new_show12(x0) 33.93/18.00 new_show13(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_@0) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.00 new_primShowInt0(Pos(Zero)) 33.93/18.00 new_primModNatS3(Zero, Zero, x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Char) 33.93/18.00 new_show11(x0) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.00 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.00 new_primDivNatS2(Zero, Zero, x0) 33.93/18.00 new_div(x0, x1) 33.93/18.00 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.00 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.00 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_show8(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.00 new_showsPrec(x0, x1, ty_Float) 33.93/18.00 new_primShowInt0(Pos(Succ(x0))) 33.93/18.00 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.00 new_psPs0([], x0) 33.93/18.00 new_show9(x0, x1, x2) 33.93/18.00 new_showsPrec(x0, x1, ty_Bool) 33.93/18.00 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.00 new_show2(x0) 33.93/18.00 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.00 new_showsPrec(x0, x1, ty_Double) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.00 new_show14(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.00 new_primDivNatS01(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_Integer) 33.93/18.00 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.00 new_psPs0(:(x0, x1), x2) 33.93/18.00 new_primModNatS4(x0) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Succ(x0), Zero) 33.93/18.00 new_show7(x0, x1, x2) 33.93/18.00 new_primDivNatS3(Zero, Zero) 33.93/18.00 33.93/18.00 We have to consider all minimal (P,Q,R)-chains. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (117) TransformationProof (EQUIVALENT) 33.93/18.00 By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_psPs0([], new_showsPrec(ww142, ww148, cd))))), cd, cd) at position [5,1,1,1] we obtained the following new rules [LPAR04]: 33.93/18.00 33.93/18.00 (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd)) 33.93/18.00 33.93/18.00 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (118) 33.93/18.00 Obligation: 33.93/18.00 Q DP problem: 33.93/18.00 The TRS P consists of the following rules: 33.93/18.00 33.93/18.00 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.00 33.93/18.00 The TRS R consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.00 new_show10(ww7) -> error([]) 33.93/18.00 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.00 new_show(ww7) -> error([]) 33.93/18.00 new_show7(ww7, dc, dd) -> error([]) 33.93/18.00 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.00 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.00 new_show14(ww7) -> error([]) 33.93/18.00 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.00 new_show3(ww7) -> error([]) 33.93/18.00 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.00 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.00 new_show8(ww7) -> error([]) 33.93/18.00 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.00 new_primModNatS4(ww212) -> Zero 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.00 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_show4(ww7) -> error([]) 33.93/18.00 new_show13(ww7, fa) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.00 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.00 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.00 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.00 new_psPs0([], ww106) -> ww106 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.00 new_show12(ww7) -> error([]) 33.93/18.00 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.00 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.00 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.00 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.00 new_show9(ww7, de, df) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.00 new_show5(ww7, db) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.00 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.00 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.00 new_show1(ww7, da) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.00 new_show6(ww7) -> error([]) 33.93/18.00 new_show11(ww7) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.00 new_show15(ww7) -> error([]) 33.93/18.00 new_primDivNatS4(ww216) -> Zero 33.93/18.00 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 33.93/18.00 The set Q consists of the following terms: 33.93/18.00 33.93/18.00 new_show0(x0, x1, x2, x3) 33.93/18.00 new_show4(x0) 33.93/18.00 new_show1(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.00 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.00 new_primShowInt0(Neg(x0)) 33.93/18.00 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.00 new_show3(x0) 33.93/18.00 new_show5(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_IOError) 33.93/18.00 new_show15(x0) 33.93/18.00 new_primModNatS2(Zero, Succ(x0)) 33.93/18.00 new_show10(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.00 new_primModNatS2(Succ(x0), Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.00 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.00 new_show6(x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Int) 33.93/18.00 new_primDivNatS4(x0) 33.93/18.00 new_primModNatS2(Zero, Zero) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.00 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.00 new_primModNatS02(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.00 new_primIntToChar(x0, x1) 33.93/18.00 new_show(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.00 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.00 new_show12(x0) 33.93/18.00 new_show13(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_@0) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.00 new_primShowInt0(Pos(Zero)) 33.93/18.00 new_primModNatS3(Zero, Zero, x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Char) 33.93/18.00 new_show11(x0) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.00 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.00 new_primDivNatS2(Zero, Zero, x0) 33.93/18.00 new_div(x0, x1) 33.93/18.00 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.00 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.00 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_show8(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.00 new_showsPrec(x0, x1, ty_Float) 33.93/18.00 new_primShowInt0(Pos(Succ(x0))) 33.93/18.00 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.00 new_psPs0([], x0) 33.93/18.00 new_show9(x0, x1, x2) 33.93/18.00 new_showsPrec(x0, x1, ty_Bool) 33.93/18.00 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.00 new_show2(x0) 33.93/18.00 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.00 new_showsPrec(x0, x1, ty_Double) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.00 new_show14(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.00 new_primDivNatS01(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_Integer) 33.93/18.00 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.00 new_psPs0(:(x0, x1), x2) 33.93/18.00 new_primModNatS4(x0) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Succ(x0), Zero) 33.93/18.00 new_show7(x0, x1, x2) 33.93/18.00 new_primDivNatS3(Zero, Zero) 33.93/18.00 33.93/18.00 We have to consider all minimal (P,Q,R)-chains. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (119) TransformationProof (EQUIVALENT) 33.93/18.00 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 33.93/18.00 33.93/18.00 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6))) 33.93/18.00 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6))) 33.93/18.00 33.93/18.00 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (120) 33.93/18.00 Obligation: 33.93/18.00 Q DP problem: 33.93/18.00 The TRS P consists of the following rules: 33.93/18.00 33.93/18.00 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.00 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)) 33.93/18.00 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6)) 33.93/18.00 33.93/18.00 The TRS R consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.00 new_show10(ww7) -> error([]) 33.93/18.00 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.00 new_show(ww7) -> error([]) 33.93/18.00 new_show7(ww7, dc, dd) -> error([]) 33.93/18.00 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.00 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.00 new_show14(ww7) -> error([]) 33.93/18.00 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.00 new_show3(ww7) -> error([]) 33.93/18.00 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.00 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.00 new_show8(ww7) -> error([]) 33.93/18.00 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.00 new_primModNatS4(ww212) -> Zero 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.00 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_show4(ww7) -> error([]) 33.93/18.00 new_show13(ww7, fa) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.00 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.00 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.00 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.00 new_psPs0([], ww106) -> ww106 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.00 new_show12(ww7) -> error([]) 33.93/18.00 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.00 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.00 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.00 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.00 new_show9(ww7, de, df) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.00 new_show5(ww7, db) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.00 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.00 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.00 new_show1(ww7, da) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.00 new_show6(ww7) -> error([]) 33.93/18.00 new_show11(ww7) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.00 new_show15(ww7) -> error([]) 33.93/18.00 new_primDivNatS4(ww216) -> Zero 33.93/18.00 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 33.93/18.00 The set Q consists of the following terms: 33.93/18.00 33.93/18.00 new_show0(x0, x1, x2, x3) 33.93/18.00 new_show4(x0) 33.93/18.00 new_show1(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.00 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.00 new_primShowInt0(Neg(x0)) 33.93/18.00 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.00 new_show3(x0) 33.93/18.00 new_show5(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_IOError) 33.93/18.00 new_show15(x0) 33.93/18.00 new_primModNatS2(Zero, Succ(x0)) 33.93/18.00 new_show10(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.00 new_primModNatS2(Succ(x0), Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.00 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.00 new_show6(x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Int) 33.93/18.00 new_primDivNatS4(x0) 33.93/18.00 new_primModNatS2(Zero, Zero) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.00 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.00 new_primModNatS02(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.00 new_primIntToChar(x0, x1) 33.93/18.00 new_show(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.00 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.00 new_show12(x0) 33.93/18.00 new_show13(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_@0) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.00 new_primShowInt0(Pos(Zero)) 33.93/18.00 new_primModNatS3(Zero, Zero, x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Char) 33.93/18.00 new_show11(x0) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.00 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.00 new_primDivNatS2(Zero, Zero, x0) 33.93/18.00 new_div(x0, x1) 33.93/18.00 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.00 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.00 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_show8(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.00 new_showsPrec(x0, x1, ty_Float) 33.93/18.00 new_primShowInt0(Pos(Succ(x0))) 33.93/18.00 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.00 new_psPs0([], x0) 33.93/18.00 new_show9(x0, x1, x2) 33.93/18.00 new_showsPrec(x0, x1, ty_Bool) 33.93/18.00 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.00 new_show2(x0) 33.93/18.00 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.00 new_showsPrec(x0, x1, ty_Double) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.00 new_show14(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.00 new_primDivNatS01(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_Integer) 33.93/18.00 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.00 new_psPs0(:(x0, x1), x2) 33.93/18.00 new_primModNatS4(x0) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Succ(x0), Zero) 33.93/18.00 new_show7(x0, x1, x2) 33.93/18.00 new_primDivNatS3(Zero, Zero) 33.93/18.00 33.93/18.00 We have to consider all minimal (P,Q,R)-chains. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (121) DependencyGraphProof (EQUIVALENT) 33.93/18.00 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (122) 33.93/18.00 Obligation: 33.93/18.00 Q DP problem: 33.93/18.00 The TRS P consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.00 33.93/18.00 The TRS R consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.00 new_show10(ww7) -> error([]) 33.93/18.00 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.00 new_show(ww7) -> error([]) 33.93/18.00 new_show7(ww7, dc, dd) -> error([]) 33.93/18.00 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.00 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.00 new_show14(ww7) -> error([]) 33.93/18.00 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.00 new_show3(ww7) -> error([]) 33.93/18.00 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.00 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.00 new_show8(ww7) -> error([]) 33.93/18.00 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.00 new_primModNatS4(ww212) -> Zero 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.00 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_show4(ww7) -> error([]) 33.93/18.00 new_show13(ww7, fa) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.00 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.00 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.00 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.00 new_psPs0([], ww106) -> ww106 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.00 new_show12(ww7) -> error([]) 33.93/18.00 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.00 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.00 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.00 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.00 new_show9(ww7, de, df) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.00 new_show5(ww7, db) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.00 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.00 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.00 new_show1(ww7, da) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.00 new_show6(ww7) -> error([]) 33.93/18.00 new_show11(ww7) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.00 new_show15(ww7) -> error([]) 33.93/18.00 new_primDivNatS4(ww216) -> Zero 33.93/18.00 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 33.93/18.00 The set Q consists of the following terms: 33.93/18.00 33.93/18.00 new_show0(x0, x1, x2, x3) 33.93/18.00 new_show4(x0) 33.93/18.00 new_show1(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.00 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.00 new_primShowInt0(Neg(x0)) 33.93/18.00 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.00 new_show3(x0) 33.93/18.00 new_show5(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_IOError) 33.93/18.00 new_show15(x0) 33.93/18.00 new_primModNatS2(Zero, Succ(x0)) 33.93/18.00 new_show10(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.00 new_primModNatS2(Succ(x0), Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.00 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.00 new_show6(x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Int) 33.93/18.00 new_primDivNatS4(x0) 33.93/18.00 new_primModNatS2(Zero, Zero) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.00 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.00 new_primModNatS02(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.00 new_primIntToChar(x0, x1) 33.93/18.00 new_show(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.00 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.00 new_show12(x0) 33.93/18.00 new_show13(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_@0) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.00 new_primShowInt0(Pos(Zero)) 33.93/18.00 new_primModNatS3(Zero, Zero, x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Char) 33.93/18.00 new_show11(x0) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.00 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.00 new_primDivNatS2(Zero, Zero, x0) 33.93/18.00 new_div(x0, x1) 33.93/18.00 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.00 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.00 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_show8(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.00 new_showsPrec(x0, x1, ty_Float) 33.93/18.00 new_primShowInt0(Pos(Succ(x0))) 33.93/18.00 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.00 new_psPs0([], x0) 33.93/18.00 new_show9(x0, x1, x2) 33.93/18.00 new_showsPrec(x0, x1, ty_Bool) 33.93/18.00 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.00 new_show2(x0) 33.93/18.00 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.00 new_showsPrec(x0, x1, ty_Double) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.00 new_show14(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.00 new_primDivNatS01(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_Integer) 33.93/18.00 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.00 new_psPs0(:(x0, x1), x2) 33.93/18.00 new_primModNatS4(x0) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Succ(x0), Zero) 33.93/18.00 new_show7(x0, x1, x2) 33.93/18.00 new_primDivNatS3(Zero, Zero) 33.93/18.00 33.93/18.00 We have to consider all minimal (P,Q,R)-chains. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (123) TransformationProof (EQUIVALENT) 33.93/18.00 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 33.93/18.00 33.93/18.00 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError)) 33.93/18.00 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError)) 33.93/18.00 33.93/18.00 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (124) 33.93/18.00 Obligation: 33.93/18.00 Q DP problem: 33.93/18.00 The TRS P consists of the following rules: 33.93/18.00 33.93/18.00 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.00 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError) 33.93/18.00 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError) 33.93/18.00 33.93/18.00 The TRS R consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.00 new_show10(ww7) -> error([]) 33.93/18.00 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.00 new_show(ww7) -> error([]) 33.93/18.00 new_show7(ww7, dc, dd) -> error([]) 33.93/18.00 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.00 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.00 new_show14(ww7) -> error([]) 33.93/18.00 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.00 new_show3(ww7) -> error([]) 33.93/18.00 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.00 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.00 new_show8(ww7) -> error([]) 33.93/18.00 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.00 new_primModNatS4(ww212) -> Zero 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.00 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_show4(ww7) -> error([]) 33.93/18.00 new_show13(ww7, fa) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.00 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.00 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.00 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.00 new_psPs0([], ww106) -> ww106 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.00 new_show12(ww7) -> error([]) 33.93/18.00 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.00 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.00 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.00 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.00 new_show9(ww7, de, df) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.00 new_show5(ww7, db) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.00 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.00 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.00 new_show1(ww7, da) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.00 new_show6(ww7) -> error([]) 33.93/18.00 new_show11(ww7) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.00 new_show15(ww7) -> error([]) 33.93/18.00 new_primDivNatS4(ww216) -> Zero 33.93/18.00 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 33.93/18.00 The set Q consists of the following terms: 33.93/18.00 33.93/18.00 new_show0(x0, x1, x2, x3) 33.93/18.00 new_show4(x0) 33.93/18.00 new_show1(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.00 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.00 new_primShowInt0(Neg(x0)) 33.93/18.00 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.00 new_show3(x0) 33.93/18.00 new_show5(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_IOError) 33.93/18.00 new_show15(x0) 33.93/18.00 new_primModNatS2(Zero, Succ(x0)) 33.93/18.00 new_show10(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.00 new_primModNatS2(Succ(x0), Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.00 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.00 new_show6(x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Int) 33.93/18.00 new_primDivNatS4(x0) 33.93/18.00 new_primModNatS2(Zero, Zero) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.00 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.00 new_primModNatS02(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.00 new_primIntToChar(x0, x1) 33.93/18.00 new_show(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.00 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.00 new_show12(x0) 33.93/18.00 new_show13(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_@0) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.00 new_primShowInt0(Pos(Zero)) 33.93/18.00 new_primModNatS3(Zero, Zero, x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Char) 33.93/18.00 new_show11(x0) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.00 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.00 new_primDivNatS2(Zero, Zero, x0) 33.93/18.00 new_div(x0, x1) 33.93/18.00 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.00 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.00 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_show8(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.00 new_showsPrec(x0, x1, ty_Float) 33.93/18.00 new_primShowInt0(Pos(Succ(x0))) 33.93/18.00 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.00 new_psPs0([], x0) 33.93/18.00 new_show9(x0, x1, x2) 33.93/18.00 new_showsPrec(x0, x1, ty_Bool) 33.93/18.00 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.00 new_show2(x0) 33.93/18.00 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.00 new_showsPrec(x0, x1, ty_Double) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.00 new_show14(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.00 new_primDivNatS01(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_Integer) 33.93/18.00 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.00 new_psPs0(:(x0, x1), x2) 33.93/18.00 new_primModNatS4(x0) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Succ(x0), Zero) 33.93/18.00 new_show7(x0, x1, x2) 33.93/18.00 new_primDivNatS3(Zero, Zero) 33.93/18.00 33.93/18.00 We have to consider all minimal (P,Q,R)-chains. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (125) DependencyGraphProof (EQUIVALENT) 33.93/18.00 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (126) 33.93/18.00 Obligation: 33.93/18.00 Q DP problem: 33.93/18.00 The TRS P consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.00 33.93/18.00 The TRS R consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.00 new_show10(ww7) -> error([]) 33.93/18.00 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.00 new_show(ww7) -> error([]) 33.93/18.00 new_show7(ww7, dc, dd) -> error([]) 33.93/18.00 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.00 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.00 new_show14(ww7) -> error([]) 33.93/18.00 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.00 new_show3(ww7) -> error([]) 33.93/18.00 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.00 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.00 new_show8(ww7) -> error([]) 33.93/18.00 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.00 new_primModNatS4(ww212) -> Zero 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.00 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_show4(ww7) -> error([]) 33.93/18.00 new_show13(ww7, fa) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.00 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.00 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.00 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.00 new_psPs0([], ww106) -> ww106 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.00 new_show12(ww7) -> error([]) 33.93/18.00 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.00 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.00 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.00 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.00 new_show9(ww7, de, df) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.00 new_show5(ww7, db) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.00 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.00 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.00 new_show1(ww7, da) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.00 new_show6(ww7) -> error([]) 33.93/18.00 new_show11(ww7) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.00 new_show15(ww7) -> error([]) 33.93/18.00 new_primDivNatS4(ww216) -> Zero 33.93/18.00 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 33.93/18.00 The set Q consists of the following terms: 33.93/18.00 33.93/18.00 new_show0(x0, x1, x2, x3) 33.93/18.00 new_show4(x0) 33.93/18.00 new_show1(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.00 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.00 new_primShowInt0(Neg(x0)) 33.93/18.00 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.00 new_show3(x0) 33.93/18.00 new_show5(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_IOError) 33.93/18.00 new_show15(x0) 33.93/18.00 new_primModNatS2(Zero, Succ(x0)) 33.93/18.00 new_show10(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.00 new_primModNatS2(Succ(x0), Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.00 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.00 new_show6(x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Int) 33.93/18.00 new_primDivNatS4(x0) 33.93/18.00 new_primModNatS2(Zero, Zero) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.00 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.00 new_primModNatS02(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.00 new_primIntToChar(x0, x1) 33.93/18.00 new_show(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.00 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.00 new_show12(x0) 33.93/18.00 new_show13(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_@0) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.00 new_primShowInt0(Pos(Zero)) 33.93/18.00 new_primModNatS3(Zero, Zero, x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Char) 33.93/18.00 new_show11(x0) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.00 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.00 new_primDivNatS2(Zero, Zero, x0) 33.93/18.00 new_div(x0, x1) 33.93/18.00 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.00 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.00 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_show8(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.00 new_showsPrec(x0, x1, ty_Float) 33.93/18.00 new_primShowInt0(Pos(Succ(x0))) 33.93/18.00 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.00 new_psPs0([], x0) 33.93/18.00 new_show9(x0, x1, x2) 33.93/18.00 new_showsPrec(x0, x1, ty_Bool) 33.93/18.00 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.00 new_show2(x0) 33.93/18.00 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.00 new_showsPrec(x0, x1, ty_Double) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.00 new_show14(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.00 new_primDivNatS01(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_Integer) 33.93/18.00 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.00 new_psPs0(:(x0, x1), x2) 33.93/18.00 new_primModNatS4(x0) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Succ(x0), Zero) 33.93/18.00 new_show7(x0, x1, x2) 33.93/18.00 new_primDivNatS3(Zero, Zero) 33.93/18.00 33.93/18.00 We have to consider all minimal (P,Q,R)-chains. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (127) TransformationProof (EQUIVALENT) 33.93/18.00 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 33.93/18.00 33.93/18.00 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering)) 33.93/18.00 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering)) 33.93/18.00 33.93/18.00 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (128) 33.93/18.00 Obligation: 33.93/18.00 Q DP problem: 33.93/18.00 The TRS P consists of the following rules: 33.93/18.00 33.93/18.00 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.00 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Ordering) 33.93/18.00 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering, ty_Ordering) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Ordering) 33.93/18.00 33.93/18.00 The TRS R consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.00 new_show10(ww7) -> error([]) 33.93/18.00 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.00 new_show(ww7) -> error([]) 33.93/18.00 new_show7(ww7, dc, dd) -> error([]) 33.93/18.00 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.00 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.00 new_show14(ww7) -> error([]) 33.93/18.00 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.00 new_show3(ww7) -> error([]) 33.93/18.00 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.00 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.00 new_show8(ww7) -> error([]) 33.93/18.00 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.00 new_primModNatS4(ww212) -> Zero 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.00 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_show4(ww7) -> error([]) 33.93/18.00 new_show13(ww7, fa) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.00 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.00 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.00 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.00 new_psPs0([], ww106) -> ww106 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.00 new_show12(ww7) -> error([]) 33.93/18.00 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.00 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.00 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.00 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.00 new_show9(ww7, de, df) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.00 new_show5(ww7, db) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.00 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.00 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.00 new_show1(ww7, da) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.00 new_show6(ww7) -> error([]) 33.93/18.00 new_show11(ww7) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.00 new_show15(ww7) -> error([]) 33.93/18.00 new_primDivNatS4(ww216) -> Zero 33.93/18.00 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 33.93/18.00 The set Q consists of the following terms: 33.93/18.00 33.93/18.00 new_show0(x0, x1, x2, x3) 33.93/18.00 new_show4(x0) 33.93/18.00 new_show1(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.00 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.00 new_primShowInt0(Neg(x0)) 33.93/18.00 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.00 new_show3(x0) 33.93/18.00 new_show5(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_IOError) 33.93/18.00 new_show15(x0) 33.93/18.00 new_primModNatS2(Zero, Succ(x0)) 33.93/18.00 new_show10(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.00 new_primModNatS2(Succ(x0), Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.00 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.00 new_show6(x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Int) 33.93/18.00 new_primDivNatS4(x0) 33.93/18.00 new_primModNatS2(Zero, Zero) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.00 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.00 new_primModNatS02(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.00 new_primIntToChar(x0, x1) 33.93/18.00 new_show(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.00 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.00 new_show12(x0) 33.93/18.00 new_show13(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_@0) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.00 new_primShowInt0(Pos(Zero)) 33.93/18.00 new_primModNatS3(Zero, Zero, x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Char) 33.93/18.00 new_show11(x0) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.00 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.00 new_primDivNatS2(Zero, Zero, x0) 33.93/18.00 new_div(x0, x1) 33.93/18.00 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.00 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.00 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_show8(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.00 new_showsPrec(x0, x1, ty_Float) 33.93/18.00 new_primShowInt0(Pos(Succ(x0))) 33.93/18.00 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.00 new_psPs0([], x0) 33.93/18.00 new_show9(x0, x1, x2) 33.93/18.00 new_showsPrec(x0, x1, ty_Bool) 33.93/18.00 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.00 new_show2(x0) 33.93/18.00 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.00 new_showsPrec(x0, x1, ty_Double) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.00 new_show14(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.00 new_primDivNatS01(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_Integer) 33.93/18.00 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.00 new_psPs0(:(x0, x1), x2) 33.93/18.00 new_primModNatS4(x0) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Succ(x0), Zero) 33.93/18.00 new_show7(x0, x1, x2) 33.93/18.00 new_primDivNatS3(Zero, Zero) 33.93/18.00 33.93/18.00 We have to consider all minimal (P,Q,R)-chains. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (129) DependencyGraphProof (EQUIVALENT) 33.93/18.00 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (130) 33.93/18.00 Obligation: 33.93/18.00 Q DP problem: 33.93/18.00 The TRS P consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.00 33.93/18.00 The TRS R consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.00 new_show10(ww7) -> error([]) 33.93/18.00 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.00 new_show(ww7) -> error([]) 33.93/18.00 new_show7(ww7, dc, dd) -> error([]) 33.93/18.00 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.00 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.00 new_show14(ww7) -> error([]) 33.93/18.00 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.00 new_show3(ww7) -> error([]) 33.93/18.00 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.00 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.00 new_show8(ww7) -> error([]) 33.93/18.00 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.00 new_primModNatS4(ww212) -> Zero 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.00 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_show4(ww7) -> error([]) 33.93/18.00 new_show13(ww7, fa) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.00 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.00 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.00 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.00 new_psPs0([], ww106) -> ww106 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.00 new_show12(ww7) -> error([]) 33.93/18.00 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.00 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.00 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.00 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.00 new_show9(ww7, de, df) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.00 new_show5(ww7, db) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.00 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.00 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.00 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.00 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.00 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.00 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.00 new_show1(ww7, da) -> error([]) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.00 new_show6(ww7) -> error([]) 33.93/18.00 new_show11(ww7) -> error([]) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.00 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.00 new_show15(ww7) -> error([]) 33.93/18.00 new_primDivNatS4(ww216) -> Zero 33.93/18.00 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 33.93/18.00 The set Q consists of the following terms: 33.93/18.00 33.93/18.00 new_show0(x0, x1, x2, x3) 33.93/18.00 new_show4(x0) 33.93/18.00 new_show1(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.00 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.00 new_primShowInt0(Neg(x0)) 33.93/18.00 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.00 new_show3(x0) 33.93/18.00 new_show5(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_IOError) 33.93/18.00 new_show15(x0) 33.93/18.00 new_primModNatS2(Zero, Succ(x0)) 33.93/18.00 new_show10(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.00 new_primModNatS2(Succ(x0), Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.00 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.00 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.00 new_show6(x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Int) 33.93/18.00 new_primDivNatS4(x0) 33.93/18.00 new_primModNatS2(Zero, Zero) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.00 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.00 new_primModNatS02(x0, x1) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.00 new_primIntToChar(x0, x1) 33.93/18.00 new_show(x0) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.00 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.00 new_show12(x0) 33.93/18.00 new_show13(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_@0) 33.93/18.00 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.00 new_primShowInt0(Pos(Zero)) 33.93/18.00 new_primModNatS3(Zero, Zero, x0) 33.93/18.00 new_showsPrec(x0, x1, ty_Char) 33.93/18.00 new_show11(x0) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.00 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.00 new_primDivNatS2(Zero, Zero, x0) 33.93/18.00 new_div(x0, x1) 33.93/18.00 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.00 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.00 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.00 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.00 new_show8(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.00 new_showsPrec(x0, x1, ty_Float) 33.93/18.00 new_primShowInt0(Pos(Succ(x0))) 33.93/18.00 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.00 new_psPs0([], x0) 33.93/18.00 new_show9(x0, x1, x2) 33.93/18.00 new_showsPrec(x0, x1, ty_Bool) 33.93/18.00 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.00 new_show2(x0) 33.93/18.00 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.00 new_showsPrec(x0, x1, ty_Double) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.00 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.00 new_show14(x0) 33.93/18.00 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.00 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.00 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.00 new_primDivNatS01(x0, x1) 33.93/18.00 new_showsPrec(x0, x1, ty_Integer) 33.93/18.00 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.00 new_psPs0(:(x0, x1), x2) 33.93/18.00 new_primModNatS4(x0) 33.93/18.00 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.00 new_primDivNatS3(Succ(x0), Zero) 33.93/18.00 new_show7(x0, x1, x2) 33.93/18.00 new_primDivNatS3(Zero, Zero) 33.93/18.00 33.93/18.00 We have to consider all minimal (P,Q,R)-chains. 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (131) TransformationProof (EQUIVALENT) 33.93/18.00 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 33.93/18.00 33.93/18.00 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int)) 33.93/18.00 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int)) 33.93/18.00 33.93/18.00 33.93/18.00 ---------------------------------------- 33.93/18.00 33.93/18.00 (132) 33.93/18.00 Obligation: 33.93/18.00 Q DP problem: 33.93/18.00 The TRS P consists of the following rules: 33.93/18.00 33.93/18.00 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.00 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.00 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int) 33.93/18.00 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int) 33.93/18.00 33.93/18.00 The TRS R consists of the following rules: 33.93/18.00 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.00 new_show10(ww7) -> error([]) 33.93/18.00 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.00 new_show(ww7) -> error([]) 33.93/18.00 new_show7(ww7, dc, dd) -> error([]) 33.93/18.00 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.00 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.00 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.00 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.00 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.00 new_show14(ww7) -> error([]) 33.93/18.00 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.00 new_show3(ww7) -> error([]) 33.93/18.00 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.00 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.00 new_show8(ww7) -> error([]) 33.93/18.00 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.00 new_primModNatS4(ww212) -> Zero 33.93/18.00 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.00 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.00 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.00 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.00 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_show4(ww7) -> error([]) 33.93/18.01 new_show13(ww7, fa) -> error([]) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.01 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.01 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.01 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.01 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.01 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.01 new_psPs0([], ww106) -> ww106 33.93/18.01 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.01 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.01 new_show12(ww7) -> error([]) 33.93/18.01 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.01 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.01 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.01 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.01 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.01 new_show9(ww7, de, df) -> error([]) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.01 new_show5(ww7, db) -> error([]) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.01 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.01 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.01 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.01 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.01 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.01 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.01 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.01 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.01 new_show1(ww7, da) -> error([]) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.01 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.01 new_show6(ww7) -> error([]) 33.93/18.01 new_show11(ww7) -> error([]) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.01 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.01 new_show15(ww7) -> error([]) 33.93/18.01 new_primDivNatS4(ww216) -> Zero 33.93/18.01 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 33.93/18.01 The set Q consists of the following terms: 33.93/18.01 33.93/18.01 new_show0(x0, x1, x2, x3) 33.93/18.01 new_show4(x0) 33.93/18.01 new_show1(x0, x1) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.01 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.01 new_primShowInt0(Neg(x0)) 33.93/18.01 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.01 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.01 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.01 new_show3(x0) 33.93/18.01 new_show5(x0, x1) 33.93/18.01 new_showsPrec(x0, x1, ty_IOError) 33.93/18.01 new_show15(x0) 33.93/18.01 new_primModNatS2(Zero, Succ(x0)) 33.93/18.01 new_show10(x0) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.01 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.01 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.01 new_primModNatS2(Succ(x0), Zero) 33.93/18.01 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.01 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.01 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.01 new_show6(x0) 33.93/18.01 new_showsPrec(x0, x1, ty_Int) 33.93/18.01 new_primDivNatS4(x0) 33.93/18.01 new_primModNatS2(Zero, Zero) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.01 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.01 new_primModNatS02(x0, x1) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.01 new_primIntToChar(x0, x1) 33.93/18.01 new_show(x0) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.01 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.01 new_show12(x0) 33.93/18.01 new_show13(x0, x1) 33.93/18.01 new_showsPrec(x0, x1, ty_@0) 33.93/18.01 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.01 new_primShowInt0(Pos(Zero)) 33.93/18.01 new_primModNatS3(Zero, Zero, x0) 33.93/18.01 new_showsPrec(x0, x1, ty_Char) 33.93/18.01 new_show11(x0) 33.93/18.01 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.01 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.01 new_primDivNatS2(Zero, Zero, x0) 33.93/18.01 new_div(x0, x1) 33.93/18.01 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.01 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.01 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.01 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.01 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.01 new_show8(x0) 33.93/18.01 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.01 new_showsPrec(x0, x1, ty_Float) 33.93/18.01 new_primShowInt0(Pos(Succ(x0))) 33.93/18.01 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.01 new_psPs0([], x0) 33.93/18.01 new_show9(x0, x1, x2) 33.93/18.01 new_showsPrec(x0, x1, ty_Bool) 33.93/18.01 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.01 new_show2(x0) 33.93/18.01 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.01 new_showsPrec(x0, x1, ty_Double) 33.93/18.01 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.01 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.01 new_show14(x0) 33.93/18.01 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.01 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.01 new_primDivNatS01(x0, x1) 33.93/18.01 new_showsPrec(x0, x1, ty_Integer) 33.93/18.01 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.01 new_psPs0(:(x0, x1), x2) 33.93/18.01 new_primModNatS4(x0) 33.93/18.01 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.01 new_primDivNatS3(Succ(x0), Zero) 33.93/18.01 new_show7(x0, x1, x2) 33.93/18.01 new_primDivNatS3(Zero, Zero) 33.93/18.01 33.93/18.01 We have to consider all minimal (P,Q,R)-chains. 33.93/18.01 ---------------------------------------- 33.93/18.01 33.93/18.01 (133) DependencyGraphProof (EQUIVALENT) 33.93/18.01 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 33.93/18.01 ---------------------------------------- 33.93/18.01 33.93/18.01 (134) 33.93/18.01 Obligation: 33.93/18.01 Q DP problem: 33.93/18.01 The TRS P consists of the following rules: 33.93/18.01 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.01 33.93/18.01 The TRS R consists of the following rules: 33.93/18.01 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.01 new_show10(ww7) -> error([]) 33.93/18.01 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.01 new_show(ww7) -> error([]) 33.93/18.01 new_show7(ww7, dc, dd) -> error([]) 33.93/18.01 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.01 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.01 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.01 new_show14(ww7) -> error([]) 33.93/18.01 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.01 new_show3(ww7) -> error([]) 33.93/18.01 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.01 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.01 new_show8(ww7) -> error([]) 33.93/18.01 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.01 new_primModNatS4(ww212) -> Zero 33.93/18.01 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.01 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.01 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.01 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_show4(ww7) -> error([]) 33.93/18.01 new_show13(ww7, fa) -> error([]) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.01 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.01 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.01 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.01 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.01 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.01 new_psPs0([], ww106) -> ww106 33.93/18.01 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.01 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.01 new_show12(ww7) -> error([]) 33.93/18.01 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.01 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.01 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.01 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.01 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.01 new_show9(ww7, de, df) -> error([]) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.01 new_show5(ww7, db) -> error([]) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.01 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.01 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.01 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.01 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.01 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.01 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.01 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.01 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.01 new_show1(ww7, da) -> error([]) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.01 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.01 new_show6(ww7) -> error([]) 33.93/18.01 new_show11(ww7) -> error([]) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.01 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.01 new_show15(ww7) -> error([]) 33.93/18.01 new_primDivNatS4(ww216) -> Zero 33.93/18.01 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 33.93/18.01 The set Q consists of the following terms: 33.93/18.01 33.93/18.01 new_show0(x0, x1, x2, x3) 33.93/18.01 new_show4(x0) 33.93/18.01 new_show1(x0, x1) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.01 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.01 new_primShowInt0(Neg(x0)) 33.93/18.01 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.01 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.01 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.01 new_show3(x0) 33.93/18.01 new_show5(x0, x1) 33.93/18.01 new_showsPrec(x0, x1, ty_IOError) 33.93/18.01 new_show15(x0) 33.93/18.01 new_primModNatS2(Zero, Succ(x0)) 33.93/18.01 new_show10(x0) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.01 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.01 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.01 new_primModNatS2(Succ(x0), Zero) 33.93/18.01 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.01 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.01 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.01 new_show6(x0) 33.93/18.01 new_showsPrec(x0, x1, ty_Int) 33.93/18.01 new_primDivNatS4(x0) 33.93/18.01 new_primModNatS2(Zero, Zero) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.01 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.01 new_primModNatS02(x0, x1) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.01 new_primIntToChar(x0, x1) 33.93/18.01 new_show(x0) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.01 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.01 new_show12(x0) 33.93/18.01 new_show13(x0, x1) 33.93/18.01 new_showsPrec(x0, x1, ty_@0) 33.93/18.01 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.01 new_primShowInt0(Pos(Zero)) 33.93/18.01 new_primModNatS3(Zero, Zero, x0) 33.93/18.01 new_showsPrec(x0, x1, ty_Char) 33.93/18.01 new_show11(x0) 33.93/18.01 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.01 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.01 new_primDivNatS2(Zero, Zero, x0) 33.93/18.01 new_div(x0, x1) 33.93/18.01 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.01 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.01 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.01 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.01 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.01 new_show8(x0) 33.93/18.01 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.01 new_showsPrec(x0, x1, ty_Float) 33.93/18.01 new_primShowInt0(Pos(Succ(x0))) 33.93/18.01 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.01 new_psPs0([], x0) 33.93/18.01 new_show9(x0, x1, x2) 33.93/18.01 new_showsPrec(x0, x1, ty_Bool) 33.93/18.01 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.01 new_show2(x0) 33.93/18.01 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.01 new_showsPrec(x0, x1, ty_Double) 33.93/18.01 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.01 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.01 new_show14(x0) 33.93/18.01 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.01 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.01 new_primDivNatS01(x0, x1) 33.93/18.01 new_showsPrec(x0, x1, ty_Integer) 33.93/18.01 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.01 new_psPs0(:(x0, x1), x2) 33.93/18.01 new_primModNatS4(x0) 33.93/18.01 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.01 new_primDivNatS3(Succ(x0), Zero) 33.93/18.01 new_show7(x0, x1, x2) 33.93/18.01 new_primDivNatS3(Zero, Zero) 33.93/18.01 33.93/18.01 We have to consider all minimal (P,Q,R)-chains. 33.93/18.01 ---------------------------------------- 33.93/18.01 33.93/18.01 (135) TransformationProof (EQUIVALENT) 33.93/18.01 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 33.93/18.01 33.93/18.01 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6))) 33.93/18.01 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6))) 33.93/18.01 33.93/18.01 33.93/18.01 ---------------------------------------- 33.93/18.01 33.93/18.01 (136) 33.93/18.01 Obligation: 33.93/18.01 Q DP problem: 33.93/18.01 The TRS P consists of the following rules: 33.93/18.01 33.93/18.01 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.01 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6)) 33.93/18.01 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6)) 33.93/18.01 33.93/18.01 The TRS R consists of the following rules: 33.93/18.01 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.01 new_show10(ww7) -> error([]) 33.93/18.01 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.01 new_show(ww7) -> error([]) 33.93/18.01 new_show7(ww7, dc, dd) -> error([]) 33.93/18.01 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.01 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.01 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.01 new_show14(ww7) -> error([]) 33.93/18.01 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.01 new_show3(ww7) -> error([]) 33.93/18.01 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.01 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.01 new_show8(ww7) -> error([]) 33.93/18.01 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.01 new_primModNatS4(ww212) -> Zero 33.93/18.01 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.01 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.01 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.01 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_show4(ww7) -> error([]) 33.93/18.01 new_show13(ww7, fa) -> error([]) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 33.93/18.01 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 33.93/18.01 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 33.93/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 33.93/18.01 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 33.93/18.01 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 33.93/18.01 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 33.93/18.01 new_psPs0([], ww106) -> ww106 33.93/18.01 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 33.93/18.01 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 33.93/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 33.93/18.01 new_show12(ww7) -> error([]) 33.93/18.01 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 33.93/18.01 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 33.93/18.01 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 33.93/18.01 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 33.93/18.01 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 33.93/18.01 new_show9(ww7, de, df) -> error([]) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 33.93/18.01 new_show5(ww7, db) -> error([]) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 33.93/18.01 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 33.93/18.01 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 33.93/18.01 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 33.93/18.01 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 33.93/18.01 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.01 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 33.93/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 33.93/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 33.93/18.01 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 33.93/18.01 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 33.93/18.01 new_show1(ww7, da) -> error([]) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.01 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 33.93/18.01 new_show6(ww7) -> error([]) 33.93/18.01 new_show11(ww7) -> error([]) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 33.93/18.01 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 33.93/18.01 new_show15(ww7) -> error([]) 33.93/18.01 new_primDivNatS4(ww216) -> Zero 33.93/18.01 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 33.93/18.01 The set Q consists of the following terms: 33.93/18.01 33.93/18.01 new_show0(x0, x1, x2, x3) 33.93/18.01 new_show4(x0) 33.93/18.01 new_show1(x0, x1) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 33.93/18.01 new_showsPrec(x0, x1, ty_Ordering) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 33.93/18.01 new_primShowInt0(Neg(x0)) 33.93/18.01 new_showsPrec(x0, x1, ty_IOErrorKind) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 33.93/18.01 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 33.93/18.01 new_primDivNatS3(Zero, Succ(x0)) 33.93/18.01 new_show3(x0) 33.93/18.01 new_show5(x0, x1) 33.93/18.01 new_showsPrec(x0, x1, ty_IOError) 33.93/18.01 new_show15(x0) 33.93/18.01 new_primModNatS2(Zero, Succ(x0)) 33.93/18.01 new_show10(x0) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 33.93/18.01 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 33.93/18.01 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 33.93/18.01 new_primModNatS2(Succ(x0), Zero) 33.93/18.01 new_primDivNatS2(Succ(x0), Zero, x1) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 33.93/18.01 new_primDivNatS02(x0, x1, Succ(x2), Zero) 33.93/18.01 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 33.93/18.01 new_show6(x0) 33.93/18.01 new_showsPrec(x0, x1, ty_Int) 33.93/18.01 new_primDivNatS4(x0) 33.93/18.01 new_primModNatS2(Zero, Zero) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 33.93/18.01 new_primModNatS2(Succ(x0), Succ(x1)) 33.93/18.01 new_primModNatS02(x0, x1) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 33.93/18.01 new_primIntToChar(x0, x1) 33.93/18.01 new_show(x0) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 33.93/18.01 new_showsPrec(x0, x1, ty_HugsException) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 33.93/18.01 new_show12(x0) 33.93/18.01 new_show13(x0, x1) 33.93/18.01 new_showsPrec(x0, x1, ty_@0) 33.93/18.01 new_primDivNatS02(x0, x1, Zero, Zero) 33.93/18.01 new_primShowInt0(Pos(Zero)) 33.93/18.01 new_primModNatS3(Zero, Zero, x0) 33.93/18.01 new_showsPrec(x0, x1, ty_Char) 33.93/18.01 new_show11(x0) 33.93/18.01 new_primModNatS01(x0, x1, Succ(x2), Zero) 33.93/18.01 new_primDivNatS3(Succ(x0), Succ(x1)) 33.93/18.01 new_primDivNatS2(Zero, Zero, x0) 33.93/18.01 new_div(x0, x1) 33.93/18.01 new_primDivNatS2(Zero, Succ(x0), x1) 33.93/18.01 new_pt0(x0, x1, x2, x3, x4, x5) 33.93/18.01 new_primModNatS3(Zero, Succ(x0), x1) 33.93/18.01 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 33.93/18.01 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 33.93/18.01 new_show8(x0) 33.93/18.01 new_showsPrec(x0, x1, app(ty_IO, x2)) 33.93/18.01 new_showsPrec(x0, x1, ty_Float) 33.93/18.01 new_primShowInt0(Pos(Succ(x0))) 33.93/18.01 new_primModNatS3(Succ(x0), Succ(x1), x2) 33.93/18.01 new_psPs0([], x0) 33.93/18.01 new_show9(x0, x1, x2) 33.93/18.01 new_showsPrec(x0, x1, ty_Bool) 33.93/18.01 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 33.93/18.01 new_show2(x0) 33.93/18.01 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 33.93/18.01 new_showsPrec(x0, x1, ty_Double) 33.93/18.01 new_primModNatS01(x0, x1, Zero, Zero) 33.93/18.01 new_primDivNatS2(Succ(x0), Succ(x1), x2) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 33.93/18.01 new_show14(x0) 33.93/18.01 new_showsPrec(x0, x1, app(ty_[], x2)) 33.93/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 33.93/18.01 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 33.93/18.01 new_primDivNatS01(x0, x1) 33.93/18.01 new_showsPrec(x0, x1, ty_Integer) 33.93/18.01 new_primModNatS3(Succ(x0), Zero, x1) 33.93/18.01 new_psPs0(:(x0, x1), x2) 33.93/18.01 new_primModNatS4(x0) 33.93/18.01 new_primModNatS01(x0, x1, Zero, Succ(x2)) 33.93/18.01 new_primDivNatS3(Succ(x0), Zero) 33.93/18.01 new_show7(x0, x1, x2) 33.93/18.01 new_primDivNatS3(Zero, Zero) 33.93/18.01 33.93/18.01 We have to consider all minimal (P,Q,R)-chains. 33.93/18.01 ---------------------------------------- 33.93/18.01 33.93/18.01 (137) DependencyGraphProof (EQUIVALENT) 33.93/18.01 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 33.93/18.01 ---------------------------------------- 33.93/18.01 33.93/18.01 (138) 33.93/18.01 Obligation: 33.93/18.01 Q DP problem: 33.93/18.01 The TRS P consists of the following rules: 33.93/18.01 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 33.93/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 33.93/18.01 33.93/18.01 The TRS R consists of the following rules: 33.93/18.01 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 33.93/18.01 new_show10(ww7) -> error([]) 33.93/18.01 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 33.93/18.01 new_show(ww7) -> error([]) 33.93/18.01 new_show7(ww7, dc, dd) -> error([]) 33.93/18.01 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 33.93/18.01 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 33.93/18.01 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 33.93/18.01 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 33.93/18.01 new_show14(ww7) -> error([]) 33.93/18.01 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 33.93/18.01 new_show3(ww7) -> error([]) 33.93/18.01 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 33.93/18.01 new_show2(ww7) -> new_primShowInt0(ww7) 33.93/18.01 new_show8(ww7) -> error([]) 33.93/18.01 new_show0(ww7, ce, cf, cg) -> error([]) 33.93/18.01 new_primModNatS4(ww212) -> Zero 33.93/18.01 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 33.93/18.01 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 33.93/18.01 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 33.93/18.01 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 33.93/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 33.93/18.01 new_show4(ww7) -> error([]) 33.93/18.01 new_show13(ww7, fa) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.01 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.01 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.01 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.01 new_psPs0([], ww106) -> ww106 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.01 new_show12(ww7) -> error([]) 34.17/18.01 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.01 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.01 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.01 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.01 new_show9(ww7, de, df) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.01 new_show5(ww7, db) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.01 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.01 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.01 new_show1(ww7, da) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.01 new_show6(ww7) -> error([]) 34.17/18.01 new_show11(ww7) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.01 new_show15(ww7) -> error([]) 34.17/18.01 new_primDivNatS4(ww216) -> Zero 34.17/18.01 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 34.17/18.01 The set Q consists of the following terms: 34.17/18.01 34.17/18.01 new_show0(x0, x1, x2, x3) 34.17/18.01 new_show4(x0) 34.17/18.01 new_show1(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.01 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.01 new_primShowInt0(Neg(x0)) 34.17/18.01 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.01 new_show3(x0) 34.17/18.01 new_show5(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_IOError) 34.17/18.01 new_show15(x0) 34.17/18.01 new_primModNatS2(Zero, Succ(x0)) 34.17/18.01 new_show10(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.01 new_primModNatS2(Succ(x0), Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.01 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.01 new_show6(x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Int) 34.17/18.01 new_primDivNatS4(x0) 34.17/18.01 new_primModNatS2(Zero, Zero) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.01 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.01 new_primModNatS02(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.01 new_primIntToChar(x0, x1) 34.17/18.01 new_show(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.01 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.01 new_show12(x0) 34.17/18.01 new_show13(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_@0) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.01 new_primShowInt0(Pos(Zero)) 34.17/18.01 new_primModNatS3(Zero, Zero, x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Char) 34.17/18.01 new_show11(x0) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.01 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.01 new_primDivNatS2(Zero, Zero, x0) 34.17/18.01 new_div(x0, x1) 34.17/18.01 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.01 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.01 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_show8(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.01 new_showsPrec(x0, x1, ty_Float) 34.17/18.01 new_primShowInt0(Pos(Succ(x0))) 34.17/18.01 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.01 new_psPs0([], x0) 34.17/18.01 new_show9(x0, x1, x2) 34.17/18.01 new_showsPrec(x0, x1, ty_Bool) 34.17/18.01 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.01 new_show2(x0) 34.17/18.01 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.01 new_showsPrec(x0, x1, ty_Double) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.01 new_show14(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.01 new_primDivNatS01(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_Integer) 34.17/18.01 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.01 new_psPs0(:(x0, x1), x2) 34.17/18.01 new_primModNatS4(x0) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Succ(x0), Zero) 34.17/18.01 new_show7(x0, x1, x2) 34.17/18.01 new_primDivNatS3(Zero, Zero) 34.17/18.01 34.17/18.01 We have to consider all minimal (P,Q,R)-chains. 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (139) TransformationProof (EQUIVALENT) 34.17/18.01 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.01 34.17/18.01 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool)) 34.17/18.01 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool)) 34.17/18.01 34.17/18.01 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (140) 34.17/18.01 Obligation: 34.17/18.01 Q DP problem: 34.17/18.01 The TRS P consists of the following rules: 34.17/18.01 34.17/18.01 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.01 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool) 34.17/18.01 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool) 34.17/18.01 34.17/18.01 The TRS R consists of the following rules: 34.17/18.01 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.01 new_show10(ww7) -> error([]) 34.17/18.01 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.01 new_show(ww7) -> error([]) 34.17/18.01 new_show7(ww7, dc, dd) -> error([]) 34.17/18.01 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.01 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.01 new_show14(ww7) -> error([]) 34.17/18.01 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.01 new_show3(ww7) -> error([]) 34.17/18.01 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.01 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.01 new_show8(ww7) -> error([]) 34.17/18.01 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.01 new_primModNatS4(ww212) -> Zero 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.01 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_show4(ww7) -> error([]) 34.17/18.01 new_show13(ww7, fa) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.01 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.01 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.01 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.01 new_psPs0([], ww106) -> ww106 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.01 new_show12(ww7) -> error([]) 34.17/18.01 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.01 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.01 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.01 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.01 new_show9(ww7, de, df) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.01 new_show5(ww7, db) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.01 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.01 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.01 new_show1(ww7, da) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.01 new_show6(ww7) -> error([]) 34.17/18.01 new_show11(ww7) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.01 new_show15(ww7) -> error([]) 34.17/18.01 new_primDivNatS4(ww216) -> Zero 34.17/18.01 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 34.17/18.01 The set Q consists of the following terms: 34.17/18.01 34.17/18.01 new_show0(x0, x1, x2, x3) 34.17/18.01 new_show4(x0) 34.17/18.01 new_show1(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.01 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.01 new_primShowInt0(Neg(x0)) 34.17/18.01 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.01 new_show3(x0) 34.17/18.01 new_show5(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_IOError) 34.17/18.01 new_show15(x0) 34.17/18.01 new_primModNatS2(Zero, Succ(x0)) 34.17/18.01 new_show10(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.01 new_primModNatS2(Succ(x0), Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.01 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.01 new_show6(x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Int) 34.17/18.01 new_primDivNatS4(x0) 34.17/18.01 new_primModNatS2(Zero, Zero) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.01 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.01 new_primModNatS02(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.01 new_primIntToChar(x0, x1) 34.17/18.01 new_show(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.01 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.01 new_show12(x0) 34.17/18.01 new_show13(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_@0) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.01 new_primShowInt0(Pos(Zero)) 34.17/18.01 new_primModNatS3(Zero, Zero, x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Char) 34.17/18.01 new_show11(x0) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.01 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.01 new_primDivNatS2(Zero, Zero, x0) 34.17/18.01 new_div(x0, x1) 34.17/18.01 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.01 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.01 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_show8(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.01 new_showsPrec(x0, x1, ty_Float) 34.17/18.01 new_primShowInt0(Pos(Succ(x0))) 34.17/18.01 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.01 new_psPs0([], x0) 34.17/18.01 new_show9(x0, x1, x2) 34.17/18.01 new_showsPrec(x0, x1, ty_Bool) 34.17/18.01 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.01 new_show2(x0) 34.17/18.01 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.01 new_showsPrec(x0, x1, ty_Double) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.01 new_show14(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.01 new_primDivNatS01(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_Integer) 34.17/18.01 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.01 new_psPs0(:(x0, x1), x2) 34.17/18.01 new_primModNatS4(x0) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Succ(x0), Zero) 34.17/18.01 new_show7(x0, x1, x2) 34.17/18.01 new_primDivNatS3(Zero, Zero) 34.17/18.01 34.17/18.01 We have to consider all minimal (P,Q,R)-chains. 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (141) DependencyGraphProof (EQUIVALENT) 34.17/18.01 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (142) 34.17/18.01 Obligation: 34.17/18.01 Q DP problem: 34.17/18.01 The TRS P consists of the following rules: 34.17/18.01 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.01 34.17/18.01 The TRS R consists of the following rules: 34.17/18.01 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.01 new_show10(ww7) -> error([]) 34.17/18.01 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.01 new_show(ww7) -> error([]) 34.17/18.01 new_show7(ww7, dc, dd) -> error([]) 34.17/18.01 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.01 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.01 new_show14(ww7) -> error([]) 34.17/18.01 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.01 new_show3(ww7) -> error([]) 34.17/18.01 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.01 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.01 new_show8(ww7) -> error([]) 34.17/18.01 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.01 new_primModNatS4(ww212) -> Zero 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.01 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_show4(ww7) -> error([]) 34.17/18.01 new_show13(ww7, fa) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.01 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.01 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.01 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.01 new_psPs0([], ww106) -> ww106 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.01 new_show12(ww7) -> error([]) 34.17/18.01 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.01 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.01 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.01 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.01 new_show9(ww7, de, df) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.01 new_show5(ww7, db) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.01 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.01 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.01 new_show1(ww7, da) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.01 new_show6(ww7) -> error([]) 34.17/18.01 new_show11(ww7) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.01 new_show15(ww7) -> error([]) 34.17/18.01 new_primDivNatS4(ww216) -> Zero 34.17/18.01 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 34.17/18.01 The set Q consists of the following terms: 34.17/18.01 34.17/18.01 new_show0(x0, x1, x2, x3) 34.17/18.01 new_show4(x0) 34.17/18.01 new_show1(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.01 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.01 new_primShowInt0(Neg(x0)) 34.17/18.01 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.01 new_show3(x0) 34.17/18.01 new_show5(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_IOError) 34.17/18.01 new_show15(x0) 34.17/18.01 new_primModNatS2(Zero, Succ(x0)) 34.17/18.01 new_show10(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.01 new_primModNatS2(Succ(x0), Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.01 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.01 new_show6(x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Int) 34.17/18.01 new_primDivNatS4(x0) 34.17/18.01 new_primModNatS2(Zero, Zero) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.01 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.01 new_primModNatS02(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.01 new_primIntToChar(x0, x1) 34.17/18.01 new_show(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.01 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.01 new_show12(x0) 34.17/18.01 new_show13(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_@0) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.01 new_primShowInt0(Pos(Zero)) 34.17/18.01 new_primModNatS3(Zero, Zero, x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Char) 34.17/18.01 new_show11(x0) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.01 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.01 new_primDivNatS2(Zero, Zero, x0) 34.17/18.01 new_div(x0, x1) 34.17/18.01 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.01 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.01 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_show8(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.01 new_showsPrec(x0, x1, ty_Float) 34.17/18.01 new_primShowInt0(Pos(Succ(x0))) 34.17/18.01 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.01 new_psPs0([], x0) 34.17/18.01 new_show9(x0, x1, x2) 34.17/18.01 new_showsPrec(x0, x1, ty_Bool) 34.17/18.01 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.01 new_show2(x0) 34.17/18.01 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.01 new_showsPrec(x0, x1, ty_Double) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.01 new_show14(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.01 new_primDivNatS01(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_Integer) 34.17/18.01 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.01 new_psPs0(:(x0, x1), x2) 34.17/18.01 new_primModNatS4(x0) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Succ(x0), Zero) 34.17/18.01 new_show7(x0, x1, x2) 34.17/18.01 new_primDivNatS3(Zero, Zero) 34.17/18.01 34.17/18.01 We have to consider all minimal (P,Q,R)-chains. 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (143) TransformationProof (EQUIVALENT) 34.17/18.01 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.01 34.17/18.01 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double)) 34.17/18.01 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double)) 34.17/18.01 34.17/18.01 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (144) 34.17/18.01 Obligation: 34.17/18.01 Q DP problem: 34.17/18.01 The TRS P consists of the following rules: 34.17/18.01 34.17/18.01 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.01 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double) 34.17/18.01 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double) 34.17/18.01 34.17/18.01 The TRS R consists of the following rules: 34.17/18.01 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.01 new_show10(ww7) -> error([]) 34.17/18.01 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.01 new_show(ww7) -> error([]) 34.17/18.01 new_show7(ww7, dc, dd) -> error([]) 34.17/18.01 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.01 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.01 new_show14(ww7) -> error([]) 34.17/18.01 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.01 new_show3(ww7) -> error([]) 34.17/18.01 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.01 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.01 new_show8(ww7) -> error([]) 34.17/18.01 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.01 new_primModNatS4(ww212) -> Zero 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.01 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_show4(ww7) -> error([]) 34.17/18.01 new_show13(ww7, fa) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.01 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.01 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.01 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.01 new_psPs0([], ww106) -> ww106 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.01 new_show12(ww7) -> error([]) 34.17/18.01 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.01 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.01 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.01 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.01 new_show9(ww7, de, df) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.01 new_show5(ww7, db) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.01 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.01 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.01 new_show1(ww7, da) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.01 new_show6(ww7) -> error([]) 34.17/18.01 new_show11(ww7) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.01 new_show15(ww7) -> error([]) 34.17/18.01 new_primDivNatS4(ww216) -> Zero 34.17/18.01 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 34.17/18.01 The set Q consists of the following terms: 34.17/18.01 34.17/18.01 new_show0(x0, x1, x2, x3) 34.17/18.01 new_show4(x0) 34.17/18.01 new_show1(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.01 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.01 new_primShowInt0(Neg(x0)) 34.17/18.01 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.01 new_show3(x0) 34.17/18.01 new_show5(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_IOError) 34.17/18.01 new_show15(x0) 34.17/18.01 new_primModNatS2(Zero, Succ(x0)) 34.17/18.01 new_show10(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.01 new_primModNatS2(Succ(x0), Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.01 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.01 new_show6(x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Int) 34.17/18.01 new_primDivNatS4(x0) 34.17/18.01 new_primModNatS2(Zero, Zero) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.01 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.01 new_primModNatS02(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.01 new_primIntToChar(x0, x1) 34.17/18.01 new_show(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.01 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.01 new_show12(x0) 34.17/18.01 new_show13(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_@0) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.01 new_primShowInt0(Pos(Zero)) 34.17/18.01 new_primModNatS3(Zero, Zero, x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Char) 34.17/18.01 new_show11(x0) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.01 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.01 new_primDivNatS2(Zero, Zero, x0) 34.17/18.01 new_div(x0, x1) 34.17/18.01 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.01 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.01 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_show8(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.01 new_showsPrec(x0, x1, ty_Float) 34.17/18.01 new_primShowInt0(Pos(Succ(x0))) 34.17/18.01 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.01 new_psPs0([], x0) 34.17/18.01 new_show9(x0, x1, x2) 34.17/18.01 new_showsPrec(x0, x1, ty_Bool) 34.17/18.01 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.01 new_show2(x0) 34.17/18.01 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.01 new_showsPrec(x0, x1, ty_Double) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.01 new_show14(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.01 new_primDivNatS01(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_Integer) 34.17/18.01 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.01 new_psPs0(:(x0, x1), x2) 34.17/18.01 new_primModNatS4(x0) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Succ(x0), Zero) 34.17/18.01 new_show7(x0, x1, x2) 34.17/18.01 new_primDivNatS3(Zero, Zero) 34.17/18.01 34.17/18.01 We have to consider all minimal (P,Q,R)-chains. 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (145) DependencyGraphProof (EQUIVALENT) 34.17/18.01 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (146) 34.17/18.01 Obligation: 34.17/18.01 Q DP problem: 34.17/18.01 The TRS P consists of the following rules: 34.17/18.01 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.01 34.17/18.01 The TRS R consists of the following rules: 34.17/18.01 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.01 new_show10(ww7) -> error([]) 34.17/18.01 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.01 new_show(ww7) -> error([]) 34.17/18.01 new_show7(ww7, dc, dd) -> error([]) 34.17/18.01 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.01 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.01 new_show14(ww7) -> error([]) 34.17/18.01 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.01 new_show3(ww7) -> error([]) 34.17/18.01 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.01 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.01 new_show8(ww7) -> error([]) 34.17/18.01 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.01 new_primModNatS4(ww212) -> Zero 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.01 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_show4(ww7) -> error([]) 34.17/18.01 new_show13(ww7, fa) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.01 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.01 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.01 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.01 new_psPs0([], ww106) -> ww106 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.01 new_show12(ww7) -> error([]) 34.17/18.01 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.01 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.01 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.01 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.01 new_show9(ww7, de, df) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.01 new_show5(ww7, db) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.01 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.01 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.01 new_show1(ww7, da) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.01 new_show6(ww7) -> error([]) 34.17/18.01 new_show11(ww7) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.01 new_show15(ww7) -> error([]) 34.17/18.01 new_primDivNatS4(ww216) -> Zero 34.17/18.01 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 34.17/18.01 The set Q consists of the following terms: 34.17/18.01 34.17/18.01 new_show0(x0, x1, x2, x3) 34.17/18.01 new_show4(x0) 34.17/18.01 new_show1(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.01 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.01 new_primShowInt0(Neg(x0)) 34.17/18.01 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.01 new_show3(x0) 34.17/18.01 new_show5(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_IOError) 34.17/18.01 new_show15(x0) 34.17/18.01 new_primModNatS2(Zero, Succ(x0)) 34.17/18.01 new_show10(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.01 new_primModNatS2(Succ(x0), Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.01 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.01 new_show6(x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Int) 34.17/18.01 new_primDivNatS4(x0) 34.17/18.01 new_primModNatS2(Zero, Zero) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.01 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.01 new_primModNatS02(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.01 new_primIntToChar(x0, x1) 34.17/18.01 new_show(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.01 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.01 new_show12(x0) 34.17/18.01 new_show13(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_@0) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.01 new_primShowInt0(Pos(Zero)) 34.17/18.01 new_primModNatS3(Zero, Zero, x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Char) 34.17/18.01 new_show11(x0) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.01 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.01 new_primDivNatS2(Zero, Zero, x0) 34.17/18.01 new_div(x0, x1) 34.17/18.01 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.01 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.01 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_show8(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.01 new_showsPrec(x0, x1, ty_Float) 34.17/18.01 new_primShowInt0(Pos(Succ(x0))) 34.17/18.01 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.01 new_psPs0([], x0) 34.17/18.01 new_show9(x0, x1, x2) 34.17/18.01 new_showsPrec(x0, x1, ty_Bool) 34.17/18.01 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.01 new_show2(x0) 34.17/18.01 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.01 new_showsPrec(x0, x1, ty_Double) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.01 new_show14(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.01 new_primDivNatS01(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_Integer) 34.17/18.01 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.01 new_psPs0(:(x0, x1), x2) 34.17/18.01 new_primModNatS4(x0) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Succ(x0), Zero) 34.17/18.01 new_show7(x0, x1, x2) 34.17/18.01 new_primDivNatS3(Zero, Zero) 34.17/18.01 34.17/18.01 We have to consider all minimal (P,Q,R)-chains. 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (147) TransformationProof (EQUIVALENT) 34.17/18.01 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.01 34.17/18.01 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char)) 34.17/18.01 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char)) 34.17/18.01 34.17/18.01 34.17/18.01 ---------------------------------------- 34.17/18.01 34.17/18.01 (148) 34.17/18.01 Obligation: 34.17/18.01 Q DP problem: 34.17/18.01 The TRS P consists of the following rules: 34.17/18.01 34.17/18.01 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.01 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.01 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char) 34.17/18.01 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char) 34.17/18.01 34.17/18.01 The TRS R consists of the following rules: 34.17/18.01 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.01 new_show10(ww7) -> error([]) 34.17/18.01 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.01 new_show(ww7) -> error([]) 34.17/18.01 new_show7(ww7, dc, dd) -> error([]) 34.17/18.01 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.01 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.01 new_show14(ww7) -> error([]) 34.17/18.01 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.01 new_show3(ww7) -> error([]) 34.17/18.01 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.01 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.01 new_show8(ww7) -> error([]) 34.17/18.01 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.01 new_primModNatS4(ww212) -> Zero 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.01 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.01 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_show4(ww7) -> error([]) 34.17/18.01 new_show13(ww7, fa) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.01 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.01 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.01 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.01 new_psPs0([], ww106) -> ww106 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.01 new_show12(ww7) -> error([]) 34.17/18.01 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.01 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.01 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.01 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.01 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.01 new_show9(ww7, de, df) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.01 new_show5(ww7, db) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.01 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.01 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.01 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.01 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.01 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.01 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.01 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.01 new_show1(ww7, da) -> error([]) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.01 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.01 new_show6(ww7) -> error([]) 34.17/18.01 new_show11(ww7) -> error([]) 34.17/18.01 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.01 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.01 new_show15(ww7) -> error([]) 34.17/18.01 new_primDivNatS4(ww216) -> Zero 34.17/18.01 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.01 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.01 34.17/18.01 The set Q consists of the following terms: 34.17/18.01 34.17/18.01 new_show0(x0, x1, x2, x3) 34.17/18.01 new_show4(x0) 34.17/18.01 new_show1(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.01 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.01 new_primShowInt0(Neg(x0)) 34.17/18.01 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.01 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.01 new_show3(x0) 34.17/18.01 new_show5(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_IOError) 34.17/18.01 new_show15(x0) 34.17/18.01 new_primModNatS2(Zero, Succ(x0)) 34.17/18.01 new_show10(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.01 new_primModNatS2(Succ(x0), Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.01 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.01 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.01 new_show6(x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Int) 34.17/18.01 new_primDivNatS4(x0) 34.17/18.01 new_primModNatS2(Zero, Zero) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.01 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.01 new_primModNatS02(x0, x1) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.01 new_primIntToChar(x0, x1) 34.17/18.01 new_show(x0) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.01 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.01 new_show12(x0) 34.17/18.01 new_show13(x0, x1) 34.17/18.01 new_showsPrec(x0, x1, ty_@0) 34.17/18.01 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.01 new_primShowInt0(Pos(Zero)) 34.17/18.01 new_primModNatS3(Zero, Zero, x0) 34.17/18.01 new_showsPrec(x0, x1, ty_Char) 34.17/18.01 new_show11(x0) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.01 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.01 new_primDivNatS2(Zero, Zero, x0) 34.17/18.01 new_div(x0, x1) 34.17/18.01 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.01 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.01 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.01 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.01 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.01 new_show8(x0) 34.17/18.01 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.01 new_showsPrec(x0, x1, ty_Float) 34.17/18.01 new_primShowInt0(Pos(Succ(x0))) 34.17/18.01 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.01 new_psPs0([], x0) 34.17/18.01 new_show9(x0, x1, x2) 34.17/18.01 new_showsPrec(x0, x1, ty_Bool) 34.17/18.01 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.01 new_show2(x0) 34.17/18.01 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.01 new_showsPrec(x0, x1, ty_Double) 34.17/18.01 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.01 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.01 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.02 new_show14(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.02 new_primDivNatS01(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_Integer) 34.17/18.02 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.02 new_psPs0(:(x0, x1), x2) 34.17/18.02 new_primModNatS4(x0) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Succ(x0), Zero) 34.17/18.02 new_show7(x0, x1, x2) 34.17/18.02 new_primDivNatS3(Zero, Zero) 34.17/18.02 34.17/18.02 We have to consider all minimal (P,Q,R)-chains. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (149) DependencyGraphProof (EQUIVALENT) 34.17/18.02 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (150) 34.17/18.02 Obligation: 34.17/18.02 Q DP problem: 34.17/18.02 The TRS P consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.02 34.17/18.02 The TRS R consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.02 new_show10(ww7) -> error([]) 34.17/18.02 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.02 new_show(ww7) -> error([]) 34.17/18.02 new_show7(ww7, dc, dd) -> error([]) 34.17/18.02 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.02 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.02 new_show14(ww7) -> error([]) 34.17/18.02 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.02 new_show3(ww7) -> error([]) 34.17/18.02 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.02 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.02 new_show8(ww7) -> error([]) 34.17/18.02 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.02 new_primModNatS4(ww212) -> Zero 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.02 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_show4(ww7) -> error([]) 34.17/18.02 new_show13(ww7, fa) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.02 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.02 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.02 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.02 new_psPs0([], ww106) -> ww106 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.02 new_show12(ww7) -> error([]) 34.17/18.02 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.02 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.02 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.02 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.02 new_show9(ww7, de, df) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.02 new_show5(ww7, db) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.02 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.02 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.02 new_show1(ww7, da) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.02 new_show6(ww7) -> error([]) 34.17/18.02 new_show11(ww7) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.02 new_show15(ww7) -> error([]) 34.17/18.02 new_primDivNatS4(ww216) -> Zero 34.17/18.02 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 34.17/18.02 The set Q consists of the following terms: 34.17/18.02 34.17/18.02 new_show0(x0, x1, x2, x3) 34.17/18.02 new_show4(x0) 34.17/18.02 new_show1(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.02 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.02 new_primShowInt0(Neg(x0)) 34.17/18.02 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.02 new_show3(x0) 34.17/18.02 new_show5(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_IOError) 34.17/18.02 new_show15(x0) 34.17/18.02 new_primModNatS2(Zero, Succ(x0)) 34.17/18.02 new_show10(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.02 new_primModNatS2(Succ(x0), Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.02 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.02 new_show6(x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Int) 34.17/18.02 new_primDivNatS4(x0) 34.17/18.02 new_primModNatS2(Zero, Zero) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.02 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.02 new_primModNatS02(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.02 new_primIntToChar(x0, x1) 34.17/18.02 new_show(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.02 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.02 new_show12(x0) 34.17/18.02 new_show13(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_@0) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.02 new_primShowInt0(Pos(Zero)) 34.17/18.02 new_primModNatS3(Zero, Zero, x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Char) 34.17/18.02 new_show11(x0) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.02 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.02 new_primDivNatS2(Zero, Zero, x0) 34.17/18.02 new_div(x0, x1) 34.17/18.02 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.02 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.02 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_show8(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.02 new_showsPrec(x0, x1, ty_Float) 34.17/18.02 new_primShowInt0(Pos(Succ(x0))) 34.17/18.02 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.02 new_psPs0([], x0) 34.17/18.02 new_show9(x0, x1, x2) 34.17/18.02 new_showsPrec(x0, x1, ty_Bool) 34.17/18.02 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.02 new_show2(x0) 34.17/18.02 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.02 new_showsPrec(x0, x1, ty_Double) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.02 new_show14(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.02 new_primDivNatS01(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_Integer) 34.17/18.02 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.02 new_psPs0(:(x0, x1), x2) 34.17/18.02 new_primModNatS4(x0) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Succ(x0), Zero) 34.17/18.02 new_show7(x0, x1, x2) 34.17/18.02 new_primDivNatS3(Zero, Zero) 34.17/18.02 34.17/18.02 We have to consider all minimal (P,Q,R)-chains. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (151) TransformationProof (EQUIVALENT) 34.17/18.02 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.02 34.17/18.02 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7))) 34.17/18.02 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7))) 34.17/18.02 34.17/18.02 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (152) 34.17/18.02 Obligation: 34.17/18.02 Q DP problem: 34.17/18.02 The TRS P consists of the following rules: 34.17/18.02 34.17/18.02 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.02 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7)) 34.17/18.02 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7)) 34.17/18.02 34.17/18.02 The TRS R consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.02 new_show10(ww7) -> error([]) 34.17/18.02 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.02 new_show(ww7) -> error([]) 34.17/18.02 new_show7(ww7, dc, dd) -> error([]) 34.17/18.02 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.02 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.02 new_show14(ww7) -> error([]) 34.17/18.02 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.02 new_show3(ww7) -> error([]) 34.17/18.02 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.02 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.02 new_show8(ww7) -> error([]) 34.17/18.02 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.02 new_primModNatS4(ww212) -> Zero 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.02 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_show4(ww7) -> error([]) 34.17/18.02 new_show13(ww7, fa) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.02 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.02 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.02 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.02 new_psPs0([], ww106) -> ww106 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.02 new_show12(ww7) -> error([]) 34.17/18.02 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.02 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.02 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.02 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.02 new_show9(ww7, de, df) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.02 new_show5(ww7, db) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.02 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.02 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.02 new_show1(ww7, da) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.02 new_show6(ww7) -> error([]) 34.17/18.02 new_show11(ww7) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.02 new_show15(ww7) -> error([]) 34.17/18.02 new_primDivNatS4(ww216) -> Zero 34.17/18.02 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 34.17/18.02 The set Q consists of the following terms: 34.17/18.02 34.17/18.02 new_show0(x0, x1, x2, x3) 34.17/18.02 new_show4(x0) 34.17/18.02 new_show1(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.02 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.02 new_primShowInt0(Neg(x0)) 34.17/18.02 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.02 new_show3(x0) 34.17/18.02 new_show5(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_IOError) 34.17/18.02 new_show15(x0) 34.17/18.02 new_primModNatS2(Zero, Succ(x0)) 34.17/18.02 new_show10(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.02 new_primModNatS2(Succ(x0), Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.02 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.02 new_show6(x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Int) 34.17/18.02 new_primDivNatS4(x0) 34.17/18.02 new_primModNatS2(Zero, Zero) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.02 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.02 new_primModNatS02(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.02 new_primIntToChar(x0, x1) 34.17/18.02 new_show(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.02 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.02 new_show12(x0) 34.17/18.02 new_show13(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_@0) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.02 new_primShowInt0(Pos(Zero)) 34.17/18.02 new_primModNatS3(Zero, Zero, x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Char) 34.17/18.02 new_show11(x0) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.02 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.02 new_primDivNatS2(Zero, Zero, x0) 34.17/18.02 new_div(x0, x1) 34.17/18.02 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.02 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.02 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_show8(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.02 new_showsPrec(x0, x1, ty_Float) 34.17/18.02 new_primShowInt0(Pos(Succ(x0))) 34.17/18.02 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.02 new_psPs0([], x0) 34.17/18.02 new_show9(x0, x1, x2) 34.17/18.02 new_showsPrec(x0, x1, ty_Bool) 34.17/18.02 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.02 new_show2(x0) 34.17/18.02 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.02 new_showsPrec(x0, x1, ty_Double) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.02 new_show14(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.02 new_primDivNatS01(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_Integer) 34.17/18.02 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.02 new_psPs0(:(x0, x1), x2) 34.17/18.02 new_primModNatS4(x0) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Succ(x0), Zero) 34.17/18.02 new_show7(x0, x1, x2) 34.17/18.02 new_primDivNatS3(Zero, Zero) 34.17/18.02 34.17/18.02 We have to consider all minimal (P,Q,R)-chains. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (153) DependencyGraphProof (EQUIVALENT) 34.17/18.02 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (154) 34.17/18.02 Obligation: 34.17/18.02 Q DP problem: 34.17/18.02 The TRS P consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.02 34.17/18.02 The TRS R consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.02 new_show10(ww7) -> error([]) 34.17/18.02 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.02 new_show(ww7) -> error([]) 34.17/18.02 new_show7(ww7, dc, dd) -> error([]) 34.17/18.02 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.02 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.02 new_show14(ww7) -> error([]) 34.17/18.02 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.02 new_show3(ww7) -> error([]) 34.17/18.02 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.02 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.02 new_show8(ww7) -> error([]) 34.17/18.02 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.02 new_primModNatS4(ww212) -> Zero 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.02 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_show4(ww7) -> error([]) 34.17/18.02 new_show13(ww7, fa) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.02 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.02 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.02 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.02 new_psPs0([], ww106) -> ww106 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.02 new_show12(ww7) -> error([]) 34.17/18.02 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.02 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.02 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.02 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.02 new_show9(ww7, de, df) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.02 new_show5(ww7, db) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.02 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.02 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.02 new_show1(ww7, da) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.02 new_show6(ww7) -> error([]) 34.17/18.02 new_show11(ww7) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.02 new_show15(ww7) -> error([]) 34.17/18.02 new_primDivNatS4(ww216) -> Zero 34.17/18.02 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 34.17/18.02 The set Q consists of the following terms: 34.17/18.02 34.17/18.02 new_show0(x0, x1, x2, x3) 34.17/18.02 new_show4(x0) 34.17/18.02 new_show1(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.02 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.02 new_primShowInt0(Neg(x0)) 34.17/18.02 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.02 new_show3(x0) 34.17/18.02 new_show5(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_IOError) 34.17/18.02 new_show15(x0) 34.17/18.02 new_primModNatS2(Zero, Succ(x0)) 34.17/18.02 new_show10(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.02 new_primModNatS2(Succ(x0), Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.02 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.02 new_show6(x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Int) 34.17/18.02 new_primDivNatS4(x0) 34.17/18.02 new_primModNatS2(Zero, Zero) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.02 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.02 new_primModNatS02(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.02 new_primIntToChar(x0, x1) 34.17/18.02 new_show(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.02 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.02 new_show12(x0) 34.17/18.02 new_show13(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_@0) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.02 new_primShowInt0(Pos(Zero)) 34.17/18.02 new_primModNatS3(Zero, Zero, x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Char) 34.17/18.02 new_show11(x0) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.02 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.02 new_primDivNatS2(Zero, Zero, x0) 34.17/18.02 new_div(x0, x1) 34.17/18.02 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.02 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.02 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_show8(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.02 new_showsPrec(x0, x1, ty_Float) 34.17/18.02 new_primShowInt0(Pos(Succ(x0))) 34.17/18.02 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.02 new_psPs0([], x0) 34.17/18.02 new_show9(x0, x1, x2) 34.17/18.02 new_showsPrec(x0, x1, ty_Bool) 34.17/18.02 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.02 new_show2(x0) 34.17/18.02 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.02 new_showsPrec(x0, x1, ty_Double) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.02 new_show14(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.02 new_primDivNatS01(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_Integer) 34.17/18.02 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.02 new_psPs0(:(x0, x1), x2) 34.17/18.02 new_primModNatS4(x0) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Succ(x0), Zero) 34.17/18.02 new_show7(x0, x1, x2) 34.17/18.02 new_primDivNatS3(Zero, Zero) 34.17/18.02 34.17/18.02 We have to consider all minimal (P,Q,R)-chains. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (155) TransformationProof (EQUIVALENT) 34.17/18.02 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.02 34.17/18.02 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6))) 34.17/18.02 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6))) 34.17/18.02 34.17/18.02 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (156) 34.17/18.02 Obligation: 34.17/18.02 Q DP problem: 34.17/18.02 The TRS P consists of the following rules: 34.17/18.02 34.17/18.02 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.02 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6)) 34.17/18.02 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6)) 34.17/18.02 34.17/18.02 The TRS R consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.02 new_show10(ww7) -> error([]) 34.17/18.02 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.02 new_show(ww7) -> error([]) 34.17/18.02 new_show7(ww7, dc, dd) -> error([]) 34.17/18.02 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.02 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.02 new_show14(ww7) -> error([]) 34.17/18.02 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.02 new_show3(ww7) -> error([]) 34.17/18.02 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.02 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.02 new_show8(ww7) -> error([]) 34.17/18.02 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.02 new_primModNatS4(ww212) -> Zero 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.02 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_show4(ww7) -> error([]) 34.17/18.02 new_show13(ww7, fa) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.02 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.02 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.02 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.02 new_psPs0([], ww106) -> ww106 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.02 new_show12(ww7) -> error([]) 34.17/18.02 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.02 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.02 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.02 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.02 new_show9(ww7, de, df) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.02 new_show5(ww7, db) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.02 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.02 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.02 new_show1(ww7, da) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.02 new_show6(ww7) -> error([]) 34.17/18.02 new_show11(ww7) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.02 new_show15(ww7) -> error([]) 34.17/18.02 new_primDivNatS4(ww216) -> Zero 34.17/18.02 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 34.17/18.02 The set Q consists of the following terms: 34.17/18.02 34.17/18.02 new_show0(x0, x1, x2, x3) 34.17/18.02 new_show4(x0) 34.17/18.02 new_show1(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.02 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.02 new_primShowInt0(Neg(x0)) 34.17/18.02 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.02 new_show3(x0) 34.17/18.02 new_show5(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_IOError) 34.17/18.02 new_show15(x0) 34.17/18.02 new_primModNatS2(Zero, Succ(x0)) 34.17/18.02 new_show10(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.02 new_primModNatS2(Succ(x0), Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.02 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.02 new_show6(x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Int) 34.17/18.02 new_primDivNatS4(x0) 34.17/18.02 new_primModNatS2(Zero, Zero) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.02 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.02 new_primModNatS02(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.02 new_primIntToChar(x0, x1) 34.17/18.02 new_show(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.02 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.02 new_show12(x0) 34.17/18.02 new_show13(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_@0) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.02 new_primShowInt0(Pos(Zero)) 34.17/18.02 new_primModNatS3(Zero, Zero, x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Char) 34.17/18.02 new_show11(x0) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.02 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.02 new_primDivNatS2(Zero, Zero, x0) 34.17/18.02 new_div(x0, x1) 34.17/18.02 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.02 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.02 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_show8(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.02 new_showsPrec(x0, x1, ty_Float) 34.17/18.02 new_primShowInt0(Pos(Succ(x0))) 34.17/18.02 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.02 new_psPs0([], x0) 34.17/18.02 new_show9(x0, x1, x2) 34.17/18.02 new_showsPrec(x0, x1, ty_Bool) 34.17/18.02 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.02 new_show2(x0) 34.17/18.02 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.02 new_showsPrec(x0, x1, ty_Double) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.02 new_show14(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.02 new_primDivNatS01(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_Integer) 34.17/18.02 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.02 new_psPs0(:(x0, x1), x2) 34.17/18.02 new_primModNatS4(x0) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Succ(x0), Zero) 34.17/18.02 new_show7(x0, x1, x2) 34.17/18.02 new_primDivNatS3(Zero, Zero) 34.17/18.02 34.17/18.02 We have to consider all minimal (P,Q,R)-chains. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (157) DependencyGraphProof (EQUIVALENT) 34.17/18.02 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (158) 34.17/18.02 Obligation: 34.17/18.02 Q DP problem: 34.17/18.02 The TRS P consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.02 34.17/18.02 The TRS R consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.02 new_show10(ww7) -> error([]) 34.17/18.02 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.02 new_show(ww7) -> error([]) 34.17/18.02 new_show7(ww7, dc, dd) -> error([]) 34.17/18.02 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.02 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.02 new_show14(ww7) -> error([]) 34.17/18.02 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.02 new_show3(ww7) -> error([]) 34.17/18.02 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.02 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.02 new_show8(ww7) -> error([]) 34.17/18.02 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.02 new_primModNatS4(ww212) -> Zero 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.02 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_show4(ww7) -> error([]) 34.17/18.02 new_show13(ww7, fa) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.02 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.02 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.02 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.02 new_psPs0([], ww106) -> ww106 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.02 new_show12(ww7) -> error([]) 34.17/18.02 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.02 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.02 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.02 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.02 new_show9(ww7, de, df) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.02 new_show5(ww7, db) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.02 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.02 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.02 new_show1(ww7, da) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.02 new_show6(ww7) -> error([]) 34.17/18.02 new_show11(ww7) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.02 new_show15(ww7) -> error([]) 34.17/18.02 new_primDivNatS4(ww216) -> Zero 34.17/18.02 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 34.17/18.02 The set Q consists of the following terms: 34.17/18.02 34.17/18.02 new_show0(x0, x1, x2, x3) 34.17/18.02 new_show4(x0) 34.17/18.02 new_show1(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.02 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.02 new_primShowInt0(Neg(x0)) 34.17/18.02 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.02 new_show3(x0) 34.17/18.02 new_show5(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_IOError) 34.17/18.02 new_show15(x0) 34.17/18.02 new_primModNatS2(Zero, Succ(x0)) 34.17/18.02 new_show10(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.02 new_primModNatS2(Succ(x0), Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.02 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.02 new_show6(x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Int) 34.17/18.02 new_primDivNatS4(x0) 34.17/18.02 new_primModNatS2(Zero, Zero) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.02 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.02 new_primModNatS02(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.02 new_primIntToChar(x0, x1) 34.17/18.02 new_show(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.02 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.02 new_show12(x0) 34.17/18.02 new_show13(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_@0) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.02 new_primShowInt0(Pos(Zero)) 34.17/18.02 new_primModNatS3(Zero, Zero, x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Char) 34.17/18.02 new_show11(x0) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.02 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.02 new_primDivNatS2(Zero, Zero, x0) 34.17/18.02 new_div(x0, x1) 34.17/18.02 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.02 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.02 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_show8(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.02 new_showsPrec(x0, x1, ty_Float) 34.17/18.02 new_primShowInt0(Pos(Succ(x0))) 34.17/18.02 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.02 new_psPs0([], x0) 34.17/18.02 new_show9(x0, x1, x2) 34.17/18.02 new_showsPrec(x0, x1, ty_Bool) 34.17/18.02 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.02 new_show2(x0) 34.17/18.02 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.02 new_showsPrec(x0, x1, ty_Double) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.02 new_show14(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.02 new_primDivNatS01(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_Integer) 34.17/18.02 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.02 new_psPs0(:(x0, x1), x2) 34.17/18.02 new_primModNatS4(x0) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Succ(x0), Zero) 34.17/18.02 new_show7(x0, x1, x2) 34.17/18.02 new_primDivNatS3(Zero, Zero) 34.17/18.02 34.17/18.02 We have to consider all minimal (P,Q,R)-chains. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (159) TransformationProof (EQUIVALENT) 34.17/18.02 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.02 34.17/18.02 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float)) 34.17/18.02 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float)) 34.17/18.02 34.17/18.02 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (160) 34.17/18.02 Obligation: 34.17/18.02 Q DP problem: 34.17/18.02 The TRS P consists of the following rules: 34.17/18.02 34.17/18.02 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.02 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float) 34.17/18.02 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float) 34.17/18.02 34.17/18.02 The TRS R consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.02 new_show10(ww7) -> error([]) 34.17/18.02 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.02 new_show(ww7) -> error([]) 34.17/18.02 new_show7(ww7, dc, dd) -> error([]) 34.17/18.02 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.02 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.02 new_show14(ww7) -> error([]) 34.17/18.02 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.02 new_show3(ww7) -> error([]) 34.17/18.02 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.02 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.02 new_show8(ww7) -> error([]) 34.17/18.02 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.02 new_primModNatS4(ww212) -> Zero 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.02 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_show4(ww7) -> error([]) 34.17/18.02 new_show13(ww7, fa) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.02 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.02 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.02 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.02 new_psPs0([], ww106) -> ww106 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.02 new_show12(ww7) -> error([]) 34.17/18.02 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.02 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.02 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.02 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.02 new_show9(ww7, de, df) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.02 new_show5(ww7, db) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.02 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.02 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.02 new_show1(ww7, da) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.02 new_show6(ww7) -> error([]) 34.17/18.02 new_show11(ww7) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.02 new_show15(ww7) -> error([]) 34.17/18.02 new_primDivNatS4(ww216) -> Zero 34.17/18.02 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 34.17/18.02 The set Q consists of the following terms: 34.17/18.02 34.17/18.02 new_show0(x0, x1, x2, x3) 34.17/18.02 new_show4(x0) 34.17/18.02 new_show1(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.02 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.02 new_primShowInt0(Neg(x0)) 34.17/18.02 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.02 new_show3(x0) 34.17/18.02 new_show5(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_IOError) 34.17/18.02 new_show15(x0) 34.17/18.02 new_primModNatS2(Zero, Succ(x0)) 34.17/18.02 new_show10(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.02 new_primModNatS2(Succ(x0), Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.02 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.02 new_show6(x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Int) 34.17/18.02 new_primDivNatS4(x0) 34.17/18.02 new_primModNatS2(Zero, Zero) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.02 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.02 new_primModNatS02(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.02 new_primIntToChar(x0, x1) 34.17/18.02 new_show(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.02 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.02 new_show12(x0) 34.17/18.02 new_show13(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_@0) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.02 new_primShowInt0(Pos(Zero)) 34.17/18.02 new_primModNatS3(Zero, Zero, x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Char) 34.17/18.02 new_show11(x0) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.02 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.02 new_primDivNatS2(Zero, Zero, x0) 34.17/18.02 new_div(x0, x1) 34.17/18.02 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.02 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.02 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_show8(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.02 new_showsPrec(x0, x1, ty_Float) 34.17/18.02 new_primShowInt0(Pos(Succ(x0))) 34.17/18.02 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.02 new_psPs0([], x0) 34.17/18.02 new_show9(x0, x1, x2) 34.17/18.02 new_showsPrec(x0, x1, ty_Bool) 34.17/18.02 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.02 new_show2(x0) 34.17/18.02 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.02 new_showsPrec(x0, x1, ty_Double) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.02 new_show14(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.02 new_primDivNatS01(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_Integer) 34.17/18.02 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.02 new_psPs0(:(x0, x1), x2) 34.17/18.02 new_primModNatS4(x0) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Succ(x0), Zero) 34.17/18.02 new_show7(x0, x1, x2) 34.17/18.02 new_primDivNatS3(Zero, Zero) 34.17/18.02 34.17/18.02 We have to consider all minimal (P,Q,R)-chains. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (161) DependencyGraphProof (EQUIVALENT) 34.17/18.02 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (162) 34.17/18.02 Obligation: 34.17/18.02 Q DP problem: 34.17/18.02 The TRS P consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.02 34.17/18.02 The TRS R consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.02 new_show10(ww7) -> error([]) 34.17/18.02 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.02 new_show(ww7) -> error([]) 34.17/18.02 new_show7(ww7, dc, dd) -> error([]) 34.17/18.02 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.02 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.02 new_show14(ww7) -> error([]) 34.17/18.02 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.02 new_show3(ww7) -> error([]) 34.17/18.02 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.02 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.02 new_show8(ww7) -> error([]) 34.17/18.02 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.02 new_primModNatS4(ww212) -> Zero 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.02 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_show4(ww7) -> error([]) 34.17/18.02 new_show13(ww7, fa) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.02 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.02 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.02 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.02 new_psPs0([], ww106) -> ww106 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.02 new_show12(ww7) -> error([]) 34.17/18.02 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.02 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.02 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.02 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.02 new_show9(ww7, de, df) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.02 new_show5(ww7, db) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.02 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.02 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.02 new_show1(ww7, da) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.02 new_show6(ww7) -> error([]) 34.17/18.02 new_show11(ww7) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.02 new_show15(ww7) -> error([]) 34.17/18.02 new_primDivNatS4(ww216) -> Zero 34.17/18.02 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 34.17/18.02 The set Q consists of the following terms: 34.17/18.02 34.17/18.02 new_show0(x0, x1, x2, x3) 34.17/18.02 new_show4(x0) 34.17/18.02 new_show1(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.02 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.02 new_primShowInt0(Neg(x0)) 34.17/18.02 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.02 new_show3(x0) 34.17/18.02 new_show5(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_IOError) 34.17/18.02 new_show15(x0) 34.17/18.02 new_primModNatS2(Zero, Succ(x0)) 34.17/18.02 new_show10(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.02 new_primModNatS2(Succ(x0), Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.02 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.02 new_show6(x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Int) 34.17/18.02 new_primDivNatS4(x0) 34.17/18.02 new_primModNatS2(Zero, Zero) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.02 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.02 new_primModNatS02(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.02 new_primIntToChar(x0, x1) 34.17/18.02 new_show(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.02 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.02 new_show12(x0) 34.17/18.02 new_show13(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_@0) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.02 new_primShowInt0(Pos(Zero)) 34.17/18.02 new_primModNatS3(Zero, Zero, x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Char) 34.17/18.02 new_show11(x0) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.02 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.02 new_primDivNatS2(Zero, Zero, x0) 34.17/18.02 new_div(x0, x1) 34.17/18.02 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.02 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.02 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_show8(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.02 new_showsPrec(x0, x1, ty_Float) 34.17/18.02 new_primShowInt0(Pos(Succ(x0))) 34.17/18.02 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.02 new_psPs0([], x0) 34.17/18.02 new_show9(x0, x1, x2) 34.17/18.02 new_showsPrec(x0, x1, ty_Bool) 34.17/18.02 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.02 new_show2(x0) 34.17/18.02 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.02 new_showsPrec(x0, x1, ty_Double) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.02 new_show14(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.02 new_primDivNatS01(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_Integer) 34.17/18.02 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.02 new_psPs0(:(x0, x1), x2) 34.17/18.02 new_primModNatS4(x0) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Succ(x0), Zero) 34.17/18.02 new_show7(x0, x1, x2) 34.17/18.02 new_primDivNatS3(Zero, Zero) 34.17/18.02 34.17/18.02 We have to consider all minimal (P,Q,R)-chains. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (163) TransformationProof (EQUIVALENT) 34.17/18.02 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.02 34.17/18.02 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException)) 34.17/18.02 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException)) 34.17/18.02 34.17/18.02 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (164) 34.17/18.02 Obligation: 34.17/18.02 Q DP problem: 34.17/18.02 The TRS P consists of the following rules: 34.17/18.02 34.17/18.02 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.02 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException) 34.17/18.02 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException) 34.17/18.02 34.17/18.02 The TRS R consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.02 new_show10(ww7) -> error([]) 34.17/18.02 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.02 new_show(ww7) -> error([]) 34.17/18.02 new_show7(ww7, dc, dd) -> error([]) 34.17/18.02 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.02 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.02 new_show14(ww7) -> error([]) 34.17/18.02 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.02 new_show3(ww7) -> error([]) 34.17/18.02 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.02 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.02 new_show8(ww7) -> error([]) 34.17/18.02 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.02 new_primModNatS4(ww212) -> Zero 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.02 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_show4(ww7) -> error([]) 34.17/18.02 new_show13(ww7, fa) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.02 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.02 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.02 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.02 new_psPs0([], ww106) -> ww106 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.02 new_show12(ww7) -> error([]) 34.17/18.02 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.02 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.02 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.02 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.02 new_show9(ww7, de, df) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.02 new_show5(ww7, db) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.02 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.02 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.02 new_show1(ww7, da) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.02 new_show6(ww7) -> error([]) 34.17/18.02 new_show11(ww7) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.02 new_show15(ww7) -> error([]) 34.17/18.02 new_primDivNatS4(ww216) -> Zero 34.17/18.02 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 34.17/18.02 The set Q consists of the following terms: 34.17/18.02 34.17/18.02 new_show0(x0, x1, x2, x3) 34.17/18.02 new_show4(x0) 34.17/18.02 new_show1(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.02 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.02 new_primShowInt0(Neg(x0)) 34.17/18.02 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.02 new_show3(x0) 34.17/18.02 new_show5(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_IOError) 34.17/18.02 new_show15(x0) 34.17/18.02 new_primModNatS2(Zero, Succ(x0)) 34.17/18.02 new_show10(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.02 new_primModNatS2(Succ(x0), Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.02 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.02 new_show6(x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Int) 34.17/18.02 new_primDivNatS4(x0) 34.17/18.02 new_primModNatS2(Zero, Zero) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.02 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.02 new_primModNatS02(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.02 new_primIntToChar(x0, x1) 34.17/18.02 new_show(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.02 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.02 new_show12(x0) 34.17/18.02 new_show13(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_@0) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.02 new_primShowInt0(Pos(Zero)) 34.17/18.02 new_primModNatS3(Zero, Zero, x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Char) 34.17/18.02 new_show11(x0) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.02 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.02 new_primDivNatS2(Zero, Zero, x0) 34.17/18.02 new_div(x0, x1) 34.17/18.02 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.02 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.02 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_show8(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.02 new_showsPrec(x0, x1, ty_Float) 34.17/18.02 new_primShowInt0(Pos(Succ(x0))) 34.17/18.02 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.02 new_psPs0([], x0) 34.17/18.02 new_show9(x0, x1, x2) 34.17/18.02 new_showsPrec(x0, x1, ty_Bool) 34.17/18.02 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.02 new_show2(x0) 34.17/18.02 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.02 new_showsPrec(x0, x1, ty_Double) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.02 new_show14(x0) 34.17/18.02 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.02 new_primDivNatS01(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_Integer) 34.17/18.02 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.02 new_psPs0(:(x0, x1), x2) 34.17/18.02 new_primModNatS4(x0) 34.17/18.02 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Succ(x0), Zero) 34.17/18.02 new_show7(x0, x1, x2) 34.17/18.02 new_primDivNatS3(Zero, Zero) 34.17/18.02 34.17/18.02 We have to consider all minimal (P,Q,R)-chains. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (165) DependencyGraphProof (EQUIVALENT) 34.17/18.02 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.02 ---------------------------------------- 34.17/18.02 34.17/18.02 (166) 34.17/18.02 Obligation: 34.17/18.02 Q DP problem: 34.17/18.02 The TRS P consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.02 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.02 34.17/18.02 The TRS R consists of the following rules: 34.17/18.02 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.02 new_show10(ww7) -> error([]) 34.17/18.02 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.02 new_show(ww7) -> error([]) 34.17/18.02 new_show7(ww7, dc, dd) -> error([]) 34.17/18.02 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.02 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.02 new_show14(ww7) -> error([]) 34.17/18.02 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.02 new_show3(ww7) -> error([]) 34.17/18.02 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.02 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.02 new_show8(ww7) -> error([]) 34.17/18.02 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.02 new_primModNatS4(ww212) -> Zero 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.02 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.02 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_show4(ww7) -> error([]) 34.17/18.02 new_show13(ww7, fa) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.02 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.02 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.02 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.02 new_psPs0([], ww106) -> ww106 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.02 new_show12(ww7) -> error([]) 34.17/18.02 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.02 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.02 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.02 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.02 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.02 new_show9(ww7, de, df) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.02 new_show5(ww7, db) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.02 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.02 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.02 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.02 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.02 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.02 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.02 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.02 new_show1(ww7, da) -> error([]) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.02 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.02 new_show6(ww7) -> error([]) 34.17/18.02 new_show11(ww7) -> error([]) 34.17/18.02 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.02 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.02 new_show15(ww7) -> error([]) 34.17/18.02 new_primDivNatS4(ww216) -> Zero 34.17/18.02 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.02 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.02 34.17/18.02 The set Q consists of the following terms: 34.17/18.02 34.17/18.02 new_show0(x0, x1, x2, x3) 34.17/18.02 new_show4(x0) 34.17/18.02 new_show1(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.02 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.02 new_primShowInt0(Neg(x0)) 34.17/18.02 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.02 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.02 new_show3(x0) 34.17/18.02 new_show5(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_IOError) 34.17/18.02 new_show15(x0) 34.17/18.02 new_primModNatS2(Zero, Succ(x0)) 34.17/18.02 new_show10(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.02 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.02 new_primModNatS2(Succ(x0), Zero) 34.17/18.02 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.02 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.02 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.02 new_show6(x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Int) 34.17/18.02 new_primDivNatS4(x0) 34.17/18.02 new_primModNatS2(Zero, Zero) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.02 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.02 new_primModNatS02(x0, x1) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.02 new_primIntToChar(x0, x1) 34.17/18.02 new_show(x0) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.02 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.02 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.02 new_show12(x0) 34.17/18.02 new_show13(x0, x1) 34.17/18.02 new_showsPrec(x0, x1, ty_@0) 34.17/18.02 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.02 new_primShowInt0(Pos(Zero)) 34.17/18.02 new_primModNatS3(Zero, Zero, x0) 34.17/18.02 new_showsPrec(x0, x1, ty_Char) 34.17/18.02 new_show11(x0) 34.17/18.02 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.02 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.02 new_primDivNatS2(Zero, Zero, x0) 34.17/18.02 new_div(x0, x1) 34.17/18.02 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.02 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.02 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.02 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_show8(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.03 new_showsPrec(x0, x1, ty_Float) 34.17/18.03 new_primShowInt0(Pos(Succ(x0))) 34.17/18.03 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.03 new_psPs0([], x0) 34.17/18.03 new_show9(x0, x1, x2) 34.17/18.03 new_showsPrec(x0, x1, ty_Bool) 34.17/18.03 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.03 new_show2(x0) 34.17/18.03 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.03 new_showsPrec(x0, x1, ty_Double) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.03 new_show14(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.03 new_primDivNatS01(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_Integer) 34.17/18.03 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.03 new_psPs0(:(x0, x1), x2) 34.17/18.03 new_primModNatS4(x0) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Succ(x0), Zero) 34.17/18.03 new_show7(x0, x1, x2) 34.17/18.03 new_primDivNatS3(Zero, Zero) 34.17/18.03 34.17/18.03 We have to consider all minimal (P,Q,R)-chains. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (167) TransformationProof (EQUIVALENT) 34.17/18.03 By instantiating [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.03 34.17/18.03 (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7))) 34.17/18.03 (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7))) 34.17/18.03 34.17/18.03 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (168) 34.17/18.03 Obligation: 34.17/18.03 Q DP problem: 34.17/18.03 The TRS P consists of the following rules: 34.17/18.03 34.17/18.03 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.03 34.17/18.03 The TRS R consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.03 new_show10(ww7) -> error([]) 34.17/18.03 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.03 new_show(ww7) -> error([]) 34.17/18.03 new_show7(ww7, dc, dd) -> error([]) 34.17/18.03 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.03 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.03 new_show14(ww7) -> error([]) 34.17/18.03 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.03 new_show3(ww7) -> error([]) 34.17/18.03 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.03 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.03 new_show8(ww7) -> error([]) 34.17/18.03 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.03 new_primModNatS4(ww212) -> Zero 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.03 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_show4(ww7) -> error([]) 34.17/18.03 new_show13(ww7, fa) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.03 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.03 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.03 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.03 new_psPs0([], ww106) -> ww106 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.03 new_show12(ww7) -> error([]) 34.17/18.03 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.03 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.03 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.03 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.03 new_show9(ww7, de, df) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.03 new_show5(ww7, db) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.03 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.03 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.03 new_show1(ww7, da) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.03 new_show6(ww7) -> error([]) 34.17/18.03 new_show11(ww7) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.03 new_show15(ww7) -> error([]) 34.17/18.03 new_primDivNatS4(ww216) -> Zero 34.17/18.03 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 34.17/18.03 The set Q consists of the following terms: 34.17/18.03 34.17/18.03 new_show0(x0, x1, x2, x3) 34.17/18.03 new_show4(x0) 34.17/18.03 new_show1(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.03 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.03 new_primShowInt0(Neg(x0)) 34.17/18.03 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.03 new_show3(x0) 34.17/18.03 new_show5(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_IOError) 34.17/18.03 new_show15(x0) 34.17/18.03 new_primModNatS2(Zero, Succ(x0)) 34.17/18.03 new_show10(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.03 new_primModNatS2(Succ(x0), Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.03 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.03 new_show6(x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Int) 34.17/18.03 new_primDivNatS4(x0) 34.17/18.03 new_primModNatS2(Zero, Zero) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.03 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.03 new_primModNatS02(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.03 new_primIntToChar(x0, x1) 34.17/18.03 new_show(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.03 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.03 new_show12(x0) 34.17/18.03 new_show13(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_@0) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.03 new_primShowInt0(Pos(Zero)) 34.17/18.03 new_primModNatS3(Zero, Zero, x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Char) 34.17/18.03 new_show11(x0) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.03 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.03 new_primDivNatS2(Zero, Zero, x0) 34.17/18.03 new_div(x0, x1) 34.17/18.03 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.03 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.03 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_show8(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.03 new_showsPrec(x0, x1, ty_Float) 34.17/18.03 new_primShowInt0(Pos(Succ(x0))) 34.17/18.03 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.03 new_psPs0([], x0) 34.17/18.03 new_show9(x0, x1, x2) 34.17/18.03 new_showsPrec(x0, x1, ty_Bool) 34.17/18.03 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.03 new_show2(x0) 34.17/18.03 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.03 new_showsPrec(x0, x1, ty_Double) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.03 new_show14(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.03 new_primDivNatS01(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_Integer) 34.17/18.03 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.03 new_psPs0(:(x0, x1), x2) 34.17/18.03 new_primModNatS4(x0) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Succ(x0), Zero) 34.17/18.03 new_show7(x0, x1, x2) 34.17/18.03 new_primDivNatS3(Zero, Zero) 34.17/18.03 34.17/18.03 We have to consider all minimal (P,Q,R)-chains. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (169) TransformationProof (EQUIVALENT) 34.17/18.03 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.03 34.17/18.03 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer)) 34.17/18.03 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer)) 34.17/18.03 34.17/18.03 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (170) 34.17/18.03 Obligation: 34.17/18.03 Q DP problem: 34.17/18.03 The TRS P consists of the following rules: 34.17/18.03 34.17/18.03 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.03 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer) 34.17/18.03 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer) 34.17/18.03 34.17/18.03 The TRS R consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.03 new_show10(ww7) -> error([]) 34.17/18.03 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.03 new_show(ww7) -> error([]) 34.17/18.03 new_show7(ww7, dc, dd) -> error([]) 34.17/18.03 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.03 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.03 new_show14(ww7) -> error([]) 34.17/18.03 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.03 new_show3(ww7) -> error([]) 34.17/18.03 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.03 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.03 new_show8(ww7) -> error([]) 34.17/18.03 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.03 new_primModNatS4(ww212) -> Zero 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.03 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_show4(ww7) -> error([]) 34.17/18.03 new_show13(ww7, fa) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.03 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.03 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.03 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.03 new_psPs0([], ww106) -> ww106 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.03 new_show12(ww7) -> error([]) 34.17/18.03 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.03 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.03 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.03 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.03 new_show9(ww7, de, df) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.03 new_show5(ww7, db) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.03 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.03 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.03 new_show1(ww7, da) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.03 new_show6(ww7) -> error([]) 34.17/18.03 new_show11(ww7) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.03 new_show15(ww7) -> error([]) 34.17/18.03 new_primDivNatS4(ww216) -> Zero 34.17/18.03 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 34.17/18.03 The set Q consists of the following terms: 34.17/18.03 34.17/18.03 new_show0(x0, x1, x2, x3) 34.17/18.03 new_show4(x0) 34.17/18.03 new_show1(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.03 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.03 new_primShowInt0(Neg(x0)) 34.17/18.03 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.03 new_show3(x0) 34.17/18.03 new_show5(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_IOError) 34.17/18.03 new_show15(x0) 34.17/18.03 new_primModNatS2(Zero, Succ(x0)) 34.17/18.03 new_show10(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.03 new_primModNatS2(Succ(x0), Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.03 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.03 new_show6(x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Int) 34.17/18.03 new_primDivNatS4(x0) 34.17/18.03 new_primModNatS2(Zero, Zero) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.03 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.03 new_primModNatS02(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.03 new_primIntToChar(x0, x1) 34.17/18.03 new_show(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.03 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.03 new_show12(x0) 34.17/18.03 new_show13(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_@0) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.03 new_primShowInt0(Pos(Zero)) 34.17/18.03 new_primModNatS3(Zero, Zero, x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Char) 34.17/18.03 new_show11(x0) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.03 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.03 new_primDivNatS2(Zero, Zero, x0) 34.17/18.03 new_div(x0, x1) 34.17/18.03 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.03 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.03 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_show8(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.03 new_showsPrec(x0, x1, ty_Float) 34.17/18.03 new_primShowInt0(Pos(Succ(x0))) 34.17/18.03 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.03 new_psPs0([], x0) 34.17/18.03 new_show9(x0, x1, x2) 34.17/18.03 new_showsPrec(x0, x1, ty_Bool) 34.17/18.03 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.03 new_show2(x0) 34.17/18.03 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.03 new_showsPrec(x0, x1, ty_Double) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.03 new_show14(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.03 new_primDivNatS01(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_Integer) 34.17/18.03 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.03 new_psPs0(:(x0, x1), x2) 34.17/18.03 new_primModNatS4(x0) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Succ(x0), Zero) 34.17/18.03 new_show7(x0, x1, x2) 34.17/18.03 new_primDivNatS3(Zero, Zero) 34.17/18.03 34.17/18.03 We have to consider all minimal (P,Q,R)-chains. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (171) DependencyGraphProof (EQUIVALENT) 34.17/18.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (172) 34.17/18.03 Obligation: 34.17/18.03 Q DP problem: 34.17/18.03 The TRS P consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.03 34.17/18.03 The TRS R consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.03 new_show10(ww7) -> error([]) 34.17/18.03 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.03 new_show(ww7) -> error([]) 34.17/18.03 new_show7(ww7, dc, dd) -> error([]) 34.17/18.03 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.03 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.03 new_show14(ww7) -> error([]) 34.17/18.03 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.03 new_show3(ww7) -> error([]) 34.17/18.03 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.03 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.03 new_show8(ww7) -> error([]) 34.17/18.03 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.03 new_primModNatS4(ww212) -> Zero 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.03 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_show4(ww7) -> error([]) 34.17/18.03 new_show13(ww7, fa) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.03 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.03 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.03 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.03 new_psPs0([], ww106) -> ww106 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.03 new_show12(ww7) -> error([]) 34.17/18.03 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.03 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.03 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.03 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.03 new_show9(ww7, de, df) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.03 new_show5(ww7, db) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.03 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.03 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.03 new_show1(ww7, da) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.03 new_show6(ww7) -> error([]) 34.17/18.03 new_show11(ww7) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.03 new_show15(ww7) -> error([]) 34.17/18.03 new_primDivNatS4(ww216) -> Zero 34.17/18.03 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 34.17/18.03 The set Q consists of the following terms: 34.17/18.03 34.17/18.03 new_show0(x0, x1, x2, x3) 34.17/18.03 new_show4(x0) 34.17/18.03 new_show1(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.03 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.03 new_primShowInt0(Neg(x0)) 34.17/18.03 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.03 new_show3(x0) 34.17/18.03 new_show5(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_IOError) 34.17/18.03 new_show15(x0) 34.17/18.03 new_primModNatS2(Zero, Succ(x0)) 34.17/18.03 new_show10(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.03 new_primModNatS2(Succ(x0), Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.03 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.03 new_show6(x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Int) 34.17/18.03 new_primDivNatS4(x0) 34.17/18.03 new_primModNatS2(Zero, Zero) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.03 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.03 new_primModNatS02(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.03 new_primIntToChar(x0, x1) 34.17/18.03 new_show(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.03 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.03 new_show12(x0) 34.17/18.03 new_show13(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_@0) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.03 new_primShowInt0(Pos(Zero)) 34.17/18.03 new_primModNatS3(Zero, Zero, x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Char) 34.17/18.03 new_show11(x0) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.03 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.03 new_primDivNatS2(Zero, Zero, x0) 34.17/18.03 new_div(x0, x1) 34.17/18.03 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.03 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.03 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_show8(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.03 new_showsPrec(x0, x1, ty_Float) 34.17/18.03 new_primShowInt0(Pos(Succ(x0))) 34.17/18.03 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.03 new_psPs0([], x0) 34.17/18.03 new_show9(x0, x1, x2) 34.17/18.03 new_showsPrec(x0, x1, ty_Bool) 34.17/18.03 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.03 new_show2(x0) 34.17/18.03 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.03 new_showsPrec(x0, x1, ty_Double) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.03 new_show14(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.03 new_primDivNatS01(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_Integer) 34.17/18.03 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.03 new_psPs0(:(x0, x1), x2) 34.17/18.03 new_primModNatS4(x0) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Succ(x0), Zero) 34.17/18.03 new_show7(x0, x1, x2) 34.17/18.03 new_primDivNatS3(Zero, Zero) 34.17/18.03 34.17/18.03 We have to consider all minimal (P,Q,R)-chains. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (173) TransformationProof (EQUIVALENT) 34.17/18.03 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.03 34.17/18.03 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0)) 34.17/18.03 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0)) 34.17/18.03 34.17/18.03 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (174) 34.17/18.03 Obligation: 34.17/18.03 Q DP problem: 34.17/18.03 The TRS P consists of the following rules: 34.17/18.03 34.17/18.03 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.03 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0) 34.17/18.03 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0) 34.17/18.03 34.17/18.03 The TRS R consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.03 new_show10(ww7) -> error([]) 34.17/18.03 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.03 new_show(ww7) -> error([]) 34.17/18.03 new_show7(ww7, dc, dd) -> error([]) 34.17/18.03 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.03 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.03 new_show14(ww7) -> error([]) 34.17/18.03 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.03 new_show3(ww7) -> error([]) 34.17/18.03 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.03 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.03 new_show8(ww7) -> error([]) 34.17/18.03 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.03 new_primModNatS4(ww212) -> Zero 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.03 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_show4(ww7) -> error([]) 34.17/18.03 new_show13(ww7, fa) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.03 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.03 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.03 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.03 new_psPs0([], ww106) -> ww106 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.03 new_show12(ww7) -> error([]) 34.17/18.03 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.03 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.03 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.03 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.03 new_show9(ww7, de, df) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.03 new_show5(ww7, db) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.03 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.03 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.03 new_show1(ww7, da) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.03 new_show6(ww7) -> error([]) 34.17/18.03 new_show11(ww7) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.03 new_show15(ww7) -> error([]) 34.17/18.03 new_primDivNatS4(ww216) -> Zero 34.17/18.03 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 34.17/18.03 The set Q consists of the following terms: 34.17/18.03 34.17/18.03 new_show0(x0, x1, x2, x3) 34.17/18.03 new_show4(x0) 34.17/18.03 new_show1(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.03 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.03 new_primShowInt0(Neg(x0)) 34.17/18.03 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.03 new_show3(x0) 34.17/18.03 new_show5(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_IOError) 34.17/18.03 new_show15(x0) 34.17/18.03 new_primModNatS2(Zero, Succ(x0)) 34.17/18.03 new_show10(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.03 new_primModNatS2(Succ(x0), Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.03 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.03 new_show6(x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Int) 34.17/18.03 new_primDivNatS4(x0) 34.17/18.03 new_primModNatS2(Zero, Zero) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.03 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.03 new_primModNatS02(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.03 new_primIntToChar(x0, x1) 34.17/18.03 new_show(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.03 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.03 new_show12(x0) 34.17/18.03 new_show13(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_@0) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.03 new_primShowInt0(Pos(Zero)) 34.17/18.03 new_primModNatS3(Zero, Zero, x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Char) 34.17/18.03 new_show11(x0) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.03 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.03 new_primDivNatS2(Zero, Zero, x0) 34.17/18.03 new_div(x0, x1) 34.17/18.03 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.03 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.03 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_show8(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.03 new_showsPrec(x0, x1, ty_Float) 34.17/18.03 new_primShowInt0(Pos(Succ(x0))) 34.17/18.03 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.03 new_psPs0([], x0) 34.17/18.03 new_show9(x0, x1, x2) 34.17/18.03 new_showsPrec(x0, x1, ty_Bool) 34.17/18.03 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.03 new_show2(x0) 34.17/18.03 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.03 new_showsPrec(x0, x1, ty_Double) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.03 new_show14(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.03 new_primDivNatS01(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_Integer) 34.17/18.03 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.03 new_psPs0(:(x0, x1), x2) 34.17/18.03 new_primModNatS4(x0) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Succ(x0), Zero) 34.17/18.03 new_show7(x0, x1, x2) 34.17/18.03 new_primDivNatS3(Zero, Zero) 34.17/18.03 34.17/18.03 We have to consider all minimal (P,Q,R)-chains. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (175) DependencyGraphProof (EQUIVALENT) 34.17/18.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (176) 34.17/18.03 Obligation: 34.17/18.03 Q DP problem: 34.17/18.03 The TRS P consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.03 34.17/18.03 The TRS R consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.03 new_show10(ww7) -> error([]) 34.17/18.03 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.03 new_show(ww7) -> error([]) 34.17/18.03 new_show7(ww7, dc, dd) -> error([]) 34.17/18.03 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.03 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.03 new_show14(ww7) -> error([]) 34.17/18.03 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.03 new_show3(ww7) -> error([]) 34.17/18.03 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.03 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.03 new_show8(ww7) -> error([]) 34.17/18.03 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.03 new_primModNatS4(ww212) -> Zero 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.03 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_show4(ww7) -> error([]) 34.17/18.03 new_show13(ww7, fa) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.03 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.03 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.03 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.03 new_psPs0([], ww106) -> ww106 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.03 new_show12(ww7) -> error([]) 34.17/18.03 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.03 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.03 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.03 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.03 new_show9(ww7, de, df) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.03 new_show5(ww7, db) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.03 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.03 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.03 new_show1(ww7, da) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.03 new_show6(ww7) -> error([]) 34.17/18.03 new_show11(ww7) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.03 new_show15(ww7) -> error([]) 34.17/18.03 new_primDivNatS4(ww216) -> Zero 34.17/18.03 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 34.17/18.03 The set Q consists of the following terms: 34.17/18.03 34.17/18.03 new_show0(x0, x1, x2, x3) 34.17/18.03 new_show4(x0) 34.17/18.03 new_show1(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.03 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.03 new_primShowInt0(Neg(x0)) 34.17/18.03 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.03 new_show3(x0) 34.17/18.03 new_show5(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_IOError) 34.17/18.03 new_show15(x0) 34.17/18.03 new_primModNatS2(Zero, Succ(x0)) 34.17/18.03 new_show10(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.03 new_primModNatS2(Succ(x0), Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.03 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.03 new_show6(x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Int) 34.17/18.03 new_primDivNatS4(x0) 34.17/18.03 new_primModNatS2(Zero, Zero) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.03 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.03 new_primModNatS02(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.03 new_primIntToChar(x0, x1) 34.17/18.03 new_show(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.03 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.03 new_show12(x0) 34.17/18.03 new_show13(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_@0) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.03 new_primShowInt0(Pos(Zero)) 34.17/18.03 new_primModNatS3(Zero, Zero, x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Char) 34.17/18.03 new_show11(x0) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.03 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.03 new_primDivNatS2(Zero, Zero, x0) 34.17/18.03 new_div(x0, x1) 34.17/18.03 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.03 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.03 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_show8(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.03 new_showsPrec(x0, x1, ty_Float) 34.17/18.03 new_primShowInt0(Pos(Succ(x0))) 34.17/18.03 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.03 new_psPs0([], x0) 34.17/18.03 new_show9(x0, x1, x2) 34.17/18.03 new_showsPrec(x0, x1, ty_Bool) 34.17/18.03 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.03 new_show2(x0) 34.17/18.03 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.03 new_showsPrec(x0, x1, ty_Double) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.03 new_show14(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.03 new_primDivNatS01(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_Integer) 34.17/18.03 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.03 new_psPs0(:(x0, x1), x2) 34.17/18.03 new_primModNatS4(x0) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Succ(x0), Zero) 34.17/18.03 new_show7(x0, x1, x2) 34.17/18.03 new_primDivNatS3(Zero, Zero) 34.17/18.03 34.17/18.03 We have to consider all minimal (P,Q,R)-chains. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (177) TransformationProof (EQUIVALENT) 34.17/18.03 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.03 34.17/18.03 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8))) 34.17/18.03 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8))) 34.17/18.03 34.17/18.03 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (178) 34.17/18.03 Obligation: 34.17/18.03 Q DP problem: 34.17/18.03 The TRS P consists of the following rules: 34.17/18.03 34.17/18.03 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.03 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8)) 34.17/18.03 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8)) 34.17/18.03 34.17/18.03 The TRS R consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.03 new_show10(ww7) -> error([]) 34.17/18.03 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.03 new_show(ww7) -> error([]) 34.17/18.03 new_show7(ww7, dc, dd) -> error([]) 34.17/18.03 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.03 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.03 new_show14(ww7) -> error([]) 34.17/18.03 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.03 new_show3(ww7) -> error([]) 34.17/18.03 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.03 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.03 new_show8(ww7) -> error([]) 34.17/18.03 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.03 new_primModNatS4(ww212) -> Zero 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.03 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_show4(ww7) -> error([]) 34.17/18.03 new_show13(ww7, fa) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.03 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.03 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.03 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.03 new_psPs0([], ww106) -> ww106 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.03 new_show12(ww7) -> error([]) 34.17/18.03 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.03 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.03 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.03 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.03 new_show9(ww7, de, df) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.03 new_show5(ww7, db) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.03 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.03 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.03 new_show1(ww7, da) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.03 new_show6(ww7) -> error([]) 34.17/18.03 new_show11(ww7) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.03 new_show15(ww7) -> error([]) 34.17/18.03 new_primDivNatS4(ww216) -> Zero 34.17/18.03 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 34.17/18.03 The set Q consists of the following terms: 34.17/18.03 34.17/18.03 new_show0(x0, x1, x2, x3) 34.17/18.03 new_show4(x0) 34.17/18.03 new_show1(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.03 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.03 new_primShowInt0(Neg(x0)) 34.17/18.03 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.03 new_show3(x0) 34.17/18.03 new_show5(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_IOError) 34.17/18.03 new_show15(x0) 34.17/18.03 new_primModNatS2(Zero, Succ(x0)) 34.17/18.03 new_show10(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.03 new_primModNatS2(Succ(x0), Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.03 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.03 new_show6(x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Int) 34.17/18.03 new_primDivNatS4(x0) 34.17/18.03 new_primModNatS2(Zero, Zero) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.03 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.03 new_primModNatS02(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.03 new_primIntToChar(x0, x1) 34.17/18.03 new_show(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.03 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.03 new_show12(x0) 34.17/18.03 new_show13(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_@0) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.03 new_primShowInt0(Pos(Zero)) 34.17/18.03 new_primModNatS3(Zero, Zero, x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Char) 34.17/18.03 new_show11(x0) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.03 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.03 new_primDivNatS2(Zero, Zero, x0) 34.17/18.03 new_div(x0, x1) 34.17/18.03 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.03 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.03 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_show8(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.03 new_showsPrec(x0, x1, ty_Float) 34.17/18.03 new_primShowInt0(Pos(Succ(x0))) 34.17/18.03 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.03 new_psPs0([], x0) 34.17/18.03 new_show9(x0, x1, x2) 34.17/18.03 new_showsPrec(x0, x1, ty_Bool) 34.17/18.03 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.03 new_show2(x0) 34.17/18.03 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.03 new_showsPrec(x0, x1, ty_Double) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.03 new_show14(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.03 new_primDivNatS01(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_Integer) 34.17/18.03 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.03 new_psPs0(:(x0, x1), x2) 34.17/18.03 new_primModNatS4(x0) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Succ(x0), Zero) 34.17/18.03 new_show7(x0, x1, x2) 34.17/18.03 new_primDivNatS3(Zero, Zero) 34.17/18.03 34.17/18.03 We have to consider all minimal (P,Q,R)-chains. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (179) DependencyGraphProof (EQUIVALENT) 34.17/18.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (180) 34.17/18.03 Obligation: 34.17/18.03 Q DP problem: 34.17/18.03 The TRS P consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) 34.17/18.03 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.03 34.17/18.03 The TRS R consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.03 new_show10(ww7) -> error([]) 34.17/18.03 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.03 new_show(ww7) -> error([]) 34.17/18.03 new_show7(ww7, dc, dd) -> error([]) 34.17/18.03 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.03 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.03 new_show14(ww7) -> error([]) 34.17/18.03 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.03 new_show3(ww7) -> error([]) 34.17/18.03 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.03 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.03 new_show8(ww7) -> error([]) 34.17/18.03 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.03 new_primModNatS4(ww212) -> Zero 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.03 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_show4(ww7) -> error([]) 34.17/18.03 new_show13(ww7, fa) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.03 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.03 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.03 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.03 new_psPs0([], ww106) -> ww106 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.03 new_show12(ww7) -> error([]) 34.17/18.03 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.03 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.03 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.03 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.03 new_show9(ww7, de, df) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.03 new_show5(ww7, db) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.03 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.03 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.03 new_show1(ww7, da) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.03 new_show6(ww7) -> error([]) 34.17/18.03 new_show11(ww7) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.03 new_show15(ww7) -> error([]) 34.17/18.03 new_primDivNatS4(ww216) -> Zero 34.17/18.03 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 34.17/18.03 The set Q consists of the following terms: 34.17/18.03 34.17/18.03 new_show0(x0, x1, x2, x3) 34.17/18.03 new_show4(x0) 34.17/18.03 new_show1(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.03 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.03 new_primShowInt0(Neg(x0)) 34.17/18.03 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.03 new_show3(x0) 34.17/18.03 new_show5(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_IOError) 34.17/18.03 new_show15(x0) 34.17/18.03 new_primModNatS2(Zero, Succ(x0)) 34.17/18.03 new_show10(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.03 new_primModNatS2(Succ(x0), Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.03 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.03 new_show6(x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Int) 34.17/18.03 new_primDivNatS4(x0) 34.17/18.03 new_primModNatS2(Zero, Zero) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.03 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.03 new_primModNatS02(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.03 new_primIntToChar(x0, x1) 34.17/18.03 new_show(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.03 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.03 new_show12(x0) 34.17/18.03 new_show13(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_@0) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.03 new_primShowInt0(Pos(Zero)) 34.17/18.03 new_primModNatS3(Zero, Zero, x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Char) 34.17/18.03 new_show11(x0) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.03 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.03 new_primDivNatS2(Zero, Zero, x0) 34.17/18.03 new_div(x0, x1) 34.17/18.03 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.03 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.03 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_show8(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.03 new_showsPrec(x0, x1, ty_Float) 34.17/18.03 new_primShowInt0(Pos(Succ(x0))) 34.17/18.03 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.03 new_psPs0([], x0) 34.17/18.03 new_show9(x0, x1, x2) 34.17/18.03 new_showsPrec(x0, x1, ty_Bool) 34.17/18.03 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.03 new_show2(x0) 34.17/18.03 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.03 new_showsPrec(x0, x1, ty_Double) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.03 new_show14(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.03 new_primDivNatS01(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_Integer) 34.17/18.03 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.03 new_psPs0(:(x0, x1), x2) 34.17/18.03 new_primModNatS4(x0) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Succ(x0), Zero) 34.17/18.03 new_show7(x0, x1, x2) 34.17/18.03 new_primDivNatS3(Zero, Zero) 34.17/18.03 34.17/18.03 We have to consider all minimal (P,Q,R)-chains. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (181) TransformationProof (EQUIVALENT) 34.17/18.03 By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_pt(ww139, ww140, ww141, ww142, ww148, bc) we obtained the following new rules [LPAR04]: 34.17/18.03 34.17/18.03 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind)) 34.17/18.03 (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind)) 34.17/18.03 34.17/18.03 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (182) 34.17/18.03 Obligation: 34.17/18.03 Q DP problem: 34.17/18.03 The TRS P consists of the following rules: 34.17/18.03 34.17/18.03 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.03 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind) 34.17/18.03 new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind) 34.17/18.03 34.17/18.03 The TRS R consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.03 new_show10(ww7) -> error([]) 34.17/18.03 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.03 new_show(ww7) -> error([]) 34.17/18.03 new_show7(ww7, dc, dd) -> error([]) 34.17/18.03 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.03 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.03 new_show14(ww7) -> error([]) 34.17/18.03 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.03 new_show3(ww7) -> error([]) 34.17/18.03 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.03 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.03 new_show8(ww7) -> error([]) 34.17/18.03 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.03 new_primModNatS4(ww212) -> Zero 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.03 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_show4(ww7) -> error([]) 34.17/18.03 new_show13(ww7, fa) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.03 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.03 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.03 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.03 new_psPs0([], ww106) -> ww106 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.03 new_show12(ww7) -> error([]) 34.17/18.03 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.03 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.03 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.03 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.03 new_show9(ww7, de, df) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.03 new_show5(ww7, db) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.03 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.03 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.03 new_show1(ww7, da) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.03 new_show6(ww7) -> error([]) 34.17/18.03 new_show11(ww7) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.03 new_show15(ww7) -> error([]) 34.17/18.03 new_primDivNatS4(ww216) -> Zero 34.17/18.03 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 34.17/18.03 The set Q consists of the following terms: 34.17/18.03 34.17/18.03 new_show0(x0, x1, x2, x3) 34.17/18.03 new_show4(x0) 34.17/18.03 new_show1(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.03 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.03 new_primShowInt0(Neg(x0)) 34.17/18.03 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.03 new_show3(x0) 34.17/18.03 new_show5(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_IOError) 34.17/18.03 new_show15(x0) 34.17/18.03 new_primModNatS2(Zero, Succ(x0)) 34.17/18.03 new_show10(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.03 new_primModNatS2(Succ(x0), Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.03 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.03 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.03 new_show6(x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Int) 34.17/18.03 new_primDivNatS4(x0) 34.17/18.03 new_primModNatS2(Zero, Zero) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.03 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.03 new_primModNatS02(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.03 new_primIntToChar(x0, x1) 34.17/18.03 new_show(x0) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.03 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.03 new_show12(x0) 34.17/18.03 new_show13(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_@0) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.03 new_primShowInt0(Pos(Zero)) 34.17/18.03 new_primModNatS3(Zero, Zero, x0) 34.17/18.03 new_showsPrec(x0, x1, ty_Char) 34.17/18.03 new_show11(x0) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.03 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.03 new_primDivNatS2(Zero, Zero, x0) 34.17/18.03 new_div(x0, x1) 34.17/18.03 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.03 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.03 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.03 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.03 new_show8(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.03 new_showsPrec(x0, x1, ty_Float) 34.17/18.03 new_primShowInt0(Pos(Succ(x0))) 34.17/18.03 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.03 new_psPs0([], x0) 34.17/18.03 new_show9(x0, x1, x2) 34.17/18.03 new_showsPrec(x0, x1, ty_Bool) 34.17/18.03 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.03 new_show2(x0) 34.17/18.03 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.03 new_showsPrec(x0, x1, ty_Double) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.03 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.03 new_show14(x0) 34.17/18.03 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.03 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.03 new_primDivNatS01(x0, x1) 34.17/18.03 new_showsPrec(x0, x1, ty_Integer) 34.17/18.03 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.03 new_psPs0(:(x0, x1), x2) 34.17/18.03 new_primModNatS4(x0) 34.17/18.03 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Succ(x0), Zero) 34.17/18.03 new_show7(x0, x1, x2) 34.17/18.03 new_primDivNatS3(Zero, Zero) 34.17/18.03 34.17/18.03 We have to consider all minimal (P,Q,R)-chains. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (183) DependencyGraphProof (EQUIVALENT) 34.17/18.03 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 34.17/18.03 ---------------------------------------- 34.17/18.03 34.17/18.03 (184) 34.17/18.03 Obligation: 34.17/18.03 Q DP problem: 34.17/18.03 The TRS P consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.03 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.03 34.17/18.03 The TRS R consists of the following rules: 34.17/18.03 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.03 new_show10(ww7) -> error([]) 34.17/18.03 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.03 new_show(ww7) -> error([]) 34.17/18.03 new_show7(ww7, dc, dd) -> error([]) 34.17/18.03 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.03 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.03 new_show14(ww7) -> error([]) 34.17/18.03 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.03 new_show3(ww7) -> error([]) 34.17/18.03 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.03 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.03 new_show8(ww7) -> error([]) 34.17/18.03 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.03 new_primModNatS4(ww212) -> Zero 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.03 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.03 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_show4(ww7) -> error([]) 34.17/18.03 new_show13(ww7, fa) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.03 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.03 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.03 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.03 new_psPs0([], ww106) -> ww106 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.03 new_show12(ww7) -> error([]) 34.17/18.03 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.03 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.03 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.03 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.03 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.03 new_show9(ww7, de, df) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.03 new_show5(ww7, db) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.03 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.03 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.03 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.03 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.03 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.03 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.03 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.03 new_show1(ww7, da) -> error([]) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.03 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.03 new_show6(ww7) -> error([]) 34.17/18.03 new_show11(ww7) -> error([]) 34.17/18.03 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.03 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.03 new_show15(ww7) -> error([]) 34.17/18.03 new_primDivNatS4(ww216) -> Zero 34.17/18.03 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.03 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.03 34.17/18.03 The set Q consists of the following terms: 34.17/18.03 34.17/18.03 new_show0(x0, x1, x2, x3) 34.17/18.03 new_show4(x0) 34.17/18.03 new_show1(x0, x1) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.03 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.03 new_primShowInt0(Neg(x0)) 34.17/18.03 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.03 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.03 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.03 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.03 new_show3(x0) 34.17/18.03 new_show5(x0, x1) 34.17/18.04 new_showsPrec(x0, x1, ty_IOError) 34.17/18.04 new_show15(x0) 34.17/18.04 new_primModNatS2(Zero, Succ(x0)) 34.17/18.04 new_show10(x0) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.04 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.04 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.04 new_primModNatS2(Succ(x0), Zero) 34.17/18.04 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.04 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.04 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.04 new_show6(x0) 34.17/18.04 new_showsPrec(x0, x1, ty_Int) 34.17/18.04 new_primDivNatS4(x0) 34.17/18.04 new_primModNatS2(Zero, Zero) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.04 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.04 new_primModNatS02(x0, x1) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.04 new_primIntToChar(x0, x1) 34.17/18.04 new_show(x0) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.04 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.04 new_show12(x0) 34.17/18.04 new_show13(x0, x1) 34.17/18.04 new_showsPrec(x0, x1, ty_@0) 34.17/18.04 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.04 new_primShowInt0(Pos(Zero)) 34.17/18.04 new_primModNatS3(Zero, Zero, x0) 34.17/18.04 new_showsPrec(x0, x1, ty_Char) 34.17/18.04 new_show11(x0) 34.17/18.04 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.04 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.04 new_primDivNatS2(Zero, Zero, x0) 34.17/18.04 new_div(x0, x1) 34.17/18.04 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.04 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.04 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.04 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.04 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.04 new_show8(x0) 34.17/18.04 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.04 new_showsPrec(x0, x1, ty_Float) 34.17/18.04 new_primShowInt0(Pos(Succ(x0))) 34.17/18.04 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.04 new_psPs0([], x0) 34.17/18.04 new_show9(x0, x1, x2) 34.17/18.04 new_showsPrec(x0, x1, ty_Bool) 34.17/18.04 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.04 new_show2(x0) 34.17/18.04 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.04 new_showsPrec(x0, x1, ty_Double) 34.17/18.04 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.04 new_show14(x0) 34.17/18.04 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.04 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.04 new_primDivNatS01(x0, x1) 34.17/18.04 new_showsPrec(x0, x1, ty_Integer) 34.17/18.04 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.04 new_psPs0(:(x0, x1), x2) 34.17/18.04 new_primModNatS4(x0) 34.17/18.04 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.04 new_primDivNatS3(Succ(x0), Zero) 34.17/18.04 new_show7(x0, x1, x2) 34.17/18.04 new_primDivNatS3(Zero, Zero) 34.17/18.04 34.17/18.04 We have to consider all minimal (P,Q,R)-chains. 34.17/18.04 ---------------------------------------- 34.17/18.04 34.17/18.04 (185) TransformationProof (EQUIVALENT) 34.17/18.04 By instantiating [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, cd)))), cd, cd) we obtained the following new rules [LPAR04]: 34.17/18.04 34.17/18.04 (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7)) 34.17/18.04 (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7)) 34.17/18.04 34.17/18.04 34.17/18.04 ---------------------------------------- 34.17/18.04 34.17/18.04 (186) 34.17/18.04 Obligation: 34.17/18.04 Q DP problem: 34.17/18.04 The TRS P consists of the following rules: 34.17/18.04 34.17/18.04 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.04 new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.04 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.04 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7) 34.17/18.04 new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7) 34.17/18.04 34.17/18.04 The TRS R consists of the following rules: 34.17/18.04 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, bh), bc) -> new_psPs0(new_show13(ww138, bh), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showsPrec(ww142, ww148, app(ty_IO, ec)) -> new_psPs0(new_show5(ww142, ec), ww148) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bc) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bc) -> new_psPs0(new_show12(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_primIntToChar(ww156, ww157) -> Char(new_primModNatS2(ww156, ww157)) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bf), bc) -> new_psPs0(new_show5(ww138, bf), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bc) -> new_psPs0(new_show0(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show6(ww142), ww148) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bc) -> new_psPs0(new_show6(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_primDivNatS3(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS02(ww1530, ww1540, ww1530, ww1540) 34.17/18.04 new_show10(ww7) -> error([]) 34.17/18.04 new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww70))) 34.17/18.04 new_show(ww7) -> error([]) 34.17/18.04 new_show7(ww7, dc, dd) -> error([]) 34.17/18.04 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bc) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bc) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_primModNatS3(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) 34.17/18.04 new_primModNatS2(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) 34.17/18.04 new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show8(ww142), ww148) 34.17/18.04 new_primDivNatS3(Zero, Succ(ww1540)) -> Zero 34.17/18.04 new_show14(ww7) -> error([]) 34.17/18.04 new_div(ww153, ww154) -> Pos(new_primDivNatS3(ww153, ww154)) 34.17/18.04 new_show3(ww7) -> error([]) 34.17/18.04 new_primModNatS02(ww205, ww206) -> new_primModNatS3(Succ(ww205), Succ(ww206), Succ(ww206)) 34.17/18.04 new_show2(ww7) -> new_primShowInt0(ww7) 34.17/18.04 new_show8(ww7) -> error([]) 34.17/18.04 new_show0(ww7, ce, cf, cg) -> error([]) 34.17/18.04 new_primModNatS4(ww212) -> Zero 34.17/18.04 new_primDivNatS02(ww200, ww201, Zero, Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.04 new_psPs0(:(ww1170, ww1171), ww106) -> :(ww1170, new_psPs0(ww1171, ww106)) 34.17/18.04 new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show4(ww142), ww148) 34.17/18.04 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], bg), bc) -> new_psPs0(new_show1(ww138, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_show4(ww7) -> error([]) 34.17/18.04 new_show13(ww7, fa) -> error([]) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bc) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bc) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showsPrec(ww142, ww148, app(app(ty_Either, dg), dh)) -> new_psPs0(new_show9(ww142, dg, dh), ww148) 34.17/18.04 new_primDivNatS2(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) 34.17/18.04 new_primModNatS3(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS3(ww2100, ww2110, ww212) 34.17/18.04 new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) 34.17/18.04 new_primDivNatS2(Succ(ww2140), Zero, ww216) -> new_primDivNatS3(ww2140, ww216) 34.17/18.04 new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show10(ww142), ww148) 34.17/18.04 new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, cd), bc) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, cd), cd, cd) 34.17/18.04 new_primModNatS3(Succ(ww2100), Zero, ww212) -> new_primModNatS2(ww2100, ww212) 34.17/18.04 new_psPs0([], ww106) -> ww106 34.17/18.04 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) 34.17/18.04 new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show7(ww142, ea, eb), ww148) 34.17/18.04 new_primDivNatS02(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS01(ww200, ww201) 34.17/18.04 new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show3(ww142), ww148) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bc) -> new_psPs0(new_show3(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_primDivNatS02(ww200, ww201, Zero, Succ(ww2030)) -> Zero 34.17/18.04 new_show12(ww7) -> error([]) 34.17/18.04 new_pt0(ww139, ww140, ww141, ww142, ww148, bc) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bc)) 34.17/18.04 new_primDivNatS3(Succ(ww1530), Zero) -> Succ(new_primDivNatS2(Succ(ww1530), Zero, Zero)) 34.17/18.04 new_primModNatS2(Succ(ww1560), Zero) -> new_primModNatS3(Succ(ww1560), Zero, Zero) 34.17/18.04 new_primModNatS2(Zero, Succ(ww1570)) -> Succ(Zero) 34.17/18.04 new_primDivNatS01(ww200, ww201) -> Succ(new_primDivNatS2(Succ(ww200), Succ(ww201), Succ(ww201))) 34.17/18.04 new_show9(ww7, de, df) -> error([]) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bc) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bc) -> new_psPs0(new_show7(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showsPrec(ww142, ww148, app(ty_[], ed)) -> new_psPs0(new_show1(ww142, ed), ww148) 34.17/18.04 new_show5(ww7, db) -> error([]) 34.17/18.04 new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show11(ww142), ww148) 34.17/18.04 new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show14(ww142), ww148) 34.17/18.04 new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show15(ww142), ww148) 34.17/18.04 new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 34.17/18.04 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 34.17/18.04 new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.04 new_primDivNatS2(Zero, Zero, ww216) -> new_primDivNatS4(ww216) 34.17/18.04 new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) 34.17/18.04 new_primDivNatS02(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS02(ww200, ww201, ww2020, ww2030) 34.17/18.04 new_primDivNatS2(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS2(ww2140, ww2150, ww216) 34.17/18.04 new_showsPrec(ww142, ww148, app(ty_Maybe, ee)) -> new_psPs0(new_show13(ww142, ee), ww148) 34.17/18.04 new_show1(ww7, da) -> error([]) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bc) -> new_psPs0(new_show4(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bc) -> new_psPs0(new_show8(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.04 new_primModNatS3(Zero, Zero, ww212) -> new_primModNatS4(ww212) 34.17/18.04 new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show12(ww142), ww148) 34.17/18.04 new_show6(ww7) -> error([]) 34.17/18.04 new_show11(ww7) -> error([]) 34.17/18.04 new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) 34.17/18.04 new_showsPrec(ww142, ww148, app(app(app(ty_@3, ef), eg), eh)) -> new_psPs0(new_show0(ww142, ef, eg, eh), ww148) 34.17/18.04 new_show15(ww7) -> error([]) 34.17/18.04 new_primDivNatS4(ww216) -> Zero 34.17/18.04 new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show(ww142), ww148) 34.17/18.04 new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, h), ba), bc) -> new_psPs0(new_show9(ww138, h, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bc)) 34.17/18.04 34.17/18.04 The set Q consists of the following terms: 34.17/18.04 34.17/18.04 new_show0(x0, x1, x2, x3) 34.17/18.04 new_show4(x0) 34.17/18.04 new_show1(x0, x1) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 34.17/18.04 new_showsPrec(x0, x1, ty_Ordering) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 34.17/18.04 new_primShowInt0(Neg(x0)) 34.17/18.04 new_showsPrec(x0, x1, ty_IOErrorKind) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 34.17/18.04 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 34.17/18.04 new_primDivNatS3(Zero, Succ(x0)) 34.17/18.04 new_show3(x0) 34.17/18.04 new_show5(x0, x1) 34.17/18.04 new_showsPrec(x0, x1, ty_IOError) 34.17/18.04 new_show15(x0) 34.17/18.04 new_primModNatS2(Zero, Succ(x0)) 34.17/18.04 new_show10(x0) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 34.17/18.04 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 34.17/18.04 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 34.17/18.04 new_primModNatS2(Succ(x0), Zero) 34.17/18.04 new_primDivNatS2(Succ(x0), Zero, x1) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 34.17/18.04 new_primDivNatS02(x0, x1, Succ(x2), Zero) 34.17/18.04 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 34.17/18.04 new_show6(x0) 34.17/18.04 new_showsPrec(x0, x1, ty_Int) 34.17/18.04 new_primDivNatS4(x0) 34.17/18.04 new_primModNatS2(Zero, Zero) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 34.17/18.04 new_primModNatS2(Succ(x0), Succ(x1)) 34.17/18.04 new_primModNatS02(x0, x1) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 34.17/18.04 new_primIntToChar(x0, x1) 34.17/18.04 new_show(x0) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 34.17/18.04 new_showsPrec(x0, x1, ty_HugsException) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 34.17/18.04 new_show12(x0) 34.17/18.04 new_show13(x0, x1) 34.17/18.04 new_showsPrec(x0, x1, ty_@0) 34.17/18.04 new_primDivNatS02(x0, x1, Zero, Zero) 34.17/18.04 new_primShowInt0(Pos(Zero)) 34.17/18.04 new_primModNatS3(Zero, Zero, x0) 34.17/18.04 new_showsPrec(x0, x1, ty_Char) 34.17/18.04 new_show11(x0) 34.17/18.04 new_primModNatS01(x0, x1, Succ(x2), Zero) 34.17/18.04 new_primDivNatS3(Succ(x0), Succ(x1)) 34.17/18.04 new_primDivNatS2(Zero, Zero, x0) 34.17/18.04 new_div(x0, x1) 34.17/18.04 new_primDivNatS2(Zero, Succ(x0), x1) 34.17/18.04 new_pt0(x0, x1, x2, x3, x4, x5) 34.17/18.04 new_primModNatS3(Zero, Succ(x0), x1) 34.17/18.04 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 34.17/18.04 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 34.17/18.04 new_show8(x0) 34.17/18.04 new_showsPrec(x0, x1, app(ty_IO, x2)) 34.17/18.04 new_showsPrec(x0, x1, ty_Float) 34.17/18.04 new_primShowInt0(Pos(Succ(x0))) 34.17/18.04 new_primModNatS3(Succ(x0), Succ(x1), x2) 34.17/18.04 new_psPs0([], x0) 34.17/18.04 new_show9(x0, x1, x2) 34.17/18.04 new_showsPrec(x0, x1, ty_Bool) 34.17/18.04 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 34.17/18.04 new_show2(x0) 34.17/18.04 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 34.17/18.04 new_showsPrec(x0, x1, ty_Double) 34.17/18.04 new_primModNatS01(x0, x1, Zero, Zero) 34.17/18.04 new_primDivNatS2(Succ(x0), Succ(x1), x2) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 34.17/18.04 new_show14(x0) 34.17/18.04 new_showsPrec(x0, x1, app(ty_[], x2)) 34.17/18.04 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 34.17/18.04 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 34.17/18.04 new_primDivNatS01(x0, x1) 34.17/18.04 new_showsPrec(x0, x1, ty_Integer) 34.17/18.04 new_primModNatS3(Succ(x0), Zero, x1) 34.17/18.04 new_psPs0(:(x0, x1), x2) 34.17/18.04 new_primModNatS4(x0) 34.17/18.04 new_primModNatS01(x0, x1, Zero, Succ(x2)) 34.17/18.04 new_primDivNatS3(Succ(x0), Zero) 34.17/18.04 new_show7(x0, x1, x2) 34.17/18.04 new_primDivNatS3(Zero, Zero) 34.17/18.04 34.17/18.04 We have to consider all minimal (P,Q,R)-chains. 34.17/18.04 ---------------------------------------- 34.17/18.04 34.17/18.04 (187) QDPSizeChangeProof (EQUIVALENT) 34.17/18.04 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. 34.17/18.04 34.17/18.04 From the DPs we obtained the following set of size-change graphs: 34.17/18.04 *new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, bb)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, bb, bb) 34.17/18.04 The graph contains the following edges 4 > 1, 4 > 5, 5 >= 6, 6 > 7, 6 > 8 34.17/18.04 34.17/18.04 34.17/18.04 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7) 34.17/18.04 The graph contains the following edges 1 > 1, 2 >= 2, 3 > 2, 4 >= 2, 3 >= 3, 2 >= 4, 3 > 4, 4 >= 4, 1 > 5, 7 > 7, 8 > 7, 7 > 8, 8 > 8 34.17/18.04 34.17/18.04 34.17/18.04 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7) 34.17/18.04 The graph contains the following edges 1 > 1, 2 >= 2, 3 > 2, 4 >= 2, 3 >= 3, 2 >= 4, 3 > 4, 4 >= 4, 1 > 5, 7 > 7, 8 > 7, 7 > 8, 8 > 8 34.17/18.04 34.17/18.04 34.17/18.04 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) 34.17/18.04 The graph contains the following edges 2 >= 1, 3 > 1, 4 >= 1, 3 >= 2, 2 >= 3, 3 > 3, 4 >= 3, 5 >= 4, 6 >= 5, 7 >= 6, 8 >= 6 34.17/18.04 34.17/18.04 34.17/18.04 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) 34.17/18.04 The graph contains the following edges 2 >= 1, 3 > 1, 4 >= 1, 3 >= 2, 2 >= 3, 3 > 3, 4 >= 3, 5 >= 4, 6 >= 5, 7 >= 6, 8 >= 6 34.17/18.04 34.17/18.04 34.17/18.04 ---------------------------------------- 34.17/18.04 34.17/18.04 (188) 34.17/18.04 YES 34.17/18.04 34.17/18.04 ---------------------------------------- 34.17/18.04 34.17/18.04 (189) Narrow (COMPLETE) 34.17/18.04 Haskell To QDPs 34.17/18.04 34.17/18.04 digraph dp_graph { 34.17/18.04 node [outthreshold=100, inthreshold=100];1[label="showList",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 34.17/18.04 3[label="showList ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 34.17/18.04 4[label="showList ww3 ww4",fontsize=16,color="burlywood",shape="triangle"];1766[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 1766[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1766 -> 5[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1767[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 1767[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1767 -> 6[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 5[label="showList (ww30 : ww31) ww4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 34.17/18.04 6[label="showList [] ww4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 34.17/18.04 7 -> 9[label="",style="dashed", color="red", weight=0]; 34.17/18.04 7[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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 ww30) . showListShowl ww31",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 7 -> 11[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 7 -> 12[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 7 -> 13[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 8 -> 18[label="",style="dashed", color="red", weight=0]; 34.17/18.04 8[label="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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) : []) ww4",fontsize=16,color="magenta"];8 -> 19[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 8 -> 20[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 8 -> 21[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 10[label="ww31",fontsize=16,color="green",shape="box"];11[label="ww4",fontsize=16,color="green",shape="box"];12[label="ww30",fontsize=16,color="green",shape="box"];13[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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"];9[label="(showChar (Char (Succ ww6))) . (shows ww7) . showListShowl ww8",fontsize=16,color="black",shape="triangle"];9 -> 17[label="",style="solid", color="black", weight=3]; 34.17/18.04 19[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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"];20[label="ww4",fontsize=16,color="green",shape="box"];21[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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"];18[label="showString (Char (Succ ww14) : Char (Succ ww15) : []) ww16",fontsize=16,color="black",shape="triangle"];18 -> 25[label="",style="solid", color="black", weight=3]; 34.17/18.04 17 -> 179[label="",style="dashed", color="red", weight=0]; 34.17/18.04 17[label="showChar (Char (Succ ww6)) ((shows ww7) . showListShowl ww8)",fontsize=16,color="magenta"];17 -> 180[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 17 -> 181[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 25 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 25[label="(++) (Char (Succ ww14) : Char (Succ ww15) : []) ww16",fontsize=16,color="magenta"];25 -> 450[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 25 -> 451[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 180[label="ww6",fontsize=16,color="green",shape="box"];181[label="(shows ww7) . showListShowl ww8",fontsize=16,color="black",shape="box"];181 -> 184[label="",style="solid", color="black", weight=3]; 34.17/18.04 179[label="showChar (Char (Succ ww57)) ww58",fontsize=16,color="black",shape="triangle"];179 -> 185[label="",style="solid", color="black", weight=3]; 34.17/18.04 450[label="ww16",fontsize=16,color="green",shape="box"];451[label="Char (Succ ww14) : Char (Succ ww15) : []",fontsize=16,color="green",shape="box"];449[label="ww117 ++ ww106",fontsize=16,color="burlywood",shape="triangle"];1768[label="ww117/ww1170 : ww1171",fontsize=10,color="white",style="solid",shape="box"];449 -> 1768[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1768 -> 589[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1769[label="ww117/[]",fontsize=10,color="white",style="solid",shape="box"];449 -> 1769[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1769 -> 590[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 184[label="shows ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];184 -> 186[label="",style="solid", color="black", weight=3]; 34.17/18.04 185[label="(:) Char (Succ ww57) ww58",fontsize=16,color="green",shape="box"];589[label="(ww1170 : ww1171) ++ ww106",fontsize=16,color="black",shape="box"];589 -> 632[label="",style="solid", color="black", weight=3]; 34.17/18.04 590[label="[] ++ ww106",fontsize=16,color="black",shape="box"];590 -> 633[label="",style="solid", color="black", weight=3]; 34.17/18.04 186[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="blue",shape="box"];1770[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1770[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1770 -> 187[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1771[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1771[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1771 -> 188[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1772[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1772[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1772 -> 189[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1773[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1773[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1773 -> 190[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1774[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1774[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1774 -> 191[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1775[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1775[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1775 -> 192[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1776[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1776[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1776 -> 193[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1777[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1777[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1777 -> 194[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1778[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1778[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1778 -> 195[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1779[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1779[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1779 -> 196[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1780[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1780[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1780 -> 197[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1781[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1781[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1781 -> 198[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1782[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1782[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1782 -> 199[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1783[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1783[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1783 -> 200[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1784[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1784[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1784 -> 201[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1785[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1785[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1785 -> 202[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1786[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1786[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1786 -> 203[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1787[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];186 -> 1787[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1787 -> 204[label="",style="solid", color="blue", weight=3]; 34.17/18.04 632[label="ww1170 : ww1171 ++ ww106",fontsize=16,color="green",shape="box"];632 -> 659[label="",style="dashed", color="green", weight=3]; 34.17/18.04 633[label="ww106",fontsize=16,color="green",shape="box"];187[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];187 -> 205[label="",style="solid", color="black", weight=3]; 34.17/18.04 188[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];188 -> 206[label="",style="solid", color="black", weight=3]; 34.17/18.04 189[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];189 -> 207[label="",style="solid", color="black", weight=3]; 34.17/18.04 190[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];190 -> 208[label="",style="solid", color="black", weight=3]; 34.17/18.04 191[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];191 -> 209[label="",style="solid", color="black", weight=3]; 34.17/18.04 192[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];192 -> 210[label="",style="solid", color="black", weight=3]; 34.17/18.04 193[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];193 -> 211[label="",style="solid", color="black", weight=3]; 34.17/18.04 194[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];194 -> 212[label="",style="solid", color="black", weight=3]; 34.17/18.04 195[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];195 -> 213[label="",style="solid", color="black", weight=3]; 34.17/18.04 196[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];196 -> 214[label="",style="solid", color="black", weight=3]; 34.17/18.04 197[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];197 -> 215[label="",style="solid", color="black", weight=3]; 34.17/18.04 198[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];198 -> 216[label="",style="solid", color="black", weight=3]; 34.17/18.04 199[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];199 -> 217[label="",style="solid", color="black", weight=3]; 34.17/18.04 200[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];200 -> 218[label="",style="solid", color="black", weight=3]; 34.17/18.04 201[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="burlywood",shape="box"];1788[label="ww7/ww70 :% ww71",fontsize=10,color="white",style="solid",shape="box"];201 -> 1788[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1788 -> 219[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 202[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];202 -> 220[label="",style="solid", color="black", weight=3]; 34.17/18.04 203[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];203 -> 221[label="",style="solid", color="black", weight=3]; 34.17/18.04 204[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];204 -> 222[label="",style="solid", color="black", weight=3]; 34.17/18.04 659 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 659[label="ww1171 ++ ww106",fontsize=16,color="magenta"];659 -> 684[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 205 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 205[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];205 -> 456[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 205 -> 457[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 206 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 206[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];206 -> 458[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 206 -> 459[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 207 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 207[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];207 -> 460[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 207 -> 461[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 208 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 208[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];208 -> 462[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 208 -> 463[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 209 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 209[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];209 -> 464[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 209 -> 465[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 210 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 210[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];210 -> 466[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 210 -> 467[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 211 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 211[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];211 -> 468[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 211 -> 469[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 212 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 212[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];212 -> 470[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 212 -> 471[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 213 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 213[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];213 -> 472[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 213 -> 473[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 214 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 214[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];214 -> 474[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 214 -> 475[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 215 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 215[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];215 -> 476[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 215 -> 477[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 216 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 216[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];216 -> 478[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 216 -> 479[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 217 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 217[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];217 -> 480[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 217 -> 481[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 218 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 218[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];218 -> 482[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 218 -> 483[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 219[label="showsPrec (Pos Zero) (ww70 :% ww71) (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];219 -> 237[label="",style="solid", color="black", weight=3]; 34.17/18.04 220 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 220[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];220 -> 484[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 220 -> 485[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 221 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 221[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];221 -> 486[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 221 -> 487[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 222 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 222[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];222 -> 488[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 222 -> 489[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 684[label="ww1171",fontsize=16,color="green",shape="box"];456 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 456[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];457[label="show ww7",fontsize=16,color="black",shape="triangle"];457 -> 591[label="",style="solid", color="black", weight=3]; 34.17/18.04 458 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 458[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];459[label="show ww7",fontsize=16,color="black",shape="triangle"];459 -> 592[label="",style="solid", color="black", weight=3]; 34.17/18.04 460 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 460[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];461[label="show ww7",fontsize=16,color="black",shape="triangle"];461 -> 593[label="",style="solid", color="black", weight=3]; 34.17/18.04 462 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 462[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];463[label="show ww7",fontsize=16,color="black",shape="triangle"];463 -> 594[label="",style="solid", color="black", weight=3]; 34.17/18.04 464 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 464[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];465[label="show ww7",fontsize=16,color="black",shape="triangle"];465 -> 595[label="",style="solid", color="black", weight=3]; 34.17/18.04 466 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 466[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];467[label="show ww7",fontsize=16,color="black",shape="triangle"];467 -> 596[label="",style="solid", color="black", weight=3]; 34.17/18.04 468 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 468[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];469[label="show ww7",fontsize=16,color="black",shape="triangle"];469 -> 597[label="",style="solid", color="black", weight=3]; 34.17/18.04 470 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 470[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];471[label="show ww7",fontsize=16,color="black",shape="triangle"];471 -> 598[label="",style="solid", color="black", weight=3]; 34.17/18.04 472 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 472[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];473[label="show ww7",fontsize=16,color="black",shape="triangle"];473 -> 599[label="",style="solid", color="black", weight=3]; 34.17/18.04 474 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 474[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];475[label="show ww7",fontsize=16,color="black",shape="triangle"];475 -> 600[label="",style="solid", color="black", weight=3]; 34.17/18.04 476 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 476[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];477[label="show ww7",fontsize=16,color="black",shape="triangle"];477 -> 601[label="",style="solid", color="black", weight=3]; 34.17/18.04 478 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 478[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];479[label="show ww7",fontsize=16,color="black",shape="triangle"];479 -> 602[label="",style="solid", color="black", weight=3]; 34.17/18.04 480 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 480[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];481[label="show ww7",fontsize=16,color="black",shape="triangle"];481 -> 603[label="",style="solid", color="black", weight=3]; 34.17/18.04 482 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 482[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];483[label="show ww7",fontsize=16,color="black",shape="triangle"];483 -> 604[label="",style="solid", color="black", weight=3]; 34.17/18.04 237 -> 688[label="",style="dashed", color="red", weight=0]; 34.17/18.04 237[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww70) . (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 ww71) (showListShowl ww8 ww9)",fontsize=16,color="magenta"];237 -> 689[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 237 -> 690[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 237 -> 691[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 237 -> 692[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 237 -> 693[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 237 -> 694[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 484 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 484[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];485[label="show ww7",fontsize=16,color="black",shape="triangle"];485 -> 605[label="",style="solid", color="black", weight=3]; 34.17/18.04 486 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 486[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];487[label="show ww7",fontsize=16,color="black",shape="triangle"];487 -> 606[label="",style="solid", color="black", weight=3]; 34.17/18.04 488 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 488[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];489[label="show ww7",fontsize=16,color="black",shape="triangle"];489 -> 607[label="",style="solid", color="black", weight=3]; 34.17/18.04 294[label="showListShowl ww8 ww9",fontsize=16,color="burlywood",shape="triangle"];1789[label="ww8/ww80 : ww81",fontsize=10,color="white",style="solid",shape="box"];294 -> 1789[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1789 -> 310[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1790[label="ww8/[]",fontsize=10,color="white",style="solid",shape="box"];294 -> 1790[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1790 -> 311[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 591[label="error []",fontsize=16,color="red",shape="box"];592[label="error []",fontsize=16,color="red",shape="box"];593[label="error []",fontsize=16,color="red",shape="box"];594[label="error []",fontsize=16,color="red",shape="box"];595[label="error []",fontsize=16,color="red",shape="box"];596[label="error []",fontsize=16,color="red",shape="box"];597[label="error []",fontsize=16,color="red",shape="box"];598[label="error []",fontsize=16,color="red",shape="box"];599[label="error []",fontsize=16,color="red",shape="box"];600[label="error []",fontsize=16,color="red",shape="box"];601[label="error []",fontsize=16,color="red",shape="box"];602[label="primShowInt ww7",fontsize=16,color="burlywood",shape="triangle"];1791[label="ww7/Pos ww70",fontsize=10,color="white",style="solid",shape="box"];602 -> 1791[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1791 -> 634[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1792[label="ww7/Neg ww70",fontsize=10,color="white",style="solid",shape="box"];602 -> 1792[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1792 -> 635[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 603[label="error []",fontsize=16,color="red",shape="box"];604[label="error []",fontsize=16,color="red",shape="box"];689 -> 294[label="",style="dashed", color="red", weight=0]; 34.17/18.04 689[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];690[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"];691[label="ww70",fontsize=16,color="green",shape="box"];692[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"];693[label="ww71",fontsize=16,color="green",shape="box"];694[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"];688[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) ww148",fontsize=16,color="black",shape="triangle"];688 -> 708[label="",style="solid", color="black", weight=3]; 34.17/18.04 605[label="error []",fontsize=16,color="red",shape="box"];606[label="error []",fontsize=16,color="red",shape="box"];607[label="error []",fontsize=16,color="red",shape="box"];310[label="showListShowl (ww80 : ww81) ww9",fontsize=16,color="black",shape="box"];310 -> 317[label="",style="solid", color="black", weight=3]; 34.17/18.04 311[label="showListShowl [] ww9",fontsize=16,color="black",shape="box"];311 -> 318[label="",style="solid", color="black", weight=3]; 34.17/18.04 634[label="primShowInt (Pos ww70)",fontsize=16,color="burlywood",shape="box"];1793[label="ww70/Succ ww700",fontsize=10,color="white",style="solid",shape="box"];634 -> 1793[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1793 -> 660[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1794[label="ww70/Zero",fontsize=10,color="white",style="solid",shape="box"];634 -> 1794[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1794 -> 661[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 635[label="primShowInt (Neg ww70)",fontsize=16,color="black",shape="box"];635 -> 662[label="",style="solid", color="black", weight=3]; 34.17/18.04 708[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww148",fontsize=16,color="black",shape="box"];708 -> 712[label="",style="solid", color="black", weight=3]; 34.17/18.04 317 -> 9[label="",style="dashed", color="red", weight=0]; 34.17/18.04 317[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 (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))) . (shows ww80) . showListShowl ww81",fontsize=16,color="magenta"];317 -> 328[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 317 -> 329[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 317 -> 330[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 318 -> 179[label="",style="dashed", color="red", weight=0]; 34.17/18.04 318[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ww9",fontsize=16,color="magenta"];318 -> 331[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 318 -> 332[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 660[label="primShowInt (Pos (Succ ww700))",fontsize=16,color="black",shape="box"];660 -> 685[label="",style="solid", color="black", weight=3]; 34.17/18.04 661[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];661 -> 686[label="",style="solid", color="black", weight=3]; 34.17/18.04 662[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 ww70)",fontsize=16,color="green",shape="box"];662 -> 687[label="",style="dashed", color="green", weight=3]; 34.17/18.04 712[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww148",fontsize=16,color="black",shape="box"];712 -> 715[label="",style="solid", color="black", weight=3]; 34.17/18.04 328[label="ww81",fontsize=16,color="green",shape="box"];329[label="ww80",fontsize=16,color="green",shape="box"];330[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 (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];331[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 (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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"];332[label="ww9",fontsize=16,color="green",shape="box"];685 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 685[label="primShowInt (div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];685 -> 709[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 685 -> 710[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 686[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"];687 -> 602[label="",style="dashed", color="red", weight=0]; 34.17/18.04 687[label="primShowInt (Pos ww70)",fontsize=16,color="magenta"];687 -> 711[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 715[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww148",fontsize=16,color="black",shape="box"];715 -> 719[label="",style="solid", color="black", weight=3]; 34.17/18.04 709[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];709 -> 713[label="",style="dashed", color="green", weight=3]; 34.17/18.04 710 -> 602[label="",style="dashed", color="red", weight=0]; 34.17/18.04 710[label="primShowInt (div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];710 -> 714[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 711[label="Pos ww70",fontsize=16,color="green",shape="box"];719[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww148",fontsize=16,color="black",shape="box"];719 -> 723[label="",style="solid", color="black", weight=3]; 34.17/18.04 713[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];713 -> 735[label="",style="solid", color="black", weight=3]; 34.17/18.04 714 -> 720[label="",style="dashed", color="red", weight=0]; 34.17/18.04 714[label="div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];714 -> 721[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 714 -> 722[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 723[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (LT == GT) ww148",fontsize=16,color="black",shape="box"];723 -> 734[label="",style="solid", color="black", weight=3]; 34.17/18.04 735 -> 747[label="",style="dashed", color="red", weight=0]; 34.17/18.04 735[label="primIntToChar (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];735 -> 748[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 735 -> 749[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 721[label="ww700",fontsize=16,color="green",shape="box"];722[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];720[label="div Pos (Succ ww153) Pos (Succ ww154)",fontsize=16,color="black",shape="triangle"];720 -> 733[label="",style="solid", color="black", weight=3]; 34.17/18.04 734[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) False ww148",fontsize=16,color="black",shape="box"];734 -> 746[label="",style="solid", color="black", weight=3]; 34.17/18.04 748[label="ww700",fontsize=16,color="green",shape="box"];749[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];747[label="primIntToChar (mod Pos (Succ ww156) Pos (Succ ww157))",fontsize=16,color="black",shape="triangle"];747 -> 750[label="",style="solid", color="black", weight=3]; 34.17/18.04 733[label="primDivInt (Pos (Succ ww153)) (Pos (Succ ww154))",fontsize=16,color="black",shape="box"];733 -> 745[label="",style="solid", color="black", weight=3]; 34.17/18.04 746[label="(shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="black",shape="box"];746 -> 751[label="",style="solid", color="black", weight=3]; 34.17/18.04 750[label="primIntToChar (primModInt (Pos (Succ ww156)) (Pos (Succ ww157)))",fontsize=16,color="black",shape="box"];750 -> 753[label="",style="solid", color="black", weight=3]; 34.17/18.04 745[label="Pos (primDivNatS (Succ ww153) (Succ ww154))",fontsize=16,color="green",shape="box"];745 -> 752[label="",style="dashed", color="green", weight=3]; 34.17/18.04 751[label="shows ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];751 -> 754[label="",style="solid", color="black", weight=3]; 34.17/18.04 753[label="primIntToChar (Pos (primModNatS (Succ ww156) (Succ ww157)))",fontsize=16,color="black",shape="box"];753 -> 756[label="",style="solid", color="black", weight=3]; 34.17/18.04 752[label="primDivNatS (Succ ww153) (Succ ww154)",fontsize=16,color="black",shape="triangle"];752 -> 755[label="",style="solid", color="black", weight=3]; 34.17/18.04 754[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="blue",shape="box"];1795[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1795[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1795 -> 757[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1796[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1796[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1796 -> 758[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1797[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1797[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1797 -> 759[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1798[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1798[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1798 -> 760[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1799[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1799[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1799 -> 761[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1800[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1800[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1800 -> 762[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1801[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1801[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1801 -> 763[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1802[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1802[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1802 -> 764[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1803[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1803[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1803 -> 765[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1804[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1804[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1804 -> 766[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1805[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1805[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1805 -> 767[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1806[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1806[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1806 -> 768[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1807[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1807[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1807 -> 769[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1808[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1808[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1808 -> 770[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1809[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1809[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1809 -> 771[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1810[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1810[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1810 -> 772[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1811[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1811[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1811 -> 773[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1812[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];754 -> 1812[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1812 -> 774[label="",style="solid", color="blue", weight=3]; 34.17/18.04 756[label="Char (primModNatS (Succ ww156) (Succ ww157))",fontsize=16,color="green",shape="box"];756 -> 777[label="",style="dashed", color="green", weight=3]; 34.17/18.04 755[label="primDivNatS0 ww153 ww154 (primGEqNatS ww153 ww154)",fontsize=16,color="burlywood",shape="box"];1813[label="ww153/Succ ww1530",fontsize=10,color="white",style="solid",shape="box"];755 -> 1813[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1813 -> 775[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1814[label="ww153/Zero",fontsize=10,color="white",style="solid",shape="box"];755 -> 1814[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1814 -> 776[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 757[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];757 -> 778[label="",style="solid", color="black", weight=3]; 34.17/18.04 758[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];758 -> 779[label="",style="solid", color="black", weight=3]; 34.17/18.04 759[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];759 -> 780[label="",style="solid", color="black", weight=3]; 34.17/18.04 760[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];760 -> 781[label="",style="solid", color="black", weight=3]; 34.17/18.04 761[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];761 -> 782[label="",style="solid", color="black", weight=3]; 34.17/18.04 762[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];762 -> 783[label="",style="solid", color="black", weight=3]; 34.17/18.04 763[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];763 -> 784[label="",style="solid", color="black", weight=3]; 34.17/18.04 764[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];764 -> 785[label="",style="solid", color="black", weight=3]; 34.17/18.04 765[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];765 -> 786[label="",style="solid", color="black", weight=3]; 34.17/18.04 766[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];766 -> 787[label="",style="solid", color="black", weight=3]; 34.17/18.04 767[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];767 -> 788[label="",style="solid", color="black", weight=3]; 34.17/18.04 768[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];768 -> 789[label="",style="solid", color="black", weight=3]; 34.17/18.04 769[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];769 -> 790[label="",style="solid", color="black", weight=3]; 34.17/18.04 770[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];770 -> 791[label="",style="solid", color="black", weight=3]; 34.17/18.04 771[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="burlywood",shape="box"];1815[label="ww138/ww1380 :% ww1381",fontsize=10,color="white",style="solid",shape="box"];771 -> 1815[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1815 -> 792[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 772[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];772 -> 793[label="",style="solid", color="black", weight=3]; 34.17/18.04 773[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];773 -> 794[label="",style="solid", color="black", weight=3]; 34.17/18.04 774[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];774 -> 795[label="",style="solid", color="black", weight=3]; 34.17/18.04 777[label="primModNatS (Succ ww156) (Succ ww157)",fontsize=16,color="black",shape="triangle"];777 -> 800[label="",style="solid", color="black", weight=3]; 34.17/18.04 775[label="primDivNatS0 (Succ ww1530) ww154 (primGEqNatS (Succ ww1530) ww154)",fontsize=16,color="burlywood",shape="box"];1816[label="ww154/Succ ww1540",fontsize=10,color="white",style="solid",shape="box"];775 -> 1816[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1816 -> 796[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1817[label="ww154/Zero",fontsize=10,color="white",style="solid",shape="box"];775 -> 1817[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1817 -> 797[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 776[label="primDivNatS0 Zero ww154 (primGEqNatS Zero ww154)",fontsize=16,color="burlywood",shape="box"];1818[label="ww154/Succ ww1540",fontsize=10,color="white",style="solid",shape="box"];776 -> 1818[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1818 -> 798[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1819[label="ww154/Zero",fontsize=10,color="white",style="solid",shape="box"];776 -> 1819[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1819 -> 799[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 778 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 778[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];778 -> 801[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 778 -> 802[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 779 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 779[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];779 -> 803[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 779 -> 804[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 780 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 780[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];780 -> 805[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 780 -> 806[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 781 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 781[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];781 -> 807[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 781 -> 808[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 782 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 782[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];782 -> 809[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 782 -> 810[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 783 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 783[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];783 -> 811[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 783 -> 812[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 784 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 784[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];784 -> 813[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 784 -> 814[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 785 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 785[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];785 -> 815[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 785 -> 816[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 786 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 786[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];786 -> 817[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 786 -> 818[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 787 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 787[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];787 -> 819[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 787 -> 820[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 788 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 788[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];788 -> 821[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 788 -> 822[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 789 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 789[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];789 -> 823[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 789 -> 824[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 790 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 790[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];790 -> 825[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 790 -> 826[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 791 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 791[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];791 -> 827[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 791 -> 828[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 792[label="showsPrec (Pos Zero) (ww1380 :% ww1381) ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];792 -> 829[label="",style="solid", color="black", weight=3]; 34.17/18.04 793 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 793[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];793 -> 830[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 793 -> 831[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 794 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 794[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];794 -> 832[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 794 -> 833[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 795 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 795[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];795 -> 834[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 795 -> 835[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 800[label="primModNatS0 ww156 ww157 (primGEqNatS ww156 ww157)",fontsize=16,color="burlywood",shape="box"];1820[label="ww156/Succ ww1560",fontsize=10,color="white",style="solid",shape="box"];800 -> 1820[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1820 -> 840[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1821[label="ww156/Zero",fontsize=10,color="white",style="solid",shape="box"];800 -> 1821[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1821 -> 841[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 796[label="primDivNatS0 (Succ ww1530) (Succ ww1540) (primGEqNatS (Succ ww1530) (Succ ww1540))",fontsize=16,color="black",shape="box"];796 -> 836[label="",style="solid", color="black", weight=3]; 34.17/18.04 797[label="primDivNatS0 (Succ ww1530) Zero (primGEqNatS (Succ ww1530) Zero)",fontsize=16,color="black",shape="box"];797 -> 837[label="",style="solid", color="black", weight=3]; 34.17/18.04 798[label="primDivNatS0 Zero (Succ ww1540) (primGEqNatS Zero (Succ ww1540))",fontsize=16,color="black",shape="box"];798 -> 838[label="",style="solid", color="black", weight=3]; 34.17/18.04 799[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];799 -> 839[label="",style="solid", color="black", weight=3]; 34.17/18.04 801[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="black",shape="triangle"];801 -> 842[label="",style="solid", color="black", weight=3]; 34.17/18.04 802 -> 457[label="",style="dashed", color="red", weight=0]; 34.17/18.04 802[label="show ww138",fontsize=16,color="magenta"];802 -> 843[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 803 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 803[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];804 -> 459[label="",style="dashed", color="red", weight=0]; 34.17/18.04 804[label="show ww138",fontsize=16,color="magenta"];804 -> 844[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 805 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 805[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];806 -> 461[label="",style="dashed", color="red", weight=0]; 34.17/18.04 806[label="show ww138",fontsize=16,color="magenta"];806 -> 845[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 807 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 807[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];808 -> 463[label="",style="dashed", color="red", weight=0]; 34.17/18.04 808[label="show ww138",fontsize=16,color="magenta"];808 -> 846[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 809 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 809[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];810 -> 465[label="",style="dashed", color="red", weight=0]; 34.17/18.04 810[label="show ww138",fontsize=16,color="magenta"];810 -> 847[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 811 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 811[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];812 -> 467[label="",style="dashed", color="red", weight=0]; 34.17/18.04 812[label="show ww138",fontsize=16,color="magenta"];812 -> 848[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 813 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 813[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];814 -> 469[label="",style="dashed", color="red", weight=0]; 34.17/18.04 814[label="show ww138",fontsize=16,color="magenta"];814 -> 849[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 815 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 815[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];816 -> 471[label="",style="dashed", color="red", weight=0]; 34.17/18.04 816[label="show ww138",fontsize=16,color="magenta"];816 -> 850[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 817 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 817[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];818 -> 473[label="",style="dashed", color="red", weight=0]; 34.17/18.04 818[label="show ww138",fontsize=16,color="magenta"];818 -> 851[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 819 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 819[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];820 -> 475[label="",style="dashed", color="red", weight=0]; 34.17/18.04 820[label="show ww138",fontsize=16,color="magenta"];820 -> 852[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 821 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 821[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];822 -> 477[label="",style="dashed", color="red", weight=0]; 34.17/18.04 822[label="show ww138",fontsize=16,color="magenta"];822 -> 853[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 823 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 823[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];824 -> 479[label="",style="dashed", color="red", weight=0]; 34.17/18.04 824[label="show ww138",fontsize=16,color="magenta"];824 -> 854[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 825 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 825[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];826 -> 481[label="",style="dashed", color="red", weight=0]; 34.17/18.04 826[label="show ww138",fontsize=16,color="magenta"];826 -> 855[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 827 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 827[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];828 -> 483[label="",style="dashed", color="red", weight=0]; 34.17/18.04 828[label="show ww138",fontsize=16,color="magenta"];828 -> 856[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 829 -> 688[label="",style="dashed", color="red", weight=0]; 34.17/18.04 829[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1380) . (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 ww1381) ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="magenta"];829 -> 857[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 829 -> 858[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 829 -> 859[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 829 -> 860[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 829 -> 861[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 829 -> 862[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 830 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 830[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];831 -> 485[label="",style="dashed", color="red", weight=0]; 34.17/18.04 831[label="show ww138",fontsize=16,color="magenta"];831 -> 863[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 832 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 832[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];833 -> 487[label="",style="dashed", color="red", weight=0]; 34.17/18.04 833[label="show ww138",fontsize=16,color="magenta"];833 -> 864[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 834 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 834[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];835 -> 489[label="",style="dashed", color="red", weight=0]; 34.17/18.04 835[label="show ww138",fontsize=16,color="magenta"];835 -> 865[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 840[label="primModNatS0 (Succ ww1560) ww157 (primGEqNatS (Succ ww1560) ww157)",fontsize=16,color="burlywood",shape="box"];1822[label="ww157/Succ ww1570",fontsize=10,color="white",style="solid",shape="box"];840 -> 1822[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1822 -> 871[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1823[label="ww157/Zero",fontsize=10,color="white",style="solid",shape="box"];840 -> 1823[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1823 -> 872[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 841[label="primModNatS0 Zero ww157 (primGEqNatS Zero ww157)",fontsize=16,color="burlywood",shape="box"];1824[label="ww157/Succ ww1570",fontsize=10,color="white",style="solid",shape="box"];841 -> 1824[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1824 -> 873[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1825[label="ww157/Zero",fontsize=10,color="white",style="solid",shape="box"];841 -> 1825[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1825 -> 874[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 836 -> 1482[label="",style="dashed", color="red", weight=0]; 34.17/18.04 836[label="primDivNatS0 (Succ ww1530) (Succ ww1540) (primGEqNatS ww1530 ww1540)",fontsize=16,color="magenta"];836 -> 1483[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 836 -> 1484[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 836 -> 1485[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 836 -> 1486[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 837[label="primDivNatS0 (Succ ww1530) Zero True",fontsize=16,color="black",shape="box"];837 -> 868[label="",style="solid", color="black", weight=3]; 34.17/18.04 838[label="primDivNatS0 Zero (Succ ww1540) False",fontsize=16,color="black",shape="box"];838 -> 869[label="",style="solid", color="black", weight=3]; 34.17/18.04 839[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];839 -> 870[label="",style="solid", color="black", weight=3]; 34.17/18.04 842[label="showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []) (shows ww142 ww148)",fontsize=16,color="black",shape="box"];842 -> 875[label="",style="solid", color="black", weight=3]; 34.17/18.04 843[label="ww138",fontsize=16,color="green",shape="box"];844[label="ww138",fontsize=16,color="green",shape="box"];845[label="ww138",fontsize=16,color="green",shape="box"];846[label="ww138",fontsize=16,color="green",shape="box"];847[label="ww138",fontsize=16,color="green",shape="box"];848[label="ww138",fontsize=16,color="green",shape="box"];849[label="ww138",fontsize=16,color="green",shape="box"];850[label="ww138",fontsize=16,color="green",shape="box"];851[label="ww138",fontsize=16,color="green",shape="box"];852[label="ww138",fontsize=16,color="green",shape="box"];853[label="ww138",fontsize=16,color="green",shape="box"];854[label="ww138",fontsize=16,color="green",shape="box"];855[label="ww138",fontsize=16,color="green",shape="box"];856[label="ww138",fontsize=16,color="green",shape="box"];857 -> 801[label="",style="dashed", color="red", weight=0]; 34.17/18.04 857[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];858[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"];859[label="ww1380",fontsize=16,color="green",shape="box"];860[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"];861[label="ww1381",fontsize=16,color="green",shape="box"];862[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"];863[label="ww138",fontsize=16,color="green",shape="box"];864[label="ww138",fontsize=16,color="green",shape="box"];865[label="ww138",fontsize=16,color="green",shape="box"];871[label="primModNatS0 (Succ ww1560) (Succ ww1570) (primGEqNatS (Succ ww1560) (Succ ww1570))",fontsize=16,color="black",shape="box"];871 -> 882[label="",style="solid", color="black", weight=3]; 34.17/18.04 872[label="primModNatS0 (Succ ww1560) Zero (primGEqNatS (Succ ww1560) Zero)",fontsize=16,color="black",shape="box"];872 -> 883[label="",style="solid", color="black", weight=3]; 34.17/18.04 873[label="primModNatS0 Zero (Succ ww1570) (primGEqNatS Zero (Succ ww1570))",fontsize=16,color="black",shape="box"];873 -> 884[label="",style="solid", color="black", weight=3]; 34.17/18.04 874[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];874 -> 885[label="",style="solid", color="black", weight=3]; 34.17/18.04 1483[label="ww1530",fontsize=16,color="green",shape="box"];1484[label="ww1530",fontsize=16,color="green",shape="box"];1485[label="ww1540",fontsize=16,color="green",shape="box"];1486[label="ww1540",fontsize=16,color="green",shape="box"];1482[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS ww202 ww203)",fontsize=16,color="burlywood",shape="triangle"];1826[label="ww202/Succ ww2020",fontsize=10,color="white",style="solid",shape="box"];1482 -> 1826[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1826 -> 1523[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1827[label="ww202/Zero",fontsize=10,color="white",style="solid",shape="box"];1482 -> 1827[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1827 -> 1524[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 868[label="Succ (primDivNatS (primMinusNatS (Succ ww1530) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];868 -> 880[label="",style="dashed", color="green", weight=3]; 34.17/18.04 869[label="Zero",fontsize=16,color="green",shape="box"];870[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];870 -> 881[label="",style="dashed", color="green", weight=3]; 34.17/18.04 875 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 875[label="(++) (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []) shows ww142 ww148",fontsize=16,color="magenta"];875 -> 886[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 875 -> 887[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 882 -> 1543[label="",style="dashed", color="red", weight=0]; 34.17/18.04 882[label="primModNatS0 (Succ ww1560) (Succ ww1570) (primGEqNatS ww1560 ww1570)",fontsize=16,color="magenta"];882 -> 1544[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 882 -> 1545[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 882 -> 1546[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 882 -> 1547[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 883[label="primModNatS0 (Succ ww1560) Zero True",fontsize=16,color="black",shape="box"];883 -> 896[label="",style="solid", color="black", weight=3]; 34.17/18.04 884[label="primModNatS0 Zero (Succ ww1570) False",fontsize=16,color="black",shape="box"];884 -> 897[label="",style="solid", color="black", weight=3]; 34.17/18.04 885[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];885 -> 898[label="",style="solid", color="black", weight=3]; 34.17/18.04 1523[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) ww203)",fontsize=16,color="burlywood",shape="box"];1828[label="ww203/Succ ww2030",fontsize=10,color="white",style="solid",shape="box"];1523 -> 1828[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1828 -> 1535[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1829[label="ww203/Zero",fontsize=10,color="white",style="solid",shape="box"];1523 -> 1829[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1829 -> 1536[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1524[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero ww203)",fontsize=16,color="burlywood",shape="box"];1830[label="ww203/Succ ww2030",fontsize=10,color="white",style="solid",shape="box"];1524 -> 1830[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1830 -> 1537[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1831[label="ww203/Zero",fontsize=10,color="white",style="solid",shape="box"];1524 -> 1831[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1831 -> 1538[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 880 -> 1726[label="",style="dashed", color="red", weight=0]; 34.17/18.04 880[label="primDivNatS (primMinusNatS (Succ ww1530) Zero) (Succ Zero)",fontsize=16,color="magenta"];880 -> 1727[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 880 -> 1728[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 880 -> 1729[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 881 -> 1726[label="",style="dashed", color="red", weight=0]; 34.17/18.04 881[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];881 -> 1730[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 881 -> 1731[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 881 -> 1732[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 886[label="shows ww142 ww148",fontsize=16,color="black",shape="box"];886 -> 899[label="",style="solid", color="black", weight=3]; 34.17/18.04 887[label="Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []",fontsize=16,color="green",shape="box"];1544[label="ww1570",fontsize=16,color="green",shape="box"];1545[label="ww1560",fontsize=16,color="green",shape="box"];1546[label="ww1570",fontsize=16,color="green",shape="box"];1547[label="ww1560",fontsize=16,color="green",shape="box"];1543[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS ww207 ww208)",fontsize=16,color="burlywood",shape="triangle"];1832[label="ww207/Succ ww2070",fontsize=10,color="white",style="solid",shape="box"];1543 -> 1832[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1832 -> 1584[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1833[label="ww207/Zero",fontsize=10,color="white",style="solid",shape="box"];1543 -> 1833[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1833 -> 1585[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 896 -> 1630[label="",style="dashed", color="red", weight=0]; 34.17/18.04 896[label="primModNatS (primMinusNatS (Succ ww1560) Zero) (Succ Zero)",fontsize=16,color="magenta"];896 -> 1631[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 896 -> 1632[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 896 -> 1633[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 897[label="Succ Zero",fontsize=16,color="green",shape="box"];898 -> 1630[label="",style="dashed", color="red", weight=0]; 34.17/18.04 898[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];898 -> 1634[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 898 -> 1635[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 898 -> 1636[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1535[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) (Succ ww2030))",fontsize=16,color="black",shape="box"];1535 -> 1586[label="",style="solid", color="black", weight=3]; 34.17/18.04 1536[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) Zero)",fontsize=16,color="black",shape="box"];1536 -> 1587[label="",style="solid", color="black", weight=3]; 34.17/18.04 1537[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero (Succ ww2030))",fontsize=16,color="black",shape="box"];1537 -> 1588[label="",style="solid", color="black", weight=3]; 34.17/18.04 1538[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1538 -> 1589[label="",style="solid", color="black", weight=3]; 34.17/18.04 1727[label="Succ ww1530",fontsize=16,color="green",shape="box"];1728[label="Zero",fontsize=16,color="green",shape="box"];1729[label="Zero",fontsize=16,color="green",shape="box"];1726[label="primDivNatS (primMinusNatS ww214 ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="triangle"];1834[label="ww214/Succ ww2140",fontsize=10,color="white",style="solid",shape="box"];1726 -> 1834[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1834 -> 1751[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1835[label="ww214/Zero",fontsize=10,color="white",style="solid",shape="box"];1726 -> 1835[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1835 -> 1752[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1730[label="Zero",fontsize=16,color="green",shape="box"];1731[label="Zero",fontsize=16,color="green",shape="box"];1732[label="Zero",fontsize=16,color="green",shape="box"];899[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="blue",shape="box"];1836[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1836[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1836 -> 914[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1837[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1837[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1837 -> 915[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1838[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1838[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1838 -> 916[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1839[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1839[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1839 -> 917[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1840[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1840[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1840 -> 918[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1841[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1841[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1841 -> 919[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1842[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1842[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1842 -> 920[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1843[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1843[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1843 -> 921[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1844[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1844[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1844 -> 922[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1845[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1845[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1845 -> 923[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1846[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1846[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1846 -> 924[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1847[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1847[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1847 -> 925[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1848[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1848[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1848 -> 926[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1849[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1849[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1849 -> 927[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1850[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1850[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1850 -> 928[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1851[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1851[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1851 -> 929[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1852[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1852[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1852 -> 930[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1853[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];899 -> 1853[label="",style="solid", color="blue", weight=9]; 34.17/18.04 1853 -> 931[label="",style="solid", color="blue", weight=3]; 34.17/18.04 1584[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) ww208)",fontsize=16,color="burlywood",shape="box"];1854[label="ww208/Succ ww2080",fontsize=10,color="white",style="solid",shape="box"];1584 -> 1854[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1854 -> 1594[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1855[label="ww208/Zero",fontsize=10,color="white",style="solid",shape="box"];1584 -> 1855[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1855 -> 1595[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1585[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero ww208)",fontsize=16,color="burlywood",shape="box"];1856[label="ww208/Succ ww2080",fontsize=10,color="white",style="solid",shape="box"];1585 -> 1856[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1856 -> 1596[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1857[label="ww208/Zero",fontsize=10,color="white",style="solid",shape="box"];1585 -> 1857[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1857 -> 1597[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1631[label="Zero",fontsize=16,color="green",shape="box"];1632[label="Zero",fontsize=16,color="green",shape="box"];1633[label="Succ ww1560",fontsize=16,color="green",shape="box"];1630[label="primModNatS (primMinusNatS ww210 ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="triangle"];1858[label="ww210/Succ ww2100",fontsize=10,color="white",style="solid",shape="box"];1630 -> 1858[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1858 -> 1661[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1859[label="ww210/Zero",fontsize=10,color="white",style="solid",shape="box"];1630 -> 1859[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1859 -> 1662[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1634[label="Zero",fontsize=16,color="green",shape="box"];1635[label="Zero",fontsize=16,color="green",shape="box"];1636[label="Zero",fontsize=16,color="green",shape="box"];1586 -> 1482[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1586[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS ww2020 ww2030)",fontsize=16,color="magenta"];1586 -> 1598[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1586 -> 1599[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1587[label="primDivNatS0 (Succ ww200) (Succ ww201) True",fontsize=16,color="black",shape="triangle"];1587 -> 1600[label="",style="solid", color="black", weight=3]; 34.17/18.04 1588[label="primDivNatS0 (Succ ww200) (Succ ww201) False",fontsize=16,color="black",shape="box"];1588 -> 1601[label="",style="solid", color="black", weight=3]; 34.17/18.04 1589 -> 1587[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1589[label="primDivNatS0 (Succ ww200) (Succ ww201) True",fontsize=16,color="magenta"];1751[label="primDivNatS (primMinusNatS (Succ ww2140) ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="box"];1860[label="ww215/Succ ww2150",fontsize=10,color="white",style="solid",shape="box"];1751 -> 1860[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1860 -> 1753[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1861[label="ww215/Zero",fontsize=10,color="white",style="solid",shape="box"];1751 -> 1861[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1861 -> 1754[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1752[label="primDivNatS (primMinusNatS Zero ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="box"];1862[label="ww215/Succ ww2150",fontsize=10,color="white",style="solid",shape="box"];1752 -> 1862[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1862 -> 1755[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1863[label="ww215/Zero",fontsize=10,color="white",style="solid",shape="box"];1752 -> 1863[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1863 -> 1756[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 914[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];914 -> 945[label="",style="solid", color="black", weight=3]; 34.17/18.04 915[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];915 -> 946[label="",style="solid", color="black", weight=3]; 34.17/18.04 916[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];916 -> 947[label="",style="solid", color="black", weight=3]; 34.17/18.04 917[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];917 -> 948[label="",style="solid", color="black", weight=3]; 34.17/18.04 918[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];918 -> 949[label="",style="solid", color="black", weight=3]; 34.17/18.04 919[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];919 -> 950[label="",style="solid", color="black", weight=3]; 34.17/18.04 920[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];920 -> 951[label="",style="solid", color="black", weight=3]; 34.17/18.04 921[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];921 -> 952[label="",style="solid", color="black", weight=3]; 34.17/18.04 922[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];922 -> 953[label="",style="solid", color="black", weight=3]; 34.17/18.04 923[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];923 -> 954[label="",style="solid", color="black", weight=3]; 34.17/18.04 924[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];924 -> 955[label="",style="solid", color="black", weight=3]; 34.17/18.04 925[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];925 -> 956[label="",style="solid", color="black", weight=3]; 34.17/18.04 926[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];926 -> 957[label="",style="solid", color="black", weight=3]; 34.17/18.04 927[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];927 -> 958[label="",style="solid", color="black", weight=3]; 34.17/18.04 928[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="burlywood",shape="box"];1864[label="ww142/ww1420 :% ww1421",fontsize=10,color="white",style="solid",shape="box"];928 -> 1864[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1864 -> 959[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 929[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];929 -> 960[label="",style="solid", color="black", weight=3]; 34.17/18.04 930[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];930 -> 961[label="",style="solid", color="black", weight=3]; 34.17/18.04 931[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];931 -> 962[label="",style="solid", color="black", weight=3]; 34.17/18.04 1594[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) (Succ ww2080))",fontsize=16,color="black",shape="box"];1594 -> 1608[label="",style="solid", color="black", weight=3]; 34.17/18.04 1595[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) Zero)",fontsize=16,color="black",shape="box"];1595 -> 1609[label="",style="solid", color="black", weight=3]; 34.17/18.04 1596[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero (Succ ww2080))",fontsize=16,color="black",shape="box"];1596 -> 1610[label="",style="solid", color="black", weight=3]; 34.17/18.04 1597[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1597 -> 1611[label="",style="solid", color="black", weight=3]; 34.17/18.04 1661[label="primModNatS (primMinusNatS (Succ ww2100) ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="box"];1865[label="ww211/Succ ww2110",fontsize=10,color="white",style="solid",shape="box"];1661 -> 1865[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1865 -> 1667[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1866[label="ww211/Zero",fontsize=10,color="white",style="solid",shape="box"];1661 -> 1866[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1866 -> 1668[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1662[label="primModNatS (primMinusNatS Zero ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="box"];1867[label="ww211/Succ ww2110",fontsize=10,color="white",style="solid",shape="box"];1662 -> 1867[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1867 -> 1669[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1868[label="ww211/Zero",fontsize=10,color="white",style="solid",shape="box"];1662 -> 1868[label="",style="solid", color="burlywood", weight=9]; 34.17/18.04 1868 -> 1670[label="",style="solid", color="burlywood", weight=3]; 34.17/18.04 1598[label="ww2020",fontsize=16,color="green",shape="box"];1599[label="ww2030",fontsize=16,color="green",shape="box"];1600[label="Succ (primDivNatS (primMinusNatS (Succ ww200) (Succ ww201)) (Succ (Succ ww201)))",fontsize=16,color="green",shape="box"];1600 -> 1612[label="",style="dashed", color="green", weight=3]; 34.17/18.04 1601[label="Zero",fontsize=16,color="green",shape="box"];1753[label="primDivNatS (primMinusNatS (Succ ww2140) (Succ ww2150)) (Succ ww216)",fontsize=16,color="black",shape="box"];1753 -> 1757[label="",style="solid", color="black", weight=3]; 34.17/18.04 1754[label="primDivNatS (primMinusNatS (Succ ww2140) Zero) (Succ ww216)",fontsize=16,color="black",shape="box"];1754 -> 1758[label="",style="solid", color="black", weight=3]; 34.17/18.04 1755[label="primDivNatS (primMinusNatS Zero (Succ ww2150)) (Succ ww216)",fontsize=16,color="black",shape="box"];1755 -> 1759[label="",style="solid", color="black", weight=3]; 34.17/18.04 1756[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww216)",fontsize=16,color="black",shape="box"];1756 -> 1760[label="",style="solid", color="black", weight=3]; 34.17/18.04 945 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 945[label="show ww142 ++ ww148",fontsize=16,color="magenta"];945 -> 974[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 945 -> 975[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 946 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 946[label="show ww142 ++ ww148",fontsize=16,color="magenta"];946 -> 976[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 946 -> 977[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 947 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 947[label="show ww142 ++ ww148",fontsize=16,color="magenta"];947 -> 978[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 947 -> 979[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 948 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 948[label="show ww142 ++ ww148",fontsize=16,color="magenta"];948 -> 980[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 948 -> 981[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 949 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 949[label="show ww142 ++ ww148",fontsize=16,color="magenta"];949 -> 982[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 949 -> 983[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 950 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 950[label="show ww142 ++ ww148",fontsize=16,color="magenta"];950 -> 984[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 950 -> 985[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 951 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 951[label="show ww142 ++ ww148",fontsize=16,color="magenta"];951 -> 986[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 951 -> 987[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 952 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 952[label="show ww142 ++ ww148",fontsize=16,color="magenta"];952 -> 988[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 952 -> 989[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 953 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 953[label="show ww142 ++ ww148",fontsize=16,color="magenta"];953 -> 990[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 953 -> 991[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 954 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 954[label="show ww142 ++ ww148",fontsize=16,color="magenta"];954 -> 992[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 954 -> 993[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 955 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 955[label="show ww142 ++ ww148",fontsize=16,color="magenta"];955 -> 994[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 955 -> 995[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 956 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 956[label="show ww142 ++ ww148",fontsize=16,color="magenta"];956 -> 996[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 956 -> 997[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 957 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 957[label="show ww142 ++ ww148",fontsize=16,color="magenta"];957 -> 998[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 957 -> 999[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 958 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 958[label="show ww142 ++ ww148",fontsize=16,color="magenta"];958 -> 1000[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 958 -> 1001[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 959[label="showsPrec (Pos Zero) (ww1420 :% ww1421) ww148",fontsize=16,color="black",shape="box"];959 -> 1002[label="",style="solid", color="black", weight=3]; 34.17/18.04 960 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 960[label="show ww142 ++ ww148",fontsize=16,color="magenta"];960 -> 1003[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 960 -> 1004[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 961 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 961[label="show ww142 ++ ww148",fontsize=16,color="magenta"];961 -> 1005[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 961 -> 1006[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 962 -> 449[label="",style="dashed", color="red", weight=0]; 34.17/18.04 962[label="show ww142 ++ ww148",fontsize=16,color="magenta"];962 -> 1007[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 962 -> 1008[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1608 -> 1543[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1608[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS ww2070 ww2080)",fontsize=16,color="magenta"];1608 -> 1617[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1608 -> 1618[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1609[label="primModNatS0 (Succ ww205) (Succ ww206) True",fontsize=16,color="black",shape="triangle"];1609 -> 1619[label="",style="solid", color="black", weight=3]; 34.17/18.04 1610[label="primModNatS0 (Succ ww205) (Succ ww206) False",fontsize=16,color="black",shape="box"];1610 -> 1620[label="",style="solid", color="black", weight=3]; 34.17/18.04 1611 -> 1609[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1611[label="primModNatS0 (Succ ww205) (Succ ww206) True",fontsize=16,color="magenta"];1667[label="primModNatS (primMinusNatS (Succ ww2100) (Succ ww2110)) (Succ ww212)",fontsize=16,color="black",shape="box"];1667 -> 1675[label="",style="solid", color="black", weight=3]; 34.17/18.04 1668[label="primModNatS (primMinusNatS (Succ ww2100) Zero) (Succ ww212)",fontsize=16,color="black",shape="box"];1668 -> 1676[label="",style="solid", color="black", weight=3]; 34.17/18.04 1669[label="primModNatS (primMinusNatS Zero (Succ ww2110)) (Succ ww212)",fontsize=16,color="black",shape="box"];1669 -> 1677[label="",style="solid", color="black", weight=3]; 34.17/18.04 1670[label="primModNatS (primMinusNatS Zero Zero) (Succ ww212)",fontsize=16,color="black",shape="box"];1670 -> 1678[label="",style="solid", color="black", weight=3]; 34.17/18.04 1612 -> 1726[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1612[label="primDivNatS (primMinusNatS (Succ ww200) (Succ ww201)) (Succ (Succ ww201))",fontsize=16,color="magenta"];1612 -> 1733[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1612 -> 1734[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1612 -> 1735[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1757 -> 1726[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1757[label="primDivNatS (primMinusNatS ww2140 ww2150) (Succ ww216)",fontsize=16,color="magenta"];1757 -> 1761[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1757 -> 1762[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1758 -> 752[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1758[label="primDivNatS (Succ ww2140) (Succ ww216)",fontsize=16,color="magenta"];1758 -> 1763[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1758 -> 1764[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1759[label="primDivNatS Zero (Succ ww216)",fontsize=16,color="black",shape="triangle"];1759 -> 1765[label="",style="solid", color="black", weight=3]; 34.17/18.04 1760 -> 1759[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1760[label="primDivNatS Zero (Succ ww216)",fontsize=16,color="magenta"];974[label="ww148",fontsize=16,color="green",shape="box"];975 -> 457[label="",style="dashed", color="red", weight=0]; 34.17/18.04 975[label="show ww142",fontsize=16,color="magenta"];975 -> 1022[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 976[label="ww148",fontsize=16,color="green",shape="box"];977 -> 459[label="",style="dashed", color="red", weight=0]; 34.17/18.04 977[label="show ww142",fontsize=16,color="magenta"];977 -> 1023[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 978[label="ww148",fontsize=16,color="green",shape="box"];979 -> 461[label="",style="dashed", color="red", weight=0]; 34.17/18.04 979[label="show ww142",fontsize=16,color="magenta"];979 -> 1024[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 980[label="ww148",fontsize=16,color="green",shape="box"];981 -> 463[label="",style="dashed", color="red", weight=0]; 34.17/18.04 981[label="show ww142",fontsize=16,color="magenta"];981 -> 1025[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 982[label="ww148",fontsize=16,color="green",shape="box"];983 -> 465[label="",style="dashed", color="red", weight=0]; 34.17/18.04 983[label="show ww142",fontsize=16,color="magenta"];983 -> 1026[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 984[label="ww148",fontsize=16,color="green",shape="box"];985 -> 467[label="",style="dashed", color="red", weight=0]; 34.17/18.04 985[label="show ww142",fontsize=16,color="magenta"];985 -> 1027[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 986[label="ww148",fontsize=16,color="green",shape="box"];987 -> 469[label="",style="dashed", color="red", weight=0]; 34.17/18.04 987[label="show ww142",fontsize=16,color="magenta"];987 -> 1028[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 988[label="ww148",fontsize=16,color="green",shape="box"];989 -> 471[label="",style="dashed", color="red", weight=0]; 34.17/18.04 989[label="show ww142",fontsize=16,color="magenta"];989 -> 1029[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 990[label="ww148",fontsize=16,color="green",shape="box"];991 -> 473[label="",style="dashed", color="red", weight=0]; 34.17/18.04 991[label="show ww142",fontsize=16,color="magenta"];991 -> 1030[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 992[label="ww148",fontsize=16,color="green",shape="box"];993 -> 475[label="",style="dashed", color="red", weight=0]; 34.17/18.04 993[label="show ww142",fontsize=16,color="magenta"];993 -> 1031[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 994[label="ww148",fontsize=16,color="green",shape="box"];995 -> 477[label="",style="dashed", color="red", weight=0]; 34.17/18.04 995[label="show ww142",fontsize=16,color="magenta"];995 -> 1032[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 996[label="ww148",fontsize=16,color="green",shape="box"];997 -> 479[label="",style="dashed", color="red", weight=0]; 34.17/18.04 997[label="show ww142",fontsize=16,color="magenta"];997 -> 1033[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 998[label="ww148",fontsize=16,color="green",shape="box"];999 -> 481[label="",style="dashed", color="red", weight=0]; 34.17/18.04 999[label="show ww142",fontsize=16,color="magenta"];999 -> 1034[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1000[label="ww148",fontsize=16,color="green",shape="box"];1001 -> 483[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1001[label="show ww142",fontsize=16,color="magenta"];1001 -> 1035[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1002 -> 688[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1002[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1420) . (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 ww1421) ww148",fontsize=16,color="magenta"];1002 -> 1036[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1002 -> 1037[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1002 -> 1038[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1002 -> 1039[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1002 -> 1040[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1003[label="ww148",fontsize=16,color="green",shape="box"];1004 -> 485[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1004[label="show ww142",fontsize=16,color="magenta"];1004 -> 1041[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1005[label="ww148",fontsize=16,color="green",shape="box"];1006 -> 487[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1006[label="show ww142",fontsize=16,color="magenta"];1006 -> 1042[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1007[label="ww148",fontsize=16,color="green",shape="box"];1008 -> 489[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1008[label="show ww142",fontsize=16,color="magenta"];1008 -> 1043[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1617[label="ww2070",fontsize=16,color="green",shape="box"];1618[label="ww2080",fontsize=16,color="green",shape="box"];1619 -> 1630[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1619[label="primModNatS (primMinusNatS (Succ ww205) (Succ ww206)) (Succ (Succ ww206))",fontsize=16,color="magenta"];1619 -> 1643[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1619 -> 1644[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1619 -> 1645[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1620[label="Succ (Succ ww205)",fontsize=16,color="green",shape="box"];1675 -> 1630[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1675[label="primModNatS (primMinusNatS ww2100 ww2110) (Succ ww212)",fontsize=16,color="magenta"];1675 -> 1685[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1675 -> 1686[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1676 -> 777[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1676[label="primModNatS (Succ ww2100) (Succ ww212)",fontsize=16,color="magenta"];1676 -> 1687[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1676 -> 1688[label="",style="dashed", color="magenta", weight=3]; 34.17/18.04 1677[label="primModNatS Zero (Succ ww212)",fontsize=16,color="black",shape="triangle"];1677 -> 1689[label="",style="solid", color="black", weight=3]; 34.17/18.04 1678 -> 1677[label="",style="dashed", color="red", weight=0]; 34.17/18.04 1678[label="primModNatS Zero (Succ ww212)",fontsize=16,color="magenta"];1733[label="Succ ww200",fontsize=16,color="green",shape="box"];1734[label="Succ ww201",fontsize=16,color="green",shape="box"];1735[label="Succ ww201",fontsize=16,color="green",shape="box"];1761[label="ww2140",fontsize=16,color="green",shape="box"];1762[label="ww2150",fontsize=16,color="green",shape="box"];1763[label="ww2140",fontsize=16,color="green",shape="box"];1764[label="ww216",fontsize=16,color="green",shape="box"];1765[label="Zero",fontsize=16,color="green",shape="box"];1022[label="ww142",fontsize=16,color="green",shape="box"];1023[label="ww142",fontsize=16,color="green",shape="box"];1024[label="ww142",fontsize=16,color="green",shape="box"];1025[label="ww142",fontsize=16,color="green",shape="box"];1026[label="ww142",fontsize=16,color="green",shape="box"];1027[label="ww142",fontsize=16,color="green",shape="box"];1028[label="ww142",fontsize=16,color="green",shape="box"];1029[label="ww142",fontsize=16,color="green",shape="box"];1030[label="ww142",fontsize=16,color="green",shape="box"];1031[label="ww142",fontsize=16,color="green",shape="box"];1032[label="ww142",fontsize=16,color="green",shape="box"];1033[label="ww142",fontsize=16,color="green",shape="box"];1034[label="ww142",fontsize=16,color="green",shape="box"];1035[label="ww142",fontsize=16,color="green",shape="box"];1036[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"];1037[label="ww1420",fontsize=16,color="green",shape="box"];1038[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"];1039[label="ww1421",fontsize=16,color="green",shape="box"];1040[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"];1041[label="ww142",fontsize=16,color="green",shape="box"];1042[label="ww142",fontsize=16,color="green",shape="box"];1043[label="ww142",fontsize=16,color="green",shape="box"];1643[label="Succ ww206",fontsize=16,color="green",shape="box"];1644[label="Succ ww206",fontsize=16,color="green",shape="box"];1645[label="Succ ww205",fontsize=16,color="green",shape="box"];1685[label="ww2110",fontsize=16,color="green",shape="box"];1686[label="ww2100",fontsize=16,color="green",shape="box"];1687[label="ww2100",fontsize=16,color="green",shape="box"];1688[label="ww212",fontsize=16,color="green",shape="box"];1689[label="Zero",fontsize=16,color="green",shape="box"];} 34.17/18.04 34.17/18.04 ---------------------------------------- 34.17/18.04 34.17/18.04 (190) 34.17/18.04 TRUE 34.26/18.11 EOF